#include "f2c.h" /* Subroutine */ int daxpy_(integer *n, doublereal *da, doublereal *dx, integer *incx, doublereal *dy, integer *incy) { /* System generated locals */ integer i__1; /* Local variables */ static integer i__, m, ix, iy, mp1; /* constant times a vector plus a vector. uses unrolled loops for increments equal to one. jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --dy; --dx; /* Function Body */ if (*n <= 0) { return 0; } if (*da == 0.) { return 0; } if (*incx == 1 && *incy == 1) { goto L20; } /* code for unequal increments or equal increments not equal to 1 */ ix = 1; iy = 1; if (*incx < 0) { ix = (-(*n) + 1) * *incx + 1; } if (*incy < 0) { iy = (-(*n) + 1) * *incy + 1; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { dy[iy] += *da * dx[ix]; ix += *incx; iy += *incy; /* L10: */ } return 0; /* code for both increments equal to 1 clean-up loop */ L20: m = *n % 4; if (m == 0) { goto L40; } i__1 = m; for (i__ = 1; i__ <= i__1; ++i__) { dy[i__] += *da * dx[i__]; /* L30: */ } if (*n < 4) { return 0; } L40: mp1 = m + 1; i__1 = *n; for (i__ = mp1; i__ <= i__1; i__ += 4) { dy[i__] += *da * dx[i__]; dy[i__ + 1] += *da * dx[i__ + 1]; dy[i__ + 2] += *da * dx[i__ + 2]; dy[i__ + 3] += *da * dx[i__ + 3]; /* L50: */ } return 0; } /* daxpy_ */ doublereal dcabs1_(doublecomplex *z__) { /* System generated locals */ doublereal ret_val; static doublecomplex equiv_0[1]; /* Local variables */ #define t ((doublereal *)equiv_0) #define zz (equiv_0) zz->r = z__->r, zz->i = z__->i; ret_val = abs(t[0]) + abs(t[1]); return ret_val; } /* dcabs1_ */ #undef zz #undef t /* Subroutine */ int dcopy_(integer *n, doublereal *dx, integer *incx, doublereal *dy, integer *incy) { /* System generated locals */ integer i__1; /* Local variables */ static integer i__, m, ix, iy, mp1; /* copies a vector, x, to a vector, y. uses unrolled loops for increments equal to one. jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --dy; --dx; /* Function Body */ if (*n <= 0) { return 0; } if (*incx == 1 && *incy == 1) { goto L20; } /* code for unequal increments or equal increments not equal to 1 */ ix = 1; iy = 1; if (*incx < 0) { ix = (-(*n) + 1) * *incx + 1; } if (*incy < 0) { iy = (-(*n) + 1) * *incy + 1; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { dy[iy] = dx[ix]; ix += *incx; iy += *incy; /* L10: */ } return 0; /* code for both increments equal to 1 clean-up loop */ L20: m = *n % 7; if (m == 0) { goto L40; } i__1 = m; for (i__ = 1; i__ <= i__1; ++i__) { dy[i__] = dx[i__]; /* L30: */ } if (*n < 7) { return 0; } L40: mp1 = m + 1; i__1 = *n; for (i__ = mp1; i__ <= i__1; i__ += 7) { dy[i__] = dx[i__]; dy[i__ + 1] = dx[i__ + 1]; dy[i__ + 2] = dx[i__ + 2]; dy[i__ + 3] = dx[i__ + 3]; dy[i__ + 4] = dx[i__ + 4]; dy[i__ + 5] = dx[i__ + 5]; dy[i__ + 6] = dx[i__ + 6]; /* L50: */ } return 0; } /* dcopy_ */ doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, integer *incy) { /* System generated locals */ integer i__1; doublereal ret_val; /* Local variables */ static integer i__, m; static doublereal dtemp; static integer ix, iy, mp1; /* forms the dot product of two vectors. uses unrolled loops for increments equal to one. jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --dy; --dx; /* Function Body */ ret_val = 0.; dtemp = 0.; if (*n <= 0) { return ret_val; } if (*incx == 1 && *incy == 1) { goto L20; } /* code for unequal increments or equal increments not equal to 1 */ ix = 1; iy = 1; if (*incx < 0) { ix = (-(*n) + 1) * *incx + 1; } if (*incy < 0) { iy = (-(*n) + 1) * *incy + 1; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { dtemp += dx[ix] * dy[iy]; ix += *incx; iy += *incy; /* L10: */ } ret_val = dtemp; return ret_val; /* code for both increments equal to 1 clean-up loop */ L20: m = *n % 5; if (m == 0) { goto L40; } i__1 = m; for (i__ = 1; i__ <= i__1; ++i__) { dtemp += dx[i__] * dy[i__]; /* L30: */ } if (*n < 5) { goto L60; } L40: mp1 = m + 1; i__1 = *n; for (i__ = mp1; i__ <= i__1; i__ += 5) { dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] + dx[ i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] + dx[i__ + 4] * dy[i__ + 4]; /* L50: */ } L60: ret_val = dtemp; return ret_val; } /* ddot_ */ /* Subroutine */ int dgemm_(char *transa, char *transb, integer *m, integer * n, integer *k, doublereal *alpha, doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *beta, doublereal *c__, integer *ldc) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3; /* Local variables */ static integer info; static logical nota, notb; static doublereal temp; static integer i__, j, l, ncola; extern logical lsame_(char *, char *); static integer nrowa, nrowb; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] #define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1] #define c___ref(a_1,a_2) c__[(a_2)*c_dim1 + a_1] /* Purpose ======= DGEMM performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = X', alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. Parameters ========== TRANSA - CHARACTER*1. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n', op( A ) = A. TRANSA = 'T' or 't', op( A ) = A'. TRANSA = 'C' or 'c', op( A ) = A'. Unchanged on exit. TRANSB - CHARACTER*1. On entry, TRANSB specifies the form of op( B ) to be used in the matrix multiplication as follows: TRANSB = 'N' or 'n', op( B ) = B. TRANSB = 'T' or 't', op( B ) = B'. TRANSB = 'C' or 'c', op( B ) = B'. Unchanged on exit. M - INTEGER. On entry, M specifies the number of rows of the matrix op( A ) and of the matrix C. M must be at least zero. Unchanged on exit. N - INTEGER. On entry, N specifies the number of columns of the matrix op( B ) and the number of columns of the matrix C. N must be at least zero. Unchanged on exit. K - INTEGER. On entry, K specifies the number of columns of the matrix op( A ) and the number of rows of the matrix op( B ). K must be at least zero. Unchanged on exit. ALPHA - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is k when TRANSA = 'N' or 'n', and is m otherwise. Before entry with TRANSA = 'N' or 'n', the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m part of the array A must contain the matrix A. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANSA = 'N' or 'n' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ). Unchanged on exit. B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is n when TRANSB = 'N' or 'n', and is k otherwise. Before entry with TRANSB = 'N' or 'n', the leading k by n part of the array B must contain the matrix B, otherwise the leading n by k part of the array B must contain the matrix B. Unchanged on exit. LDB - INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANSB = 'N' or 'n' then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ). Unchanged on exit. BETA - DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input. Unchanged on exit. C - DOUBLE PRECISION array of DIMENSION ( LDC, n ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n matrix ( alpha*op( A )*op( B ) + beta*C ). LDC - INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ). Unchanged on exit. Level 3 Blas routine. -- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd. Set NOTA and NOTB as true if A and B respectively are not transposed and set NROWA, NCOLA and NROWB as the number of rows and columns of A and the number of rows of B respectively. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; /* Function Body */ nota = lsame_(transa, "N"); notb = lsame_(transb, "N"); if (nota) { nrowa = *m; ncola = *k; } else { nrowa = *k; ncola = *m; } if (notb) { nrowb = *k; } else { nrowb = *n; } /* Test the input parameters. */ info = 0; if (! nota && ! lsame_(transa, "C") && ! lsame_( transa, "T")) { info = 1; } else if (! notb && ! lsame_(transb, "C") && ! lsame_(transb, "T")) { info = 2; } else if (*m < 0) { info = 3; } else if (*n < 0) { info = 4; } else if (*k < 0) { info = 5; } else if (*lda < max(1,nrowa)) { info = 8; } else if (*ldb < max(1,nrowb)) { info = 10; } else if (*ldc < max(1,*m)) { info = 13; } if (info != 0) { xerbla_("DGEMM ", &info); return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { return 0; } /* And if alpha.eq.zero. */ if (*alpha == 0.) { if (*beta == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = 0.; /* L10: */ } /* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = *beta * c___ref(i__, j); /* L30: */ } /* L40: */ } } return 0; } /* Start the operations. */ if (notb) { if (nota) { /* Form C := alpha*A*B + beta*C. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = 0.; /* L50: */ } } else if (*beta != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = *beta * c___ref(i__, j); /* L60: */ } } i__2 = *k; for (l = 1; l <= i__2; ++l) { if (b_ref(l, j) != 0.) { temp = *alpha * b_ref(l, j); i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { c___ref(i__, j) = c___ref(i__, j) + temp * a_ref( i__, l); /* L70: */ } } /* L80: */ } /* L90: */ } } else { /* Form C := alpha*A'*B + beta*C */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { temp += a_ref(l, i__) * b_ref(l, j); /* L100: */ } if (*beta == 0.) { c___ref(i__, j) = *alpha * temp; } else { c___ref(i__, j) = *alpha * temp + *beta * c___ref(i__, j); } /* L110: */ } /* L120: */ } } } else { if (nota) { /* Form C := alpha*A*B' + beta*C */ i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = 0.; /* L130: */ } } else if (*beta != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = *beta * c___ref(i__, j); /* L140: */ } } i__2 = *k; for (l = 1; l <= i__2; ++l) { if (b_ref(j, l) != 0.) { temp = *alpha * b_ref(j, l); i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { c___ref(i__, j) = c___ref(i__, j) + temp * a_ref( i__, l); /* L150: */ } } /* L160: */ } /* L170: */ } } else { /* Form C := alpha*A'*B' + beta*C */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { temp += a_ref(l, i__) * b_ref(j, l); /* L180: */ } if (*beta == 0.) { c___ref(i__, j) = *alpha * temp; } else { c___ref(i__, j) = *alpha * temp + *beta * c___ref(i__, j); } /* L190: */ } /* L200: */ } } } return 0; /* End of DGEMM . */ } /* dgemm_ */ #undef c___ref #undef b_ref #undef a_ref /* Subroutine */ int dgemv_(char *trans, integer *m, integer *n, doublereal * alpha, doublereal *a, integer *lda, doublereal *x, integer *incx, doublereal *beta, doublereal *y, integer *incy) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; /* Local variables */ static integer info; static doublereal temp; static integer lenx, leny, i__, j; extern logical lsame_(char *, char *); static integer ix, iy, jx, jy, kx, ky; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] /* Purpose ======= DGEMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix. Parameters ========== TRANS - CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*A'*x + beta*y. TRANS = 'C' or 'c' y := alpha*A'*x + beta*y. Unchanged on exit. M - INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit. N - INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit. ALPHA - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ). Unchanged on exit. X - DOUBLE PRECISION array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x. Unchanged on exit. INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. BETA - DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit. Y - DOUBLE PRECISION array of DIMENSION at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. INCY - INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --x; --y; /* Function Body */ info = 0; if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C") ) { info = 1; } else if (*m < 0) { info = 2; } else if (*n < 0) { info = 3; } else if (*lda < max(1,*m)) { info = 6; } else if (*incx == 0) { info = 8; } else if (*incy == 0) { info = 11; } if (info != 0) { xerbla_("DGEMV ", &info); return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) { return 0; } /* Set LENX and LENY, the lengths of the vectors x and y, and set up the start points in X and Y. */ if (lsame_(trans, "N")) { lenx = *n; leny = *m; } else { lenx = *m; leny = *n; } if (*incx > 0) { kx = 1; } else { kx = 1 - (lenx - 1) * *incx; } if (*incy > 0) { ky = 1; } else { ky = 1 - (leny - 1) * *incy; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through A. First form y := beta*y. */ if (*beta != 1.) { if (*incy == 1) { if (*beta == 0.) { i__1 = leny; for (i__ = 1; i__ <= i__1; ++i__) { y[i__] = 0.; /* L10: */ } } else { i__1 = leny; for (i__ = 1; i__ <= i__1; ++i__) { y[i__] = *beta * y[i__]; /* L20: */ } } } else { iy = ky; if (*beta == 0.) { i__1 = leny; for (i__ = 1; i__ <= i__1; ++i__) { y[iy] = 0.; iy += *incy; /* L30: */ } } else { i__1 = leny; for (i__ = 1; i__ <= i__1; ++i__) { y[iy] = *beta * y[iy]; iy += *incy; /* L40: */ } } } } if (*alpha == 0.) { return 0; } if (lsame_(trans, "N")) { /* Form y := alpha*A*x + y. */ jx = kx; if (*incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (x[jx] != 0.) { temp = *alpha * x[jx]; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { y[i__] += temp * a_ref(i__, j); /* L50: */ } } jx += *incx; /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (x[jx] != 0.) { temp = *alpha * x[jx]; iy = ky; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { y[iy] += temp * a_ref(i__, j); iy += *incy; /* L70: */ } } jx += *incx; /* L80: */ } } } else { /* Form y := alpha*A'*x + y. */ jy = ky; if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { temp = 0.; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp += a_ref(i__, j) * x[i__]; /* L90: */ } y[jy] += *alpha * temp; jy += *incy; /* L100: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { temp = 0.; ix = kx; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp += a_ref(i__, j) * x[ix]; ix += *incx; /* L110: */ } y[jy] += *alpha * temp; jy += *incy; /* L120: */ } } } return 0; /* End of DGEMV . */ } /* dgemv_ */ #undef a_ref /* Subroutine */ int dger_(integer *m, integer *n, doublereal *alpha, doublereal *x, integer *incx, doublereal *y, integer *incy, doublereal *a, integer *lda) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; /* Local variables */ static integer info; static doublereal temp; static integer i__, j, ix, jy, kx; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] /* Purpose ======= DGER performs the rank 1 operation A := alpha*x*y' + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. Parameters ========== M - INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit. N - INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit. ALPHA - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. X - DOUBLE PRECISION array of dimension at least ( 1 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m element vector x. Unchanged on exit. INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. Y - DOUBLE PRECISION array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. Unchanged on exit. INCY - INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by the updated matrix. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ). Unchanged on exit. Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. Test the input parameters. Parameter adjustments */ --x; --y; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; /* Function Body */ info = 0; if (*m < 0) { info = 1; } else if (*n < 0) { info = 2; } else if (*incx == 0) { info = 5; } else if (*incy == 0) { info = 7; } else if (*lda < max(1,*m)) { info = 9; } if (info != 0) { xerbla_("DGER ", &info); return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || *alpha == 0.) { return 0; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through A. */ if (*incy > 0) { jy = 1; } else { jy = 1 - (*n - 1) * *incy; } if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (y[jy] != 0.) { temp = *alpha * y[jy]; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { a_ref(i__, j) = a_ref(i__, j) + x[i__] * temp; /* L10: */ } } jy += *incy; /* L20: */ } } else { if (*incx > 0) { kx = 1; } else { kx = 1 - (*m - 1) * *incx; } i__1 = *n; for (j = 1; j <= i__1; ++j) { if (y[jy] != 0.) { temp = *alpha * y[jy]; ix = kx; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { a_ref(i__, j) = a_ref(i__, j) + x[ix] * temp; ix += *incx; /* L30: */ } } jy += *incy; /* L40: */ } } return 0; /* End of DGER . */ } /* dger_ */ #undef a_ref doublereal dnrm2_(integer *n, doublereal *x, integer *incx) { /* The following loop is equivalent to this call to the LAPACK auxiliary routine: CALL DLASSQ( N, X, INCX, SCALE, SSQ ) */ /* System generated locals */ integer i__1, i__2; doublereal ret_val, d__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static doublereal norm, scale, absxi; static integer ix; static doublereal ssq; /* DNRM2 returns the euclidean norm of a vector via the function name, so that DNRM2 := sqrt( x'*x ) -- This version written on 25-October-1982. Modified on 14-October-1993 to inline the call to DLASSQ. Sven Hammarling, Nag Ltd. Parameter adjustments */ --x; /* Function Body */ if (*n < 1 || *incx < 1) { norm = 0.; } else if (*n == 1) { norm = abs(x[1]); } else { scale = 0.; ssq = 1.; i__1 = (*n - 1) * *incx + 1; i__2 = *incx; for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { if (x[ix] != 0.) { absxi = (d__1 = x[ix], abs(d__1)); if (scale < absxi) { /* Computing 2nd power */ d__1 = scale / absxi; ssq = ssq * (d__1 * d__1) + 1.; scale = absxi; } else { /* Computing 2nd power */ d__1 = absxi / scale; ssq += d__1 * d__1; } } /* L10: */ } norm = scale * sqrt(ssq); } ret_val = norm; return ret_val; /* End of DNRM2. */ } /* dnrm2_ */ /* Subroutine */ int drot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, integer *incy, doublereal *c__, doublereal *s) { /* System generated locals */ integer i__1; /* Local variables */ static integer i__; static doublereal dtemp; static integer ix, iy; /* applies a plane rotation. jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --dy; --dx; /* Function Body */ if (*n <= 0) { return 0; } if (*incx == 1 && *incy == 1) { goto L20; } /* code for unequal increments or equal increments not equal to 1 */ ix = 1; iy = 1; if (*incx < 0) { ix = (-(*n) + 1) * *incx + 1; } if (*incy < 0) { iy = (-(*n) + 1) * *incy + 1; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { dtemp = *c__ * dx[ix] + *s * dy[iy]; dy[iy] = *c__ * dy[iy] - *s * dx[ix]; dx[ix] = dtemp; ix += *incx; iy += *incy; /* L10: */ } return 0; /* code for both increments equal to 1 */ L20: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { dtemp = *c__ * dx[i__] + *s * dy[i__]; dy[i__] = *c__ * dy[i__] - *s * dx[i__]; dx[i__] = dtemp; /* L30: */ } return 0; } /* drot_ */ /* Subroutine */ int dscal_(integer *n, doublereal *da, doublereal *dx, integer *incx) { /* System generated locals */ integer i__1, i__2; /* Local variables */ static integer i__, m, nincx, mp1; /* scales a vector by a constant. uses unrolled loops for increment equal to one. jack dongarra, linpack, 3/11/78. modified 3/93 to return if incx .le. 0. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --dx; /* Function Body */ if (*n <= 0 || *incx <= 0) { return 0; } if (*incx == 1) { goto L20; } /* code for increment not equal to 1 */ nincx = *n * *incx; i__1 = nincx; i__2 = *incx; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { dx[i__] = *da * dx[i__]; /* L10: */ } return 0; /* code for increment equal to 1 clean-up loop */ L20: m = *n % 5; if (m == 0) { goto L40; } i__2 = m; for (i__ = 1; i__ <= i__2; ++i__) { dx[i__] = *da * dx[i__]; /* L30: */ } if (*n < 5) { return 0; } L40: mp1 = m + 1; i__2 = *n; for (i__ = mp1; i__ <= i__2; i__ += 5) { dx[i__] = *da * dx[i__]; dx[i__ + 1] = *da * dx[i__ + 1]; dx[i__ + 2] = *da * dx[i__ + 2]; dx[i__ + 3] = *da * dx[i__ + 3]; dx[i__ + 4] = *da * dx[i__ + 4]; /* L50: */ } return 0; } /* dscal_ */ /* Subroutine */ int dswap_(integer *n, doublereal *dx, integer *incx, doublereal *dy, integer *incy) { /* System generated locals */ integer i__1; /* Local variables */ static integer i__, m; static doublereal dtemp; static integer ix, iy, mp1; /* interchanges two vectors. uses unrolled loops for increments equal one. jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --dy; --dx; /* Function Body */ if (*n <= 0) { return 0; } if (*incx == 1 && *incy == 1) { goto L20; } /* code for unequal increments or equal increments not equal to 1 */ ix = 1; iy = 1; if (*incx < 0) { ix = (-(*n) + 1) * *incx + 1; } if (*incy < 0) { iy = (-(*n) + 1) * *incy + 1; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { dtemp = dx[ix]; dx[ix] = dy[iy]; dy[iy] = dtemp; ix += *incx; iy += *incy; /* L10: */ } return 0; /* code for both increments equal to 1 clean-up loop */ L20: m = *n % 3; if (m == 0) { goto L40; } i__1 = m; for (i__ = 1; i__ <= i__1; ++i__) { dtemp = dx[i__]; dx[i__] = dy[i__]; dy[i__] = dtemp; /* L30: */ } if (*n < 3) { return 0; } L40: mp1 = m + 1; i__1 = *n; for (i__ = mp1; i__ <= i__1; i__ += 3) { dtemp = dx[i__]; dx[i__] = dy[i__]; dy[i__] = dtemp; dtemp = dx[i__ + 1]; dx[i__ + 1] = dy[i__ + 1]; dy[i__ + 1] = dtemp; dtemp = dx[i__ + 2]; dx[i__ + 2] = dy[i__ + 2]; dy[i__ + 2] = dtemp; /* L50: */ } return 0; } /* dswap_ */ /* Subroutine */ int dsymv_(char *uplo, integer *n, doublereal *alpha, doublereal *a, integer *lda, doublereal *x, integer *incx, doublereal *beta, doublereal *y, integer *incy) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; /* Local variables */ static integer info; static doublereal temp1, temp2; static integer i__, j; extern logical lsame_(char *, char *); static integer ix, iy, jx, jy, kx, ky; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] /* Purpose ======= DSYMV performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix. Parameters ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced. Unchanged on exit. N - INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. ALPHA - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). Unchanged on exit. X - DOUBLE PRECISION array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. Unchanged on exit. INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. BETA - DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit. Y - DOUBLE PRECISION array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. On exit, Y is overwritten by the updated vector y. INCY - INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --x; --y; /* Function Body */ info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { info = 1; } else if (*n < 0) { info = 2; } else if (*lda < max(1,*n)) { info = 5; } else if (*incx == 0) { info = 7; } else if (*incy == 0) { info = 10; } if (info != 0) { xerbla_("DSYMV ", &info); return 0; } /* Quick return if possible. */ if (*n == 0 || *alpha == 0. && *beta == 1.) { return 0; } /* Set up the start points in X and Y. */ if (*incx > 0) { kx = 1; } else { kx = 1 - (*n - 1) * *incx; } if (*incy > 0) { ky = 1; } else { ky = 1 - (*n - 1) * *incy; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through the triangular part of A. First form y := beta*y. */ if (*beta != 1.) { if (*incy == 1) { if (*beta == 0.) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { y[i__] = 0.; /* L10: */ } } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { y[i__] = *beta * y[i__]; /* L20: */ } } } else { iy = ky; if (*beta == 0.) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { y[iy] = 0.; iy += *incy; /* L30: */ } } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { y[iy] = *beta * y[iy]; iy += *incy; /* L40: */ } } } } if (*alpha == 0.) { return 0; } if (lsame_(uplo, "U")) { /* Form y when A is stored in upper triangle. */ if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { temp1 = *alpha * x[j]; temp2 = 0.; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { y[i__] += temp1 * a_ref(i__, j); temp2 += a_ref(i__, j) * x[i__]; /* L50: */ } y[j] = y[j] + temp1 * a_ref(j, j) + *alpha * temp2; /* L60: */ } } else { jx = kx; jy = ky; i__1 = *n; for (j = 1; j <= i__1; ++j) { temp1 = *alpha * x[jx]; temp2 = 0.; ix = kx; iy = ky; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { y[iy] += temp1 * a_ref(i__, j); temp2 += a_ref(i__, j) * x[ix]; ix += *incx; iy += *incy; /* L70: */ } y[jy] = y[jy] + temp1 * a_ref(j, j) + *alpha * temp2; jx += *incx; jy += *incy; /* L80: */ } } } else { /* Form y when A is stored in lower triangle. */ if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { temp1 = *alpha * x[j]; temp2 = 0.; y[j] += temp1 * a_ref(j, j); i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { y[i__] += temp1 * a_ref(i__, j); temp2 += a_ref(i__, j) * x[i__]; /* L90: */ } y[j] += *alpha * temp2; /* L100: */ } } else { jx = kx; jy = ky; i__1 = *n; for (j = 1; j <= i__1; ++j) { temp1 = *alpha * x[jx]; temp2 = 0.; y[jy] += temp1 * a_ref(j, j); ix = jx; iy = jy; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { ix += *incx; iy += *incy; y[iy] += temp1 * a_ref(i__, j); temp2 += a_ref(i__, j) * x[ix]; /* L110: */ } y[jy] += *alpha * temp2; jx += *incx; jy += *incy; /* L120: */ } } } return 0; /* End of DSYMV . */ } /* dsymv_ */ #undef a_ref /* Subroutine */ int dsyr2_(char *uplo, integer *n, doublereal *alpha, doublereal *x, integer *incx, doublereal *y, integer *incy, doublereal *a, integer *lda) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; /* Local variables */ static integer info; static doublereal temp1, temp2; static integer i__, j; extern logical lsame_(char *, char *); static integer ix, iy, jx, jy, kx, ky; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] /* Purpose ======= DSYR2 performs the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix. Parameters ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced. Unchanged on exit. N - INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. ALPHA - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. X - DOUBLE PRECISION array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. Unchanged on exit. INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. Y - DOUBLE PRECISION array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. Unchanged on exit. INCY - INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). Unchanged on exit. Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. Test the input parameters. Parameter adjustments */ --x; --y; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; /* Function Body */ info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { info = 1; } else if (*n < 0) { info = 2; } else if (*incx == 0) { info = 5; } else if (*incy == 0) { info = 7; } else if (*lda < max(1,*n)) { info = 9; } if (info != 0) { xerbla_("DSYR2 ", &info); return 0; } /* Quick return if possible. */ if (*n == 0 || *alpha == 0.) { return 0; } /* Set up the start points in X and Y if the increments are not both unity. */ if (*incx != 1 || *incy != 1) { if (*incx > 0) { kx = 1; } else { kx = 1 - (*n - 1) * *incx; } if (*incy > 0) { ky = 1; } else { ky = 1 - (*n - 1) * *incy; } jx = kx; jy = ky; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through the triangular part of A. */ if (lsame_(uplo, "U")) { /* Form A when A is stored in the upper triangle. */ if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (x[j] != 0. || y[j] != 0.) { temp1 = *alpha * y[j]; temp2 = *alpha * x[j]; i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { a_ref(i__, j) = a_ref(i__, j) + x[i__] * temp1 + y[ i__] * temp2; /* L10: */ } } /* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (x[jx] != 0. || y[jy] != 0.) { temp1 = *alpha * y[jy]; temp2 = *alpha * x[jx]; ix = kx; iy = ky; i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { a_ref(i__, j) = a_ref(i__, j) + x[ix] * temp1 + y[iy] * temp2; ix += *incx; iy += *incy; /* L30: */ } } jx += *incx; jy += *incy; /* L40: */ } } } else { /* Form A when A is stored in the lower triangle. */ if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (x[j] != 0. || y[j] != 0.) { temp1 = *alpha * y[j]; temp2 = *alpha * x[j]; i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { a_ref(i__, j) = a_ref(i__, j) + x[i__] * temp1 + y[ i__] * temp2; /* L50: */ } } /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (x[jx] != 0. || y[jy] != 0.) { temp1 = *alpha * y[jy]; temp2 = *alpha * x[jx]; ix = jx; iy = jy; i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { a_ref(i__, j) = a_ref(i__, j) + x[ix] * temp1 + y[iy] * temp2; ix += *incx; iy += *incy; /* L70: */ } } jx += *incx; jy += *incy; /* L80: */ } } } return 0; /* End of DSYR2 . */ } /* dsyr2_ */ #undef a_ref /* Subroutine */ int dsyr2k_(char *uplo, char *trans, integer *n, integer *k, doublereal *alpha, doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *beta, doublereal *c__, integer *ldc) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3; /* Local variables */ static integer info; static doublereal temp1, temp2; static integer i__, j, l; extern logical lsame_(char *, char *); static integer nrowa; static logical upper; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] #define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1] #define c___ref(a_1,a_2) c__[(a_2)*c_dim1 + a_1] /* Purpose ======= DSYR2K performs one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C, or C := alpha*A'*B + alpha*B'*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case. Parameters ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced. Unchanged on exit. TRANS - CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' + beta*C. TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A + beta*C. TRANS = 'C' or 'c' C := alpha*A'*B + alpha*B'*A + beta*C. Unchanged on exit. N - INTEGER. On entry, N specifies the order of the matrix C. N must be at least zero. Unchanged on exit. K - INTEGER. On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrices A and B. K must be at least zero. Unchanged on exit. ALPHA - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ). Unchanged on exit. B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B. Unchanged on exit. LDB - INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k ). Unchanged on exit. BETA - DOUBLE PRECISION. On entry, BETA specifies the scalar beta. Unchanged on exit. C - DOUBLE PRECISION array of DIMENSION ( LDC, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. LDC - INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, n ). Unchanged on exit. Level 3 Blas routine. -- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; /* Function Body */ if (lsame_(trans, "N")) { nrowa = *n; } else { nrowa = *k; } upper = lsame_(uplo, "U"); info = 0; if (! upper && ! lsame_(uplo, "L")) { info = 1; } else if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")) { info = 2; } else if (*n < 0) { info = 3; } else if (*k < 0) { info = 4; } else if (*lda < max(1,nrowa)) { info = 7; } else if (*ldb < max(1,nrowa)) { info = 9; } else if (*ldc < max(1,*n)) { info = 12; } if (info != 0) { xerbla_("DSYR2K", &info); return 0; } /* Quick return if possible. */ if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { return 0; } /* And when alpha.eq.zero. */ if (*alpha == 0.) { if (upper) { if (*beta == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = 0.; /* L10: */ } /* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = *beta * c___ref(i__, j); /* L30: */ } /* L40: */ } } } else { if (*beta == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c___ref(i__, j) = 0.; /* L50: */ } /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c___ref(i__, j) = *beta * c___ref(i__, j); /* L70: */ } /* L80: */ } } } return 0; } /* Start the operations. */ if (lsame_(trans, "N")) { /* Form C := alpha*A*B' + alpha*B*A' + C. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = 0.; /* L90: */ } } else if (*beta != 1.) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = *beta * c___ref(i__, j); /* L100: */ } } i__2 = *k; for (l = 1; l <= i__2; ++l) { if (a_ref(j, l) != 0. || b_ref(j, l) != 0.) { temp1 = *alpha * b_ref(j, l); temp2 = *alpha * a_ref(j, l); i__3 = j; for (i__ = 1; i__ <= i__3; ++i__) { c___ref(i__, j) = c___ref(i__, j) + a_ref(i__, l) * temp1 + b_ref(i__, l) * temp2; /* L110: */ } } /* L120: */ } /* L130: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c___ref(i__, j) = 0.; /* L140: */ } } else if (*beta != 1.) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c___ref(i__, j) = *beta * c___ref(i__, j); /* L150: */ } } i__2 = *k; for (l = 1; l <= i__2; ++l) { if (a_ref(j, l) != 0. || b_ref(j, l) != 0.) { temp1 = *alpha * b_ref(j, l); temp2 = *alpha * a_ref(j, l); i__3 = *n; for (i__ = j; i__ <= i__3; ++i__) { c___ref(i__, j) = c___ref(i__, j) + a_ref(i__, l) * temp1 + b_ref(i__, l) * temp2; /* L160: */ } } /* L170: */ } /* L180: */ } } } else { /* Form C := alpha*A'*B + alpha*B'*A + C. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { temp1 = 0.; temp2 = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { temp1 += a_ref(l, i__) * b_ref(l, j); temp2 += b_ref(l, i__) * a_ref(l, j); /* L190: */ } if (*beta == 0.) { c___ref(i__, j) = *alpha * temp1 + *alpha * temp2; } else { c___ref(i__, j) = *beta * c___ref(i__, j) + *alpha * temp1 + *alpha * temp2; } /* L200: */ } /* L210: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { temp1 = 0.; temp2 = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { temp1 += a_ref(l, i__) * b_ref(l, j); temp2 += b_ref(l, i__) * a_ref(l, j); /* L220: */ } if (*beta == 0.) { c___ref(i__, j) = *alpha * temp1 + *alpha * temp2; } else { c___ref(i__, j) = *beta * c___ref(i__, j) + *alpha * temp1 + *alpha * temp2; } /* L230: */ } /* L240: */ } } } return 0; /* End of DSYR2K. */ } /* dsyr2k_ */ #undef c___ref #undef b_ref #undef a_ref /* Subroutine */ int dtrmm_(char *side, char *uplo, char *transa, char *diag, integer *m, integer *n, doublereal *alpha, doublereal *a, integer * lda, doublereal *b, integer *ldb) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; /* Local variables */ static integer info; static doublereal temp; static integer i__, j, k; static logical lside; extern logical lsame_(char *, char *); static integer nrowa; static logical upper; extern /* Subroutine */ int xerbla_(char *, integer *); static logical nounit; #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] #define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1] /* Purpose ======= DTRMM performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ), where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A'. Parameters ========== SIDE - CHARACTER*1. On entry, SIDE specifies whether op( A ) multiplies B from the left or right as follows: SIDE = 'L' or 'l' B := alpha*op( A )*B. SIDE = 'R' or 'r' B := alpha*B*op( A ). Unchanged on exit. UPLO - CHARACTER*1. On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. Unchanged on exit. TRANSA - CHARACTER*1. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n' op( A ) = A. TRANSA = 'T' or 't' op( A ) = A'. TRANSA = 'C' or 'c' op( A ) = A'. Unchanged on exit. DIAG - CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. Unchanged on exit. M - INTEGER. On entry, M specifies the number of rows of B. M must be at least zero. Unchanged on exit. N - INTEGER. On entry, N specifies the number of columns of B. N must be at least zero. Unchanged on exit. ALPHA - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. Unchanged on exit. A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ). Unchanged on exit. B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the matrix B, and on exit is overwritten by the transformed matrix. LDB - INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ). Unchanged on exit. Level 3 Blas routine. -- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; /* Function Body */ lside = lsame_(side, "L"); if (lside) { nrowa = *m; } else { nrowa = *n; } nounit = lsame_(diag, "N"); upper = lsame_(uplo, "U"); info = 0; if (! lside && ! lsame_(side, "R")) { info = 1; } else if (! upper && ! lsame_(uplo, "L")) { info = 2; } else if (! lsame_(transa, "N") && ! lsame_(transa, "T") && ! lsame_(transa, "C")) { info = 3; } else if (! lsame_(diag, "U") && ! lsame_(diag, "N")) { info = 4; } else if (*m < 0) { info = 5; } else if (*n < 0) { info = 6; } else if (*lda < max(1,nrowa)) { info = 9; } else if (*ldb < max(1,*m)) { info = 11; } if (info != 0) { xerbla_("DTRMM ", &info); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } /* And when alpha.eq.zero. */ if (*alpha == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, j) = 0.; /* L10: */ } /* L20: */ } return 0; } /* Start the operations. */ if (lside) { if (lsame_(transa, "N")) { /* Form B := alpha*A*B. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (k = 1; k <= i__2; ++k) { if (b_ref(k, j) != 0.) { temp = *alpha * b_ref(k, j); i__3 = k - 1; for (i__ = 1; i__ <= i__3; ++i__) { b_ref(i__, j) = b_ref(i__, j) + temp * a_ref( i__, k); /* L30: */ } if (nounit) { temp *= a_ref(k, k); } b_ref(k, j) = temp; } /* L40: */ } /* L50: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { for (k = *m; k >= 1; --k) { if (b_ref(k, j) != 0.) { temp = *alpha * b_ref(k, j); b_ref(k, j) = temp; if (nounit) { b_ref(k, j) = b_ref(k, j) * a_ref(k, k); } i__2 = *m; for (i__ = k + 1; i__ <= i__2; ++i__) { b_ref(i__, j) = b_ref(i__, j) + temp * a_ref( i__, k); /* L60: */ } } /* L70: */ } /* L80: */ } } } else { /* Form B := alpha*A'*B. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { for (i__ = *m; i__ >= 1; --i__) { temp = b_ref(i__, j); if (nounit) { temp *= a_ref(i__, i__); } i__2 = i__ - 1; for (k = 1; k <= i__2; ++k) { temp += a_ref(k, i__) * b_ref(k, j); /* L90: */ } b_ref(i__, j) = *alpha * temp; /* L100: */ } /* L110: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp = b_ref(i__, j); if (nounit) { temp *= a_ref(i__, i__); } i__3 = *m; for (k = i__ + 1; k <= i__3; ++k) { temp += a_ref(k, i__) * b_ref(k, j); /* L120: */ } b_ref(i__, j) = *alpha * temp; /* L130: */ } /* L140: */ } } } } else { if (lsame_(transa, "N")) { /* Form B := alpha*B*A. */ if (upper) { for (j = *n; j >= 1; --j) { temp = *alpha; if (nounit) { temp *= a_ref(j, j); } i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { b_ref(i__, j) = temp * b_ref(i__, j); /* L150: */ } i__1 = j - 1; for (k = 1; k <= i__1; ++k) { if (a_ref(k, j) != 0.) { temp = *alpha * a_ref(k, j); i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, j) = b_ref(i__, j) + temp * b_ref( i__, k); /* L160: */ } } /* L170: */ } /* L180: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { temp = *alpha; if (nounit) { temp *= a_ref(j, j); } i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, j) = temp * b_ref(i__, j); /* L190: */ } i__2 = *n; for (k = j + 1; k <= i__2; ++k) { if (a_ref(k, j) != 0.) { temp = *alpha * a_ref(k, j); i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { b_ref(i__, j) = b_ref(i__, j) + temp * b_ref( i__, k); /* L200: */ } } /* L210: */ } /* L220: */ } } } else { /* Form B := alpha*B*A'. */ if (upper) { i__1 = *n; for (k = 1; k <= i__1; ++k) { i__2 = k - 1; for (j = 1; j <= i__2; ++j) { if (a_ref(j, k) != 0.) { temp = *alpha * a_ref(j, k); i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { b_ref(i__, j) = b_ref(i__, j) + temp * b_ref( i__, k); /* L230: */ } } /* L240: */ } temp = *alpha; if (nounit) { temp *= a_ref(k, k); } if (temp != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, k) = temp * b_ref(i__, k); /* L250: */ } } /* L260: */ } } else { for (k = *n; k >= 1; --k) { i__1 = *n; for (j = k + 1; j <= i__1; ++j) { if (a_ref(j, k) != 0.) { temp = *alpha * a_ref(j, k); i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, j) = b_ref(i__, j) + temp * b_ref( i__, k); /* L270: */ } } /* L280: */ } temp = *alpha; if (nounit) { temp *= a_ref(k, k); } if (temp != 1.) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { b_ref(i__, k) = temp * b_ref(i__, k); /* L290: */ } } /* L300: */ } } } } return 0; /* End of DTRMM . */ } /* dtrmm_ */ #undef b_ref #undef a_ref /* Subroutine */ int dtrmv_(char *uplo, char *trans, char *diag, integer *n, doublereal *a, integer *lda, doublereal *x, integer *incx) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; /* Local variables */ static integer info; static doublereal temp; static integer i__, j; extern logical lsame_(char *, char *); static integer ix, jx, kx; extern /* Subroutine */ int xerbla_(char *, integer *); static logical nounit; #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] /* Purpose ======= DTRMV performs one of the matrix-vector operations x := A*x, or x := A'*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix. Parameters ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. Unchanged on exit. TRANS - CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' x := A*x. TRANS = 'T' or 't' x := A'*x. TRANS = 'C' or 'c' x := A'*x. Unchanged on exit. DIAG - CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. Unchanged on exit. N - INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). Unchanged on exit. X - DOUBLE PRECISION array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the tranformed vector x. INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --x; /* Function Body */ info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { info = 1; } else if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")) { info = 2; } else if (! lsame_(diag, "U") && ! lsame_(diag, "N")) { info = 3; } else if (*n < 0) { info = 4; } else if (*lda < max(1,*n)) { info = 6; } else if (*incx == 0) { info = 8; } if (info != 0) { xerbla_("DTRMV ", &info); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } nounit = lsame_(diag, "N"); /* Set up the start point in X if the increment is not unity. This will be ( N - 1 )*INCX too small for descending loops. */ if (*incx <= 0) { kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { kx = 1; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through A. */ if (lsame_(trans, "N")) { /* Form x := A*x. */ if (lsame_(uplo, "U")) { if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (x[j] != 0.) { temp = x[j]; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { x[i__] += temp * a_ref(i__, j); /* L10: */ } if (nounit) { x[j] *= a_ref(j, j); } } /* L20: */ } } else { jx = kx; i__1 = *n; for (j = 1; j <= i__1; ++j) { if (x[jx] != 0.) { temp = x[jx]; ix = kx; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { x[ix] += temp * a_ref(i__, j); ix += *incx; /* L30: */ } if (nounit) { x[jx] *= a_ref(j, j); } } jx += *incx; /* L40: */ } } } else { if (*incx == 1) { for (j = *n; j >= 1; --j) { if (x[j] != 0.) { temp = x[j]; i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { x[i__] += temp * a_ref(i__, j); /* L50: */ } if (nounit) { x[j] *= a_ref(j, j); } } /* L60: */ } } else { kx += (*n - 1) * *incx; jx = kx; for (j = *n; j >= 1; --j) { if (x[jx] != 0.) { temp = x[jx]; ix = kx; i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { x[ix] += temp * a_ref(i__, j); ix -= *incx; /* L70: */ } if (nounit) { x[jx] *= a_ref(j, j); } } jx -= *incx; /* L80: */ } } } } else { /* Form x := A'*x. */ if (lsame_(uplo, "U")) { if (*incx == 1) { for (j = *n; j >= 1; --j) { temp = x[j]; if (nounit) { temp *= a_ref(j, j); } for (i__ = j - 1; i__ >= 1; --i__) { temp += a_ref(i__, j) * x[i__]; /* L90: */ } x[j] = temp; /* L100: */ } } else { jx = kx + (*n - 1) * *incx; for (j = *n; j >= 1; --j) { temp = x[jx]; ix = jx; if (nounit) { temp *= a_ref(j, j); } for (i__ = j - 1; i__ >= 1; --i__) { ix -= *incx; temp += a_ref(i__, j) * x[ix]; /* L110: */ } x[jx] = temp; jx -= *incx; /* L120: */ } } } else { if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { temp = x[j]; if (nounit) { temp *= a_ref(j, j); } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { temp += a_ref(i__, j) * x[i__]; /* L130: */ } x[j] = temp; /* L140: */ } } else { jx = kx; i__1 = *n; for (j = 1; j <= i__1; ++j) { temp = x[jx]; ix = jx; if (nounit) { temp *= a_ref(j, j); } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { ix += *incx; temp += a_ref(i__, j) * x[ix]; /* L150: */ } x[jx] = temp; jx += *incx; /* L160: */ } } } } return 0; /* End of DTRMV . */ } /* dtrmv_ */ #undef a_ref /* Subroutine */ int dtrsm_(char *side, char *uplo, char *transa, char *diag, integer *m, integer *n, doublereal *alpha, doublereal *a, integer * lda, doublereal *b, integer *ldb) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; /* Local variables */ static integer info; static doublereal temp; static integer i__, j, k; static logical lside; extern logical lsame_(char *, char *); static integer nrowa; static logical upper; extern /* Subroutine */ int xerbla_(char *, integer *); static logical nounit; #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] #define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1] /* Purpose ======= DTRSM solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A'. The matrix X is overwritten on B. Parameters ========== SIDE - CHARACTER*1. On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = 'L' or 'l' op( A )*X = alpha*B. SIDE = 'R' or 'r' X*op( A ) = alpha*B. Unchanged on exit. UPLO - CHARACTER*1. On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. Unchanged on exit. TRANSA - CHARACTER*1. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n' op( A ) = A. TRANSA = 'T' or 't' op( A ) = A'. TRANSA = 'C' or 'c' op( A ) = A'. Unchanged on exit. DIAG - CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. Unchanged on exit. M - INTEGER. On entry, M specifies the number of rows of B. M must be at least zero. Unchanged on exit. N - INTEGER. On entry, N specifies the number of columns of B. N must be at least zero. Unchanged on exit. ALPHA - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. Unchanged on exit. A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ). Unchanged on exit. B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X. LDB - INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ). Unchanged on exit. Level 3 Blas routine. -- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; /* Function Body */ lside = lsame_(side, "L"); if (lside) { nrowa = *m; } else { nrowa = *n; } nounit = lsame_(diag, "N"); upper = lsame_(uplo, "U"); info = 0; if (! lside && ! lsame_(side, "R")) { info = 1; } else if (! upper && ! lsame_(uplo, "L")) { info = 2; } else if (! lsame_(transa, "N") && ! lsame_(transa, "T") && ! lsame_(transa, "C")) { info = 3; } else if (! lsame_(diag, "U") && ! lsame_(diag, "N")) { info = 4; } else if (*m < 0) { info = 5; } else if (*n < 0) { info = 6; } else if (*lda < max(1,nrowa)) { info = 9; } else if (*ldb < max(1,*m)) { info = 11; } if (info != 0) { xerbla_("DTRSM ", &info); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } /* And when alpha.eq.zero. */ if (*alpha == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, j) = 0.; /* L10: */ } /* L20: */ } return 0; } /* Start the operations. */ if (lside) { if (lsame_(transa, "N")) { /* Form B := alpha*inv( A )*B. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*alpha != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, j) = *alpha * b_ref(i__, j); /* L30: */ } } for (k = *m; k >= 1; --k) { if (b_ref(k, j) != 0.) { if (nounit) { b_ref(k, j) = b_ref(k, j) / a_ref(k, k); } i__2 = k - 1; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, j) = b_ref(i__, j) - b_ref(k, j) * a_ref(i__, k); /* L40: */ } } /* L50: */ } /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*alpha != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, j) = *alpha * b_ref(i__, j); /* L70: */ } } i__2 = *m; for (k = 1; k <= i__2; ++k) { if (b_ref(k, j) != 0.) { if (nounit) { b_ref(k, j) = b_ref(k, j) / a_ref(k, k); } i__3 = *m; for (i__ = k + 1; i__ <= i__3; ++i__) { b_ref(i__, j) = b_ref(i__, j) - b_ref(k, j) * a_ref(i__, k); /* L80: */ } } /* L90: */ } /* L100: */ } } } else { /* Form B := alpha*inv( A' )*B. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp = *alpha * b_ref(i__, j); i__3 = i__ - 1; for (k = 1; k <= i__3; ++k) { temp -= a_ref(k, i__) * b_ref(k, j); /* L110: */ } if (nounit) { temp /= a_ref(i__, i__); } b_ref(i__, j) = temp; /* L120: */ } /* L130: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { for (i__ = *m; i__ >= 1; --i__) { temp = *alpha * b_ref(i__, j); i__2 = *m; for (k = i__ + 1; k <= i__2; ++k) { temp -= a_ref(k, i__) * b_ref(k, j); /* L140: */ } if (nounit) { temp /= a_ref(i__, i__); } b_ref(i__, j) = temp; /* L150: */ } /* L160: */ } } } } else { if (lsame_(transa, "N")) { /* Form B := alpha*B*inv( A ). */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*alpha != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, j) = *alpha * b_ref(i__, j); /* L170: */ } } i__2 = j - 1; for (k = 1; k <= i__2; ++k) { if (a_ref(k, j) != 0.) { i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { b_ref(i__, j) = b_ref(i__, j) - a_ref(k, j) * b_ref(i__, k); /* L180: */ } } /* L190: */ } if (nounit) { temp = 1. / a_ref(j, j); i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, j) = temp * b_ref(i__, j); /* L200: */ } } /* L210: */ } } else { for (j = *n; j >= 1; --j) { if (*alpha != 1.) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { b_ref(i__, j) = *alpha * b_ref(i__, j); /* L220: */ } } i__1 = *n; for (k = j + 1; k <= i__1; ++k) { if (a_ref(k, j) != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, j) = b_ref(i__, j) - a_ref(k, j) * b_ref(i__, k); /* L230: */ } } /* L240: */ } if (nounit) { temp = 1. / a_ref(j, j); i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { b_ref(i__, j) = temp * b_ref(i__, j); /* L250: */ } } /* L260: */ } } } else { /* Form B := alpha*B*inv( A' ). */ if (upper) { for (k = *n; k >= 1; --k) { if (nounit) { temp = 1. / a_ref(k, k); i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { b_ref(i__, k) = temp * b_ref(i__, k); /* L270: */ } } i__1 = k - 1; for (j = 1; j <= i__1; ++j) { if (a_ref(j, k) != 0.) { temp = a_ref(j, k); i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, j) = b_ref(i__, j) - temp * b_ref( i__, k); /* L280: */ } } /* L290: */ } if (*alpha != 1.) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { b_ref(i__, k) = *alpha * b_ref(i__, k); /* L300: */ } } /* L310: */ } } else { i__1 = *n; for (k = 1; k <= i__1; ++k) { if (nounit) { temp = 1. / a_ref(k, k); i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, k) = temp * b_ref(i__, k); /* L320: */ } } i__2 = *n; for (j = k + 1; j <= i__2; ++j) { if (a_ref(j, k) != 0.) { temp = a_ref(j, k); i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { b_ref(i__, j) = b_ref(i__, j) - temp * b_ref( i__, k); /* L330: */ } } /* L340: */ } if (*alpha != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b_ref(i__, k) = *alpha * b_ref(i__, k); /* L350: */ } } /* L360: */ } } } } return 0; /* End of DTRSM . */ } /* dtrsm_ */ #undef b_ref #undef a_ref doublereal dzasum_(integer *n, doublecomplex *zx, integer *incx) { /* System generated locals */ integer i__1; doublereal ret_val; /* Local variables */ static integer i__; static doublereal stemp; extern doublereal dcabs1_(doublecomplex *); static integer ix; /* takes the sum of the absolute values. jack dongarra, 3/11/78. modified 3/93 to return if incx .le. 0. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --zx; /* Function Body */ ret_val = 0.; stemp = 0.; if (*n <= 0 || *incx <= 0) { return ret_val; } if (*incx == 1) { goto L20; } /* code for increment not equal to 1 */ ix = 1; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { stemp += dcabs1_(&zx[ix]); ix += *incx; /* L10: */ } ret_val = stemp; return ret_val; /* code for increment equal to 1 */ L20: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { stemp += dcabs1_(&zx[i__]); /* L30: */ } ret_val = stemp; return ret_val; } /* dzasum_ */ doublereal dznrm2_(integer *n, doublecomplex *x, integer *incx) { /* The following loop is equivalent to this call to the LAPACK auxiliary routine: CALL ZLASSQ( N, X, INCX, SCALE, SSQ ) */ /* System generated locals */ integer i__1, i__2, i__3; doublereal ret_val, d__1; /* Builtin functions */ double d_imag(doublecomplex *), sqrt(doublereal); /* Local variables */ static doublereal temp, norm, scale; static integer ix; static doublereal ssq; /* DZNRM2 returns the euclidean norm of a vector via the function name, so that DZNRM2 := sqrt( conjg( x' )*x ) -- This version written on 25-October-1982. Modified on 14-October-1993 to inline the call to ZLASSQ. Sven Hammarling, Nag Ltd. Parameter adjustments */ --x; /* Function Body */ if (*n < 1 || *incx < 1) { norm = 0.; } else { scale = 0.; ssq = 1.; i__1 = (*n - 1) * *incx + 1; i__2 = *incx; for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { i__3 = ix; if (x[i__3].r != 0.) { i__3 = ix; temp = (d__1 = x[i__3].r, abs(d__1)); if (scale < temp) { /* Computing 2nd power */ d__1 = scale / temp; ssq = ssq * (d__1 * d__1) + 1.; scale = temp; } else { /* Computing 2nd power */ d__1 = temp / scale; ssq += d__1 * d__1; } } if (d_imag(&x[ix]) != 0.) { temp = (d__1 = d_imag(&x[ix]), abs(d__1)); if (scale < temp) { /* Computing 2nd power */ d__1 = scale / temp; ssq = ssq * (d__1 * d__1) + 1.; scale = temp; } else { /* Computing 2nd power */ d__1 = temp / scale; ssq += d__1 * d__1; } } /* L10: */ } norm = scale * sqrt(ssq); } ret_val = norm; return ret_val; /* End of DZNRM2. */ } /* dznrm2_ */ integer idamax_(integer *n, doublereal *dx, integer *incx) { /* System generated locals */ integer ret_val, i__1; doublereal d__1; /* Local variables */ static doublereal dmax__; static integer i__, ix; /* finds the index of element having max. absolute value. jack dongarra, linpack, 3/11/78. modified 3/93 to return if incx .le. 0. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --dx; /* Function Body */ ret_val = 0; if (*n < 1 || *incx <= 0) { return ret_val; } ret_val = 1; if (*n == 1) { return ret_val; } if (*incx == 1) { goto L20; } /* code for increment not equal to 1 */ ix = 1; dmax__ = abs(dx[1]); ix += *incx; i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { if ((d__1 = dx[ix], abs(d__1)) <= dmax__) { goto L5; } ret_val = i__; dmax__ = (d__1 = dx[ix], abs(d__1)); L5: ix += *incx; /* L10: */ } return ret_val; /* code for increment equal to 1 */ L20: dmax__ = abs(dx[1]); i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { if ((d__1 = dx[i__], abs(d__1)) <= dmax__) { goto L30; } ret_val = i__; dmax__ = (d__1 = dx[i__], abs(d__1)); L30: ; } return ret_val; } /* idamax_ */ integer izamax_(integer *n, doublecomplex *zx, integer *incx) { /* System generated locals */ integer ret_val, i__1; /* Local variables */ static doublereal smax; static integer i__; extern doublereal dcabs1_(doublecomplex *); static integer ix; /* finds the index of element having max. absolute value. jack dongarra, 1/15/85. modified 3/93 to return if incx .le. 0. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --zx; /* Function Body */ ret_val = 0; if (*n < 1 || *incx <= 0) { return ret_val; } ret_val = 1; if (*n == 1) { return ret_val; } if (*incx == 1) { goto L20; } /* code for increment not equal to 1 */ ix = 1; smax = dcabs1_(&zx[1]); ix += *incx; i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { if (dcabs1_(&zx[ix]) <= smax) { goto L5; } ret_val = i__; smax = dcabs1_(&zx[ix]); L5: ix += *incx; /* L10: */ } return ret_val; /* code for increment equal to 1 */ L20: smax = dcabs1_(&zx[1]); i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { if (dcabs1_(&zx[i__]) <= smax) { goto L30; } ret_val = i__; smax = dcabs1_(&zx[i__]); L30: ; } return ret_val; } /* izamax_ */ /* Subroutine */ int xerbla_(char *srname, integer *info) { /* -- LAPACK auxiliary routine (preliminary version) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University February 29, 1992 Purpose ======= XERBLA is an error handler for the LAPACK routines. It is called by an LAPACK routine if an input parameter has an invalid value. A message is printed and execution stops. Installers may consider modifying the STOP statement in order to call system-specific exception-handling facilities. Arguments ========= SRNAME (input) CHARACTER*6 The name of the routine which called XERBLA. INFO (input) INTEGER The position of the invalid parameter in the parameter list of the calling routine. */ /* Table of constant values */ static integer c__1 = 1; /* Format strings */ static char fmt_9999[] = "(\002 ** On entry to \002,a6,\002 parameter nu" "mber \002,i2,\002 had \002,\002an illegal value\002)"; /* Builtin functions */ integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Subroutine */ int s_stop(char *, ftnlen); /* Fortran I/O blocks */ static cilist io___1 = { 0, 6, 0, fmt_9999, 0 }; s_wsfe(&io___1); do_fio(&c__1, srname, (ftnlen)6); do_fio(&c__1, (char *)&(*info), (ftnlen)sizeof(integer)); e_wsfe(); s_stop("", (ftnlen)0); /* End of XERBLA */ return 0; } /* xerbla_ */ /* Subroutine */ int zaxpy_(integer *n, doublecomplex *za, doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy) { /* System generated locals */ integer i__1, i__2, i__3, i__4; doublecomplex z__1, z__2; /* Local variables */ static integer i__; extern doublereal dcabs1_(doublecomplex *); static integer ix, iy; /* constant times a vector plus a vector. jack dongarra, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --zy; --zx; /* Function Body */ if (*n <= 0) { return 0; } if (dcabs1_(za) == 0.) { return 0; } if (*incx == 1 && *incy == 1) { goto L20; } /* code for unequal increments or equal increments not equal to 1 */ ix = 1; iy = 1; if (*incx < 0) { ix = (-(*n) + 1) * *incx + 1; } if (*incy < 0) { iy = (-(*n) + 1) * *incy + 1; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = iy; i__3 = iy; i__4 = ix; z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__2.i = za->r * zx[ i__4].i + za->i * zx[i__4].r; z__1.r = zy[i__3].r + z__2.r, z__1.i = zy[i__3].i + z__2.i; zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; ix += *incx; iy += *incy; /* L10: */ } return 0; /* code for both increments equal to 1 */ L20: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; i__4 = i__; z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__2.i = za->r * zx[ i__4].i + za->i * zx[i__4].r; z__1.r = zy[i__3].r + z__2.r, z__1.i = zy[i__3].i + z__2.i; zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; /* L30: */ } return 0; } /* zaxpy_ */ /* Subroutine */ int zcopy_(integer *n, doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy) { /* System generated locals */ integer i__1, i__2, i__3; /* Local variables */ static integer i__, ix, iy; /* copies a vector, x, to a vector, y. jack dongarra, linpack, 4/11/78. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --zy; --zx; /* Function Body */ if (*n <= 0) { return 0; } if (*incx == 1 && *incy == 1) { goto L20; } /* code for unequal increments or equal increments not equal to 1 */ ix = 1; iy = 1; if (*incx < 0) { ix = (-(*n) + 1) * *incx + 1; } if (*incy < 0) { iy = (-(*n) + 1) * *incy + 1; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = iy; i__3 = ix; zy[i__2].r = zx[i__3].r, zy[i__2].i = zx[i__3].i; ix += *incx; iy += *incy; /* L10: */ } return 0; /* code for both increments equal to 1 */ L20: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; zy[i__2].r = zx[i__3].r, zy[i__2].i = zx[i__3].i; /* L30: */ } return 0; } /* zcopy_ */ /* Double Complex */ VOID zdotc_(doublecomplex * ret_val, integer *n, doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy) { /* System generated locals */ integer i__1, i__2; doublecomplex z__1, z__2, z__3; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer i__; static doublecomplex ztemp; static integer ix, iy; /* forms the dot product of a vector. jack dongarra, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --zy; --zx; /* Function Body */ ztemp.r = 0., ztemp.i = 0.; ret_val->r = 0., ret_val->i = 0.; if (*n <= 0) { return ; } if (*incx == 1 && *incy == 1) { goto L20; } /* code for unequal increments or equal increments not equal to 1 */ ix = 1; iy = 1; if (*incx < 0) { ix = (-(*n) + 1) * *incx + 1; } if (*incy < 0) { iy = (-(*n) + 1) * *incy + 1; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { d_cnjg(&z__3, &zx[ix]); i__2 = iy; z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i; ztemp.r = z__1.r, ztemp.i = z__1.i; ix += *incx; iy += *incy; /* L10: */ } ret_val->r = ztemp.r, ret_val->i = ztemp.i; return ; /* code for both increments equal to 1 */ L20: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { d_cnjg(&z__3, &zx[i__]); i__2 = i__; z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i; ztemp.r = z__1.r, ztemp.i = z__1.i; /* L30: */ } ret_val->r = ztemp.r, ret_val->i = ztemp.i; return ; } /* zdotc_ */ /* Double Complex */ VOID zdotu_(doublecomplex * ret_val, integer *n, doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy) { /* System generated locals */ integer i__1, i__2, i__3; doublecomplex z__1, z__2; /* Local variables */ static integer i__; static doublecomplex ztemp; static integer ix, iy; /* forms the dot product of two vectors. jack dongarra, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --zy; --zx; /* Function Body */ ztemp.r = 0., ztemp.i = 0.; ret_val->r = 0., ret_val->i = 0.; if (*n <= 0) { return ; } if (*incx == 1 && *incy == 1) { goto L20; } /* code for unequal increments or equal increments not equal to 1 */ ix = 1; iy = 1; if (*incx < 0) { ix = (-(*n) + 1) * *incx + 1; } if (*incy < 0) { iy = (-(*n) + 1) * *incy + 1; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = ix; i__3 = iy; z__2.r = zx[i__2].r * zy[i__3].r - zx[i__2].i * zy[i__3].i, z__2.i = zx[i__2].r * zy[i__3].i + zx[i__2].i * zy[i__3].r; z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i; ztemp.r = z__1.r, ztemp.i = z__1.i; ix += *incx; iy += *incy; /* L10: */ } ret_val->r = ztemp.r, ret_val->i = ztemp.i; return ; /* code for both increments equal to 1 */ L20: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; z__2.r = zx[i__2].r * zy[i__3].r - zx[i__2].i * zy[i__3].i, z__2.i = zx[i__2].r * zy[i__3].i + zx[i__2].i * zy[i__3].r; z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i; ztemp.r = z__1.r, ztemp.i = z__1.i; /* L30: */ } ret_val->r = ztemp.r, ret_val->i = ztemp.i; return ; } /* zdotu_ */ /* Subroutine */ int zdscal_(integer *n, doublereal *da, doublecomplex *zx, integer *incx) { /* System generated locals */ integer i__1, i__2, i__3; doublecomplex z__1, z__2; /* Local variables */ static integer i__, ix; /* scales a vector by a constant. jack dongarra, 3/11/78. modified 3/93 to return if incx .le. 0. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --zx; /* Function Body */ if (*n <= 0 || *incx <= 0) { return 0; } if (*incx == 1) { goto L20; } /* code for increment not equal to 1 */ ix = 1; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = ix; z__2.r = *da, z__2.i = 0.; i__3 = ix; z__1.r = z__2.r * zx[i__3].r - z__2.i * zx[i__3].i, z__1.i = z__2.r * zx[i__3].i + z__2.i * zx[i__3].r; zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; ix += *incx; /* L10: */ } return 0; /* code for increment equal to 1 */ L20: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; z__2.r = *da, z__2.i = 0.; i__3 = i__; z__1.r = z__2.r * zx[i__3].r - z__2.i * zx[i__3].i, z__1.i = z__2.r * zx[i__3].i + z__2.i * zx[i__3].r; zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; /* L30: */ } return 0; } /* zdscal_ */ /* Subroutine */ int zgemm_(char *transa, char *transb, integer *m, integer * n, integer *k, doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, doublecomplex *beta, doublecomplex * c__, integer *ldc) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublecomplex z__1, z__2, z__3, z__4; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static logical nota, notb; static doublecomplex temp; static integer i__, j, l; static logical conja, conjb; static integer ncola; extern logical lsame_(char *, char *); static integer nrowa, nrowb; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] #define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1 #define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)] #define c___subscr(a_1,a_2) (a_2)*c_dim1 + a_1 #define c___ref(a_1,a_2) c__[c___subscr(a_1,a_2)] /* Purpose ======= ZGEMM performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = X' or op( X ) = conjg( X' ), alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. Parameters ========== TRANSA - CHARACTER*1. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n', op( A ) = A. TRANSA = 'T' or 't', op( A ) = A'. TRANSA = 'C' or 'c', op( A ) = conjg( A' ). Unchanged on exit. TRANSB - CHARACTER*1. On entry, TRANSB specifies the form of op( B ) to be used in the matrix multiplication as follows: TRANSB = 'N' or 'n', op( B ) = B. TRANSB = 'T' or 't', op( B ) = B'. TRANSB = 'C' or 'c', op( B ) = conjg( B' ). Unchanged on exit. M - INTEGER. On entry, M specifies the number of rows of the matrix op( A ) and of the matrix C. M must be at least zero. Unchanged on exit. N - INTEGER. On entry, N specifies the number of columns of the matrix op( B ) and the number of columns of the matrix C. N must be at least zero. Unchanged on exit. K - INTEGER. On entry, K specifies the number of columns of the matrix op( A ) and the number of rows of the matrix op( B ). K must be at least zero. Unchanged on exit. ALPHA - COMPLEX*16 . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is k when TRANSA = 'N' or 'n', and is m otherwise. Before entry with TRANSA = 'N' or 'n', the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m part of the array A must contain the matrix A. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANSA = 'N' or 'n' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ). Unchanged on exit. B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is n when TRANSB = 'N' or 'n', and is k otherwise. Before entry with TRANSB = 'N' or 'n', the leading k by n part of the array B must contain the matrix B, otherwise the leading n by k part of the array B must contain the matrix B. Unchanged on exit. LDB - INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANSB = 'N' or 'n' then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ). Unchanged on exit. BETA - COMPLEX*16 . On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input. Unchanged on exit. C - COMPLEX*16 array of DIMENSION ( LDC, n ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n matrix ( alpha*op( A )*op( B ) + beta*C ). LDC - INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ). Unchanged on exit. Level 3 Blas routine. -- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd. Set NOTA and NOTB as true if A and B respectively are not conjugated or transposed, set CONJA and CONJB as true if A and B respectively are to be transposed but not conjugated and set NROWA, NCOLA and NROWB as the number of rows and columns of A and the number of rows of B respectively. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; /* Function Body */ nota = lsame_(transa, "N"); notb = lsame_(transb, "N"); conja = lsame_(transa, "C"); conjb = lsame_(transb, "C"); if (nota) { nrowa = *m; ncola = *k; } else { nrowa = *k; ncola = *m; } if (notb) { nrowb = *k; } else { nrowb = *n; } /* Test the input parameters. */ info = 0; if (! nota && ! conja && ! lsame_(transa, "T")) { info = 1; } else if (! notb && ! conjb && ! lsame_(transb, "T")) { info = 2; } else if (*m < 0) { info = 3; } else if (*n < 0) { info = 4; } else if (*k < 0) { info = 5; } else if (*lda < max(1,nrowa)) { info = 8; } else if (*ldb < max(1,nrowb)) { info = 10; } else if (*ldc < max(1,*m)) { info = 13; } if (info != 0) { xerbla_("ZGEMM ", &info); return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) && (beta->r == 1. && beta->i == 0.)) { return 0; } /* And when alpha.eq.zero. */ if (alpha->r == 0. && alpha->i == 0.) { if (beta->r == 0. && beta->i == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); c__[i__3].r = 0., c__[i__3].i = 0.; /* L10: */ } /* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, z__1.i = beta->r * c__[i__4].i + beta->i * c__[ i__4].r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L30: */ } /* L40: */ } } return 0; } /* Start the operations. */ if (notb) { if (nota) { /* Form C := alpha*A*B + beta*C. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { if (beta->r == 0. && beta->i == 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); c__[i__3].r = 0., c__[i__3].i = 0.; /* L50: */ } } else if (beta->r != 1. || beta->i != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] .i, z__1.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L60: */ } } i__2 = *k; for (l = 1; l <= i__2; ++l) { i__3 = b_subscr(l, j); if (b[i__3].r != 0. || b[i__3].i != 0.) { i__3 = b_subscr(l, j); z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, z__1.i = alpha->r * b[i__3].i + alpha->i * b[ i__3].r; temp.r = z__1.r, temp.i = z__1.i; i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = c___subscr(i__, j); i__5 = c___subscr(i__, j); i__6 = a_subscr(i__, l); z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, z__2.i = temp.r * a[i__6].i + temp.i * a[ i__6].r; z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5] .i + z__2.i; c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; /* L70: */ } } /* L80: */ } /* L90: */ } } else if (conja) { /* Form C := alpha*conjg( A' )*B + beta*C. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp.r = 0., temp.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { d_cnjg(&z__3, &a_ref(l, i__)); i__4 = b_subscr(l, j); z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] .r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L100: */ } if (beta->r == 0. && beta->i == 0.) { i__3 = c___subscr(i__, j); z__1.r = alpha->r * temp.r - alpha->i * temp.i, z__1.i = alpha->r * temp.i + alpha->i * temp.r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = c___subscr(i__, j); z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = alpha->r * temp.i + alpha->i * temp.r; i__4 = c___subscr(i__, j); z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] .i, z__3.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } /* L110: */ } /* L120: */ } } else { /* Form C := alpha*A'*B + beta*C */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp.r = 0., temp.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { i__4 = a_subscr(l, i__); i__5 = b_subscr(l, j); z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5] .i, z__2.i = a[i__4].r * b[i__5].i + a[i__4] .i * b[i__5].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L130: */ } if (beta->r == 0. && beta->i == 0.) { i__3 = c___subscr(i__, j); z__1.r = alpha->r * temp.r - alpha->i * temp.i, z__1.i = alpha->r * temp.i + alpha->i * temp.r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = c___subscr(i__, j); z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = alpha->r * temp.i + alpha->i * temp.r; i__4 = c___subscr(i__, j); z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] .i, z__3.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } /* L140: */ } /* L150: */ } } } else if (nota) { if (conjb) { /* Form C := alpha*A*conjg( B' ) + beta*C. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { if (beta->r == 0. && beta->i == 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); c__[i__3].r = 0., c__[i__3].i = 0.; /* L160: */ } } else if (beta->r != 1. || beta->i != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] .i, z__1.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L170: */ } } i__2 = *k; for (l = 1; l <= i__2; ++l) { i__3 = b_subscr(j, l); if (b[i__3].r != 0. || b[i__3].i != 0.) { d_cnjg(&z__2, &b_ref(j, l)); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = c___subscr(i__, j); i__5 = c___subscr(i__, j); i__6 = a_subscr(i__, l); z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, z__2.i = temp.r * a[i__6].i + temp.i * a[ i__6].r; z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5] .i + z__2.i; c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; /* L180: */ } } /* L190: */ } /* L200: */ } } else { /* Form C := alpha*A*B' + beta*C */ i__1 = *n; for (j = 1; j <= i__1; ++j) { if (beta->r == 0. && beta->i == 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); c__[i__3].r = 0., c__[i__3].i = 0.; /* L210: */ } } else if (beta->r != 1. || beta->i != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] .i, z__1.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L220: */ } } i__2 = *k; for (l = 1; l <= i__2; ++l) { i__3 = b_subscr(j, l); if (b[i__3].r != 0. || b[i__3].i != 0.) { i__3 = b_subscr(j, l); z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, z__1.i = alpha->r * b[i__3].i + alpha->i * b[ i__3].r; temp.r = z__1.r, temp.i = z__1.i; i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = c___subscr(i__, j); i__5 = c___subscr(i__, j); i__6 = a_subscr(i__, l); z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, z__2.i = temp.r * a[i__6].i + temp.i * a[ i__6].r; z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5] .i + z__2.i; c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; /* L230: */ } } /* L240: */ } /* L250: */ } } } else if (conja) { if (conjb) { /* Form C := alpha*conjg( A' )*conjg( B' ) + beta*C. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp.r = 0., temp.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { d_cnjg(&z__3, &a_ref(l, i__)); d_cnjg(&z__4, &b_ref(j, l)); z__2.r = z__3.r * z__4.r - z__3.i * z__4.i, z__2.i = z__3.r * z__4.i + z__3.i * z__4.r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L260: */ } if (beta->r == 0. && beta->i == 0.) { i__3 = c___subscr(i__, j); z__1.r = alpha->r * temp.r - alpha->i * temp.i, z__1.i = alpha->r * temp.i + alpha->i * temp.r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = c___subscr(i__, j); z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = alpha->r * temp.i + alpha->i * temp.r; i__4 = c___subscr(i__, j); z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] .i, z__3.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } /* L270: */ } /* L280: */ } } else { /* Form C := alpha*conjg( A' )*B' + beta*C */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp.r = 0., temp.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { d_cnjg(&z__3, &a_ref(l, i__)); i__4 = b_subscr(j, l); z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] .r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L290: */ } if (beta->r == 0. && beta->i == 0.) { i__3 = c___subscr(i__, j); z__1.r = alpha->r * temp.r - alpha->i * temp.i, z__1.i = alpha->r * temp.i + alpha->i * temp.r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = c___subscr(i__, j); z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = alpha->r * temp.i + alpha->i * temp.r; i__4 = c___subscr(i__, j); z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] .i, z__3.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } /* L300: */ } /* L310: */ } } } else { if (conjb) { /* Form C := alpha*A'*conjg( B' ) + beta*C */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp.r = 0., temp.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { i__4 = a_subscr(l, i__); d_cnjg(&z__3, &b_ref(j, l)); z__2.r = a[i__4].r * z__3.r - a[i__4].i * z__3.i, z__2.i = a[i__4].r * z__3.i + a[i__4].i * z__3.r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L320: */ } if (beta->r == 0. && beta->i == 0.) { i__3 = c___subscr(i__, j); z__1.r = alpha->r * temp.r - alpha->i * temp.i, z__1.i = alpha->r * temp.i + alpha->i * temp.r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = c___subscr(i__, j); z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = alpha->r * temp.i + alpha->i * temp.r; i__4 = c___subscr(i__, j); z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] .i, z__3.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } /* L330: */ } /* L340: */ } } else { /* Form C := alpha*A'*B' + beta*C */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp.r = 0., temp.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { i__4 = a_subscr(l, i__); i__5 = b_subscr(j, l); z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5] .i, z__2.i = a[i__4].r * b[i__5].i + a[i__4] .i * b[i__5].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L350: */ } if (beta->r == 0. && beta->i == 0.) { i__3 = c___subscr(i__, j); z__1.r = alpha->r * temp.r - alpha->i * temp.i, z__1.i = alpha->r * temp.i + alpha->i * temp.r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = c___subscr(i__, j); z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = alpha->r * temp.i + alpha->i * temp.r; i__4 = c___subscr(i__, j); z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] .i, z__3.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } /* L360: */ } /* L370: */ } } } return 0; /* End of ZGEMM . */ } /* zgemm_ */ #undef c___ref #undef c___subscr #undef b_ref #undef b_subscr #undef a_ref #undef a_subscr /* Subroutine */ int zgemv_(char *trans, integer *m, integer *n, doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * x, integer *incx, doublecomplex *beta, doublecomplex *y, integer * incy) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2, z__3; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static doublecomplex temp; static integer lenx, leny, i__, j; extern logical lsame_(char *, char *); static integer ix, iy, jx, jy, kx, ky; extern /* Subroutine */ int xerbla_(char *, integer *); static logical noconj; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] /* Purpose ======= ZGEMV performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix. Parameters ========== TRANS - CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*A'*x + beta*y. TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. Unchanged on exit. M - INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit. N - INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit. ALPHA - COMPLEX*16 . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ). Unchanged on exit. X - COMPLEX*16 array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x. Unchanged on exit. INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. BETA - COMPLEX*16 . On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit. Y - COMPLEX*16 array of DIMENSION at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. INCY - INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --x; --y; /* Function Body */ info = 0; if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C") ) { info = 1; } else if (*m < 0) { info = 2; } else if (*n < 0) { info = 3; } else if (*lda < max(1,*m)) { info = 6; } else if (*incx == 0) { info = 8; } else if (*incy == 0) { info = 11; } if (info != 0) { xerbla_("ZGEMV ", &info); return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && beta->i == 0.)) { return 0; } noconj = lsame_(trans, "T"); /* Set LENX and LENY, the lengths of the vectors x and y, and set up the start points in X and Y. */ if (lsame_(trans, "N")) { lenx = *n; leny = *m; } else { lenx = *m; leny = *n; } if (*incx > 0) { kx = 1; } else { kx = 1 - (lenx - 1) * *incx; } if (*incy > 0) { ky = 1; } else { ky = 1 - (leny - 1) * *incy; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through A. First form y := beta*y. */ if (beta->r != 1. || beta->i != 0.) { if (*incy == 1) { if (beta->r == 0. && beta->i == 0.) { i__1 = leny; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; y[i__2].r = 0., y[i__2].i = 0.; /* L10: */ } } else { i__1 = leny; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] .r; y[i__2].r = z__1.r, y[i__2].i = z__1.i; /* L20: */ } } } else { iy = ky; if (beta->r == 0. && beta->i == 0.) { i__1 = leny; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = iy; y[i__2].r = 0., y[i__2].i = 0.; iy += *incy; /* L30: */ } } else { i__1 = leny; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = iy; i__3 = iy; z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] .r; y[i__2].r = z__1.r, y[i__2].i = z__1.i; iy += *incy; /* L40: */ } } } } if (alpha->r == 0. && alpha->i == 0.) { return 0; } if (lsame_(trans, "N")) { /* Form y := alpha*A*x + y. */ jx = kx; if (*incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; if (x[i__2].r != 0. || x[i__2].i != 0.) { i__2 = jx; z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; temp.r = z__1.r, temp.i = z__1.i; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = a_subscr(i__, j); z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = temp.r * a[i__5].i + temp.i * a[i__5] .r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; /* L50: */ } } jx += *incx; /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; if (x[i__2].r != 0. || x[i__2].i != 0.) { i__2 = jx; z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; temp.r = z__1.r, temp.i = z__1.i; iy = ky; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = iy; i__4 = iy; i__5 = a_subscr(i__, j); z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = temp.r * a[i__5].i + temp.i * a[i__5] .r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; iy += *incy; /* L70: */ } } jx += *incx; /* L80: */ } } } else { /* Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. */ jy = ky; if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { temp.r = 0., temp.i = 0.; if (noconj) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); i__4 = i__; z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4] .i, z__2.i = a[i__3].r * x[i__4].i + a[i__3] .i * x[i__4].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L90: */ } } else { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { d_cnjg(&z__3, &a_ref(i__, j)); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3] .r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L100: */ } } i__2 = jy; i__3 = jy; z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = alpha->r * temp.i + alpha->i * temp.r; z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; jy += *incy; /* L110: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { temp.r = 0., temp.i = 0.; ix = kx; if (noconj) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); i__4 = ix; z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4] .i, z__2.i = a[i__3].r * x[i__4].i + a[i__3] .i * x[i__4].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix += *incx; /* L120: */ } } else { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { d_cnjg(&z__3, &a_ref(i__, j)); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3] .r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix += *incx; /* L130: */ } } i__2 = jy; i__3 = jy; z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = alpha->r * temp.i + alpha->i * temp.r; z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; jy += *incy; /* L140: */ } } } return 0; /* End of ZGEMV . */ } /* zgemv_ */ #undef a_ref #undef a_subscr /* Subroutine */ int zgerc_(integer *m, integer *n, doublecomplex *alpha, doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, doublecomplex *a, integer *lda) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static doublecomplex temp; static integer i__, j, ix, jy, kx; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] /* Purpose ======= ZGERC performs the rank 1 operation A := alpha*x*conjg( y' ) + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. Parameters ========== M - INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit. N - INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit. ALPHA - COMPLEX*16 . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. X - COMPLEX*16 array of dimension at least ( 1 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m element vector x. Unchanged on exit. INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. Y - COMPLEX*16 array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. Unchanged on exit. INCY - INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by the updated matrix. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ). Unchanged on exit. Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. Test the input parameters. Parameter adjustments */ --x; --y; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; /* Function Body */ info = 0; if (*m < 0) { info = 1; } else if (*n < 0) { info = 2; } else if (*incx == 0) { info = 5; } else if (*incy == 0) { info = 7; } else if (*lda < max(1,*m)) { info = 9; } if (info != 0) { xerbla_("ZGERC ", &info); return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0.) { return 0; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through A. */ if (*incy > 0) { jy = 1; } else { jy = 1 - (*n - 1) * *incy; } if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jy; if (y[i__2].r != 0. || y[i__2].i != 0.) { d_cnjg(&z__2, &y[jy]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); i__4 = a_subscr(i__, j); i__5 = i__; z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i = x[i__5].r * temp.i + x[i__5].i * temp.r; z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L10: */ } } jy += *incy; /* L20: */ } } else { if (*incx > 0) { kx = 1; } else { kx = 1 - (*m - 1) * *incx; } i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jy; if (y[i__2].r != 0. || y[i__2].i != 0.) { d_cnjg(&z__2, &y[jy]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; ix = kx; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); i__4 = a_subscr(i__, j); i__5 = ix; z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i = x[i__5].r * temp.i + x[i__5].i * temp.r; z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; ix += *incx; /* L30: */ } } jy += *incy; /* L40: */ } } return 0; /* End of ZGERC . */ } /* zgerc_ */ #undef a_ref #undef a_subscr /* Subroutine */ int zgeru_(integer *m, integer *n, doublecomplex *alpha, doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, doublecomplex *a, integer *lda) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2; /* Local variables */ static integer info; static doublecomplex temp; static integer i__, j, ix, jy, kx; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] /* Purpose ======= ZGERU performs the rank 1 operation A := alpha*x*y' + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. Parameters ========== M - INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit. N - INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit. ALPHA - COMPLEX*16 . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. X - COMPLEX*16 array of dimension at least ( 1 + ( m - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the m element vector x. Unchanged on exit. INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. Y - COMPLEX*16 array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. Unchanged on exit. INCY - INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. On exit, A is overwritten by the updated matrix. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ). Unchanged on exit. Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. Test the input parameters. Parameter adjustments */ --x; --y; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; /* Function Body */ info = 0; if (*m < 0) { info = 1; } else if (*n < 0) { info = 2; } else if (*incx == 0) { info = 5; } else if (*incy == 0) { info = 7; } else if (*lda < max(1,*m)) { info = 9; } if (info != 0) { xerbla_("ZGERU ", &info); return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0.) { return 0; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through A. */ if (*incy > 0) { jy = 1; } else { jy = 1 - (*n - 1) * *incy; } if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jy; if (y[i__2].r != 0. || y[i__2].i != 0.) { i__2 = jy; z__1.r = alpha->r * y[i__2].r - alpha->i * y[i__2].i, z__1.i = alpha->r * y[i__2].i + alpha->i * y[i__2].r; temp.r = z__1.r, temp.i = z__1.i; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); i__4 = a_subscr(i__, j); i__5 = i__; z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i = x[i__5].r * temp.i + x[i__5].i * temp.r; z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L10: */ } } jy += *incy; /* L20: */ } } else { if (*incx > 0) { kx = 1; } else { kx = 1 - (*m - 1) * *incx; } i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jy; if (y[i__2].r != 0. || y[i__2].i != 0.) { i__2 = jy; z__1.r = alpha->r * y[i__2].r - alpha->i * y[i__2].i, z__1.i = alpha->r * y[i__2].i + alpha->i * y[i__2].r; temp.r = z__1.r, temp.i = z__1.i; ix = kx; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); i__4 = a_subscr(i__, j); i__5 = ix; z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i = x[i__5].r * temp.i + x[i__5].i * temp.r; z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; ix += *incx; /* L30: */ } } jy += *incy; /* L40: */ } } return 0; /* End of ZGERU . */ } /* zgeru_ */ #undef a_ref #undef a_subscr /* Subroutine */ int zhemv_(char *uplo, integer *n, doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, doublecomplex *beta, doublecomplex *y, integer *incy) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublereal d__1; doublecomplex z__1, z__2, z__3, z__4; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static doublecomplex temp1, temp2; static integer i__, j; extern logical lsame_(char *, char *); static integer ix, iy, jx, jy, kx, ky; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] /* Purpose ======= ZHEMV performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian matrix. Parameters ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced. Unchanged on exit. N - INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. ALPHA - COMPLEX*16 . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). Unchanged on exit. X - COMPLEX*16 array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. Unchanged on exit. INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. BETA - COMPLEX*16 . On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit. Y - COMPLEX*16 array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. On exit, Y is overwritten by the updated vector y. INCY - INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --x; --y; /* Function Body */ info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { info = 1; } else if (*n < 0) { info = 2; } else if (*lda < max(1,*n)) { info = 5; } else if (*incx == 0) { info = 7; } else if (*incy == 0) { info = 10; } if (info != 0) { xerbla_("ZHEMV ", &info); return 0; } /* Quick return if possible. */ if (*n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && beta->i == 0.)) { return 0; } /* Set up the start points in X and Y. */ if (*incx > 0) { kx = 1; } else { kx = 1 - (*n - 1) * *incx; } if (*incy > 0) { ky = 1; } else { ky = 1 - (*n - 1) * *incy; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through the triangular part of A. First form y := beta*y. */ if (beta->r != 1. || beta->i != 0.) { if (*incy == 1) { if (beta->r == 0. && beta->i == 0.) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; y[i__2].r = 0., y[i__2].i = 0.; /* L10: */ } } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] .r; y[i__2].r = z__1.r, y[i__2].i = z__1.i; /* L20: */ } } } else { iy = ky; if (beta->r == 0. && beta->i == 0.) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = iy; y[i__2].r = 0., y[i__2].i = 0.; iy += *incy; /* L30: */ } } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = iy; i__3 = iy; z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] .r; y[i__2].r = z__1.r, y[i__2].i = z__1.i; iy += *incy; /* L40: */ } } } } if (alpha->r == 0. && alpha->i == 0.) { return 0; } if (lsame_(uplo, "U")) { /* Form y when A is stored in upper triangle. */ if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; temp1.r = z__1.r, temp1.i = z__1.i; temp2.r = 0., temp2.i = 0.; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = a_subscr(i__, j); z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] .r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; d_cnjg(&z__3, &a_ref(i__, j)); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; /* L50: */ } i__2 = j; i__3 = j; i__4 = a_subscr(j, j); d__1 = a[i__4].r; z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i; z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = alpha->r * temp2.i + alpha->i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; /* L60: */ } } else { jx = kx; jy = ky; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; temp1.r = z__1.r, temp1.i = z__1.i; temp2.r = 0., temp2.i = 0.; ix = kx; iy = ky; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = iy; i__4 = iy; i__5 = a_subscr(i__, j); z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] .r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; d_cnjg(&z__3, &a_ref(i__, j)); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; ix += *incx; iy += *incy; /* L70: */ } i__2 = jy; i__3 = jy; i__4 = a_subscr(j, j); d__1 = a[i__4].r; z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i; z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = alpha->r * temp2.i + alpha->i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; jx += *incx; jy += *incy; /* L80: */ } } } else { /* Form y when A is stored in lower triangle. */ if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; temp1.r = z__1.r, temp1.i = z__1.i; temp2.r = 0., temp2.i = 0.; i__2 = j; i__3 = j; i__4 = a_subscr(j, j); d__1 = a[i__4].r; z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i; z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = a_subscr(i__, j); z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] .r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; d_cnjg(&z__3, &a_ref(i__, j)); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; /* L90: */ } i__2 = j; i__3 = j; z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = alpha->r * temp2.i + alpha->i * temp2.r; z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; /* L100: */ } } else { jx = kx; jy = ky; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; temp1.r = z__1.r, temp1.i = z__1.i; temp2.r = 0., temp2.i = 0.; i__2 = jy; i__3 = jy; i__4 = a_subscr(j, j); d__1 = a[i__4].r; z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i; z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; ix = jx; iy = jy; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { ix += *incx; iy += *incy; i__3 = iy; i__4 = iy; i__5 = a_subscr(i__, j); z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] .r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; d_cnjg(&z__3, &a_ref(i__, j)); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; /* L110: */ } i__2 = jy; i__3 = jy; z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = alpha->r * temp2.i + alpha->i * temp2.r; z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; jx += *incx; jy += *incy; /* L120: */ } } } return 0; /* End of ZHEMV . */ } /* zhemv_ */ #undef a_ref #undef a_subscr /* Subroutine */ int zher2_(char *uplo, integer *n, doublecomplex *alpha, doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, doublecomplex *a, integer *lda) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublereal d__1; doublecomplex z__1, z__2, z__3, z__4; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static doublecomplex temp1, temp2; static integer i__, j; extern logical lsame_(char *, char *); static integer ix, iy, jx, jy, kx, ky; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] /* Purpose ======= ZHER2 performs the hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix. Parameters ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced. Unchanged on exit. N - INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. ALPHA - COMPLEX*16 . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. X - COMPLEX*16 array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. Unchanged on exit. INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. Y - COMPLEX*16 array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. Unchanged on exit. INCY - INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). Unchanged on exit. Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. Test the input parameters. Parameter adjustments */ --x; --y; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; /* Function Body */ info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { info = 1; } else if (*n < 0) { info = 2; } else if (*incx == 0) { info = 5; } else if (*incy == 0) { info = 7; } else if (*lda < max(1,*n)) { info = 9; } if (info != 0) { xerbla_("ZHER2 ", &info); return 0; } /* Quick return if possible. */ if (*n == 0 || alpha->r == 0. && alpha->i == 0.) { return 0; } /* Set up the start points in X and Y if the increments are not both unity. */ if (*incx != 1 || *incy != 1) { if (*incx > 0) { kx = 1; } else { kx = 1 - (*n - 1) * *incx; } if (*incy > 0) { ky = 1; } else { ky = 1 - (*n - 1) * *incy; } jx = kx; jy = ky; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through the triangular part of A. */ if (lsame_(uplo, "U")) { /* Form A when A is stored in the upper triangle. */ if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; i__3 = j; if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || y[i__3].i != 0.)) { d_cnjg(&z__2, &y[j]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; i__2 = j; z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; d_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); i__4 = a_subscr(i__, j); i__5 = i__; z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, z__3.i = x[i__5].r * temp1.i + x[i__5].i * temp1.r; z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + z__3.i; i__6 = i__; z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, z__4.i = y[i__6].r * temp2.i + y[i__6].i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L10: */ } i__2 = a_subscr(j, j); i__3 = a_subscr(j, j); i__4 = j; z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, z__2.i = x[i__4].r * temp1.i + x[i__4].i * temp1.r; i__5 = j; z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, z__3.i = y[i__5].r * temp2.i + y[i__5].i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = a[i__3].r + z__1.r; a[i__2].r = d__1, a[i__2].i = 0.; } else { i__2 = a_subscr(j, j); i__3 = a_subscr(j, j); d__1 = a[i__3].r; a[i__2].r = d__1, a[i__2].i = 0.; } /* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; i__3 = jy; if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || y[i__3].i != 0.)) { d_cnjg(&z__2, &y[jy]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; i__2 = jx; z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; d_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; ix = kx; iy = ky; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); i__4 = a_subscr(i__, j); i__5 = ix; z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, z__3.i = x[i__5].r * temp1.i + x[i__5].i * temp1.r; z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + z__3.i; i__6 = iy; z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, z__4.i = y[i__6].r * temp2.i + y[i__6].i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; ix += *incx; iy += *incy; /* L30: */ } i__2 = a_subscr(j, j); i__3 = a_subscr(j, j); i__4 = jx; z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, z__2.i = x[i__4].r * temp1.i + x[i__4].i * temp1.r; i__5 = jy; z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, z__3.i = y[i__5].r * temp2.i + y[i__5].i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = a[i__3].r + z__1.r; a[i__2].r = d__1, a[i__2].i = 0.; } else { i__2 = a_subscr(j, j); i__3 = a_subscr(j, j); d__1 = a[i__3].r; a[i__2].r = d__1, a[i__2].i = 0.; } jx += *incx; jy += *incy; /* L40: */ } } } else { /* Form A when A is stored in the lower triangle. */ if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; i__3 = j; if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || y[i__3].i != 0.)) { d_cnjg(&z__2, &y[j]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; i__2 = j; z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; d_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__2 = a_subscr(j, j); i__3 = a_subscr(j, j); i__4 = j; z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, z__2.i = x[i__4].r * temp1.i + x[i__4].i * temp1.r; i__5 = j; z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, z__3.i = y[i__5].r * temp2.i + y[i__5].i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = a[i__3].r + z__1.r; a[i__2].r = d__1, a[i__2].i = 0.; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); i__4 = a_subscr(i__, j); i__5 = i__; z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, z__3.i = x[i__5].r * temp1.i + x[i__5].i * temp1.r; z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + z__3.i; i__6 = i__; z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, z__4.i = y[i__6].r * temp2.i + y[i__6].i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L50: */ } } else { i__2 = a_subscr(j, j); i__3 = a_subscr(j, j); d__1 = a[i__3].r; a[i__2].r = d__1, a[i__2].i = 0.; } /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; i__3 = jy; if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || y[i__3].i != 0.)) { d_cnjg(&z__2, &y[jy]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; i__2 = jx; z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; d_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__2 = a_subscr(j, j); i__3 = a_subscr(j, j); i__4 = jx; z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, z__2.i = x[i__4].r * temp1.i + x[i__4].i * temp1.r; i__5 = jy; z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, z__3.i = y[i__5].r * temp2.i + y[i__5].i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = a[i__3].r + z__1.r; a[i__2].r = d__1, a[i__2].i = 0.; ix = jx; iy = jy; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { ix += *incx; iy += *incy; i__3 = a_subscr(i__, j); i__4 = a_subscr(i__, j); i__5 = ix; z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, z__3.i = x[i__5].r * temp1.i + x[i__5].i * temp1.r; z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + z__3.i; i__6 = iy; z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, z__4.i = y[i__6].r * temp2.i + y[i__6].i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L70: */ } } else { i__2 = a_subscr(j, j); i__3 = a_subscr(j, j); d__1 = a[i__3].r; a[i__2].r = d__1, a[i__2].i = 0.; } jx += *incx; jy += *incy; /* L80: */ } } } return 0; /* End of ZHER2 . */ } /* zher2_ */ #undef a_ref #undef a_subscr /* Subroutine */ int zher2k_(char *uplo, char *trans, integer *n, integer *k, doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * b, integer *ldb, doublereal *beta, doublecomplex *c__, integer *ldc) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7; doublereal d__1; doublecomplex z__1, z__2, z__3, z__4, z__5, z__6; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static doublecomplex temp1, temp2; static integer i__, j, l; extern logical lsame_(char *, char *); static integer nrowa; static logical upper; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] #define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1 #define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)] #define c___subscr(a_1,a_2) (a_2)*c_dim1 + a_1 #define c___ref(a_1,a_2) c__[c___subscr(a_1,a_2)] /* Purpose ======= ZHER2K performs one of the hermitian rank 2k operations C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C, or C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C, where alpha and beta are scalars with beta real, C is an n by n hermitian matrix and A and B are n by k matrices in the first case and k by n matrices in the second case. Parameters ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced. Unchanged on exit. TRANS - CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C. TRANS = 'C' or 'c' C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C. Unchanged on exit. N - INTEGER. On entry, N specifies the order of the matrix C. N must be at least zero. Unchanged on exit. K - INTEGER. On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'C' or 'c', K specifies the number of rows of the matrices A and B. K must be at least zero. Unchanged on exit. ALPHA - COMPLEX*16 . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ). Unchanged on exit. B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B. Unchanged on exit. LDB - INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k ). Unchanged on exit. BETA - DOUBLE PRECISION . On entry, BETA specifies the scalar beta. Unchanged on exit. C - COMPLEX*16 array of DIMENSION ( LDC, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. LDC - INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, n ). Unchanged on exit. Level 3 Blas routine. -- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd. -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. Ed Anderson, Cray Research Inc. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; /* Function Body */ if (lsame_(trans, "N")) { nrowa = *n; } else { nrowa = *k; } upper = lsame_(uplo, "U"); info = 0; if (! upper && ! lsame_(uplo, "L")) { info = 1; } else if (! lsame_(trans, "N") && ! lsame_(trans, "C")) { info = 2; } else if (*n < 0) { info = 3; } else if (*k < 0) { info = 4; } else if (*lda < max(1,nrowa)) { info = 7; } else if (*ldb < max(1,nrowa)) { info = 9; } else if (*ldc < max(1,*n)) { info = 12; } if (info != 0) { xerbla_("ZHER2K", &info); return 0; } /* Quick return if possible. */ if (*n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) && *beta == 1.) { return 0; } /* And when alpha.eq.zero. */ if (alpha->r == 0. && alpha->i == 0.) { if (upper) { if (*beta == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); c__[i__3].r = 0., c__[i__3].i = 0.; /* L10: */ } /* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ i__4].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L30: */ } i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = *beta * c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; /* L40: */ } } } else { if (*beta == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); c__[i__3].r = 0., c__[i__3].i = 0.; /* L50: */ } /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = *beta * c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ i__4].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L70: */ } /* L80: */ } } } return 0; } /* Start the operations. */ if (lsame_(trans, "N")) { /* Form C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + C. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); c__[i__3].r = 0., c__[i__3].i = 0.; /* L90: */ } } else if (*beta != 1.) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ i__4].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L100: */ } i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = *beta * c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; } else { i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; } i__2 = *k; for (l = 1; l <= i__2; ++l) { i__3 = a_subscr(j, l); i__4 = b_subscr(j, l); if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != 0. || b[i__4].i != 0.)) { d_cnjg(&z__2, &b_ref(j, l)); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; i__3 = a_subscr(j, l); z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, z__2.i = alpha->r * a[i__3].i + alpha->i * a[ i__3].r; d_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__3 = j - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = c___subscr(i__, j); i__5 = c___subscr(i__, j); i__6 = a_subscr(i__, l); z__3.r = a[i__6].r * temp1.r - a[i__6].i * temp1.i, z__3.i = a[i__6].r * temp1.i + a[ i__6].i * temp1.r; z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5] .i + z__3.i; i__7 = b_subscr(i__, l); z__4.r = b[i__7].r * temp2.r - b[i__7].i * temp2.i, z__4.i = b[i__7].r * temp2.i + b[ i__7].i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; /* L110: */ } i__3 = c___subscr(j, j); i__4 = c___subscr(j, j); i__5 = a_subscr(j, l); z__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i, z__2.i = a[i__5].r * temp1.i + a[i__5].i * temp1.r; i__6 = b_subscr(j, l); z__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i, z__3.i = b[i__6].r * temp2.i + b[i__6].i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = c__[i__4].r + z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } /* L120: */ } /* L130: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); c__[i__3].r = 0., c__[i__3].i = 0.; /* L140: */ } } else if (*beta != 1.) { i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ i__4].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L150: */ } i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = *beta * c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; } else { i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; } i__2 = *k; for (l = 1; l <= i__2; ++l) { i__3 = a_subscr(j, l); i__4 = b_subscr(j, l); if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != 0. || b[i__4].i != 0.)) { d_cnjg(&z__2, &b_ref(j, l)); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; i__3 = a_subscr(j, l); z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, z__2.i = alpha->r * a[i__3].i + alpha->i * a[ i__3].r; d_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__3 = *n; for (i__ = j + 1; i__ <= i__3; ++i__) { i__4 = c___subscr(i__, j); i__5 = c___subscr(i__, j); i__6 = a_subscr(i__, l); z__3.r = a[i__6].r * temp1.r - a[i__6].i * temp1.i, z__3.i = a[i__6].r * temp1.i + a[ i__6].i * temp1.r; z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5] .i + z__3.i; i__7 = b_subscr(i__, l); z__4.r = b[i__7].r * temp2.r - b[i__7].i * temp2.i, z__4.i = b[i__7].r * temp2.i + b[ i__7].i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; /* L160: */ } i__3 = c___subscr(j, j); i__4 = c___subscr(j, j); i__5 = a_subscr(j, l); z__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i, z__2.i = a[i__5].r * temp1.i + a[i__5].i * temp1.r; i__6 = b_subscr(j, l); z__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i, z__3.i = b[i__6].r * temp2.i + b[i__6].i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = c__[i__4].r + z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } /* L170: */ } /* L180: */ } } } else { /* Form C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + C. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { temp1.r = 0., temp1.i = 0.; temp2.r = 0., temp2.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { d_cnjg(&z__3, &a_ref(l, i__)); i__4 = b_subscr(l, j); z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] .r; z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i; temp1.r = z__1.r, temp1.i = z__1.i; d_cnjg(&z__3, &b_ref(l, i__)); i__4 = a_subscr(l, j); z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] .r; z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; /* L190: */ } if (i__ == j) { if (*beta == 0.) { i__3 = c___subscr(j, j); z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; d_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } else { i__3 = c___subscr(j, j); i__4 = c___subscr(j, j); z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; d_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = *beta * c__[i__4].r + z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } } else { if (*beta == 0.) { i__3 = c___subscr(i__, j); z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; d_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__3.r = *beta * c__[i__4].r, z__3.i = *beta * c__[i__4].i; z__4.r = alpha->r * temp1.r - alpha->i * temp1.i, z__4.i = alpha->r * temp1.i + alpha->i * temp1.r; z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + z__4.i; d_cnjg(&z__6, alpha); z__5.r = z__6.r * temp2.r - z__6.i * temp2.i, z__5.i = z__6.r * temp2.i + z__6.i * temp2.r; z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } } /* L200: */ } /* L210: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { temp1.r = 0., temp1.i = 0.; temp2.r = 0., temp2.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { d_cnjg(&z__3, &a_ref(l, i__)); i__4 = b_subscr(l, j); z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] .r; z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i; temp1.r = z__1.r, temp1.i = z__1.i; d_cnjg(&z__3, &b_ref(l, i__)); i__4 = a_subscr(l, j); z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] .r; z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; /* L220: */ } if (i__ == j) { if (*beta == 0.) { i__3 = c___subscr(j, j); z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; d_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } else { i__3 = c___subscr(j, j); i__4 = c___subscr(j, j); z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; d_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = *beta * c__[i__4].r + z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } } else { if (*beta == 0.) { i__3 = c___subscr(i__, j); z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; d_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__3.r = *beta * c__[i__4].r, z__3.i = *beta * c__[i__4].i; z__4.r = alpha->r * temp1.r - alpha->i * temp1.i, z__4.i = alpha->r * temp1.i + alpha->i * temp1.r; z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + z__4.i; d_cnjg(&z__6, alpha); z__5.r = z__6.r * temp2.r - z__6.i * temp2.i, z__5.i = z__6.r * temp2.i + z__6.i * temp2.r; z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } } /* L230: */ } /* L240: */ } } } return 0; /* End of ZHER2K. */ } /* zher2k_ */ #undef c___ref #undef c___subscr #undef b_ref #undef b_subscr #undef a_ref #undef a_subscr /* Subroutine */ int zscal_(integer *n, doublecomplex *za, doublecomplex *zx, integer *incx) { /* System generated locals */ integer i__1, i__2, i__3; doublecomplex z__1; /* Local variables */ static integer i__, ix; /* scales a vector by a constant. jack dongarra, 3/11/78. modified 3/93 to return if incx .le. 0. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --zx; /* Function Body */ if (*n <= 0 || *incx <= 0) { return 0; } if (*incx == 1) { goto L20; } /* code for increment not equal to 1 */ ix = 1; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = ix; i__3 = ix; z__1.r = za->r * zx[i__3].r - za->i * zx[i__3].i, z__1.i = za->r * zx[ i__3].i + za->i * zx[i__3].r; zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; ix += *incx; /* L10: */ } return 0; /* code for increment equal to 1 */ L20: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; z__1.r = za->r * zx[i__3].r - za->i * zx[i__3].i, z__1.i = za->r * zx[ i__3].i + za->i * zx[i__3].r; zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; /* L30: */ } return 0; } /* zscal_ */ /* Subroutine */ int zswap_(integer *n, doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy) { /* System generated locals */ integer i__1, i__2, i__3; /* Local variables */ static integer i__; static doublecomplex ztemp; static integer ix, iy; /* interchanges two vectors. jack dongarra, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) Parameter adjustments */ --zy; --zx; /* Function Body */ if (*n <= 0) { return 0; } if (*incx == 1 && *incy == 1) { goto L20; } /* code for unequal increments or equal increments not equal to 1 */ ix = 1; iy = 1; if (*incx < 0) { ix = (-(*n) + 1) * *incx + 1; } if (*incy < 0) { iy = (-(*n) + 1) * *incy + 1; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = ix; ztemp.r = zx[i__2].r, ztemp.i = zx[i__2].i; i__2 = ix; i__3 = iy; zx[i__2].r = zy[i__3].r, zx[i__2].i = zy[i__3].i; i__2 = iy; zy[i__2].r = ztemp.r, zy[i__2].i = ztemp.i; ix += *incx; iy += *incy; /* L10: */ } return 0; /* code for both increments equal to 1 */ L20: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; ztemp.r = zx[i__2].r, ztemp.i = zx[i__2].i; i__2 = i__; i__3 = i__; zx[i__2].r = zy[i__3].r, zx[i__2].i = zy[i__3].i; i__2 = i__; zy[i__2].r = ztemp.r, zy[i__2].i = ztemp.i; /* L30: */ } return 0; } /* zswap_ */ /* Subroutine */ int ztrmm_(char *side, char *uplo, char *transa, char *diag, integer *m, integer *n, doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublecomplex z__1, z__2, z__3; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static doublecomplex temp; static integer i__, j, k; static logical lside; extern logical lsame_(char *, char *); static integer nrowa; static logical upper; extern /* Subroutine */ int xerbla_(char *, integer *); static logical noconj, nounit; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] #define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1 #define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)] /* Purpose ======= ZTRMM performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ). Parameters ========== SIDE - CHARACTER*1. On entry, SIDE specifies whether op( A ) multiplies B from the left or right as follows: SIDE = 'L' or 'l' B := alpha*op( A )*B. SIDE = 'R' or 'r' B := alpha*B*op( A ). Unchanged on exit. UPLO - CHARACTER*1. On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. Unchanged on exit. TRANSA - CHARACTER*1. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n' op( A ) = A. TRANSA = 'T' or 't' op( A ) = A'. TRANSA = 'C' or 'c' op( A ) = conjg( A' ). Unchanged on exit. DIAG - CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. Unchanged on exit. M - INTEGER. On entry, M specifies the number of rows of B. M must be at least zero. Unchanged on exit. N - INTEGER. On entry, N specifies the number of columns of B. N must be at least zero. Unchanged on exit. ALPHA - COMPLEX*16 . On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, k ), where k is m when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ). Unchanged on exit. B - COMPLEX*16 array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the matrix B, and on exit is overwritten by the transformed matrix. LDB - INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ). Unchanged on exit. Level 3 Blas routine. -- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; /* Function Body */ lside = lsame_(side, "L"); if (lside) { nrowa = *m; } else { nrowa = *n; } noconj = lsame_(transa, "T"); nounit = lsame_(diag, "N"); upper = lsame_(uplo, "U"); info = 0; if (! lside && ! lsame_(side, "R")) { info = 1; } else if (! upper && ! lsame_(uplo, "L")) { info = 2; } else if (! lsame_(transa, "N") && ! lsame_(transa, "T") && ! lsame_(transa, "C")) { info = 3; } else if (! lsame_(diag, "U") && ! lsame_(diag, "N")) { info = 4; } else if (*m < 0) { info = 5; } else if (*n < 0) { info = 6; } else if (*lda < max(1,nrowa)) { info = 9; } else if (*ldb < max(1,*m)) { info = 11; } if (info != 0) { xerbla_("ZTRMM ", &info); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } /* And when alpha.eq.zero. */ if (alpha->r == 0. && alpha->i == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); b[i__3].r = 0., b[i__3].i = 0.; /* L10: */ } /* L20: */ } return 0; } /* Start the operations. */ if (lside) { if (lsame_(transa, "N")) { /* Form B := alpha*A*B. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (k = 1; k <= i__2; ++k) { i__3 = b_subscr(k, j); if (b[i__3].r != 0. || b[i__3].i != 0.) { i__3 = b_subscr(k, j); z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3] .i, z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3].r; temp.r = z__1.r, temp.i = z__1.i; i__3 = k - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = b_subscr(i__, j); i__5 = b_subscr(i__, j); i__6 = a_subscr(i__, k); z__2.r = temp.r * a[i__6].r - temp.i * a[i__6] .i, z__2.i = temp.r * a[i__6].i + temp.i * a[i__6].r; z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] .i + z__2.i; b[i__4].r = z__1.r, b[i__4].i = z__1.i; /* L30: */ } if (nounit) { i__3 = a_subscr(k, k); z__1.r = temp.r * a[i__3].r - temp.i * a[i__3] .i, z__1.i = temp.r * a[i__3].i + temp.i * a[i__3].r; temp.r = z__1.r, temp.i = z__1.i; } i__3 = b_subscr(k, j); b[i__3].r = temp.r, b[i__3].i = temp.i; } /* L40: */ } /* L50: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { for (k = *m; k >= 1; --k) { i__2 = b_subscr(k, j); if (b[i__2].r != 0. || b[i__2].i != 0.) { i__2 = b_subscr(k, j); z__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2] .i, z__1.i = alpha->r * b[i__2].i + alpha->i * b[i__2].r; temp.r = z__1.r, temp.i = z__1.i; i__2 = b_subscr(k, j); b[i__2].r = temp.r, b[i__2].i = temp.i; if (nounit) { i__2 = b_subscr(k, j); i__3 = b_subscr(k, j); i__4 = a_subscr(k, k); z__1.r = b[i__3].r * a[i__4].r - b[i__3].i * a[i__4].i, z__1.i = b[i__3].r * a[ i__4].i + b[i__3].i * a[i__4].r; b[i__2].r = z__1.r, b[i__2].i = z__1.i; } i__2 = *m; for (i__ = k + 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); i__4 = b_subscr(i__, j); i__5 = a_subscr(i__, k); z__2.r = temp.r * a[i__5].r - temp.i * a[i__5] .i, z__2.i = temp.r * a[i__5].i + temp.i * a[i__5].r; z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] .i + z__2.i; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L60: */ } } /* L70: */ } /* L80: */ } } } else { /* Form B := alpha*A'*B or B := alpha*conjg( A' )*B. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { for (i__ = *m; i__ >= 1; --i__) { i__2 = b_subscr(i__, j); temp.r = b[i__2].r, temp.i = b[i__2].i; if (noconj) { if (nounit) { i__2 = a_subscr(i__, i__); z__1.r = temp.r * a[i__2].r - temp.i * a[i__2] .i, z__1.i = temp.r * a[i__2].i + temp.i * a[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = i__ - 1; for (k = 1; k <= i__2; ++k) { i__3 = a_subscr(k, i__); i__4 = b_subscr(k, j); z__2.r = a[i__3].r * b[i__4].r - a[i__3].i * b[i__4].i, z__2.i = a[i__3].r * b[ i__4].i + a[i__3].i * b[i__4].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L90: */ } } else { if (nounit) { d_cnjg(&z__2, &a_ref(i__, i__)); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = i__ - 1; for (k = 1; k <= i__2; ++k) { d_cnjg(&z__3, &a_ref(k, i__)); i__3 = b_subscr(k, j); z__2.r = z__3.r * b[i__3].r - z__3.i * b[i__3] .i, z__2.i = z__3.r * b[i__3].i + z__3.i * b[i__3].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L100: */ } } i__2 = b_subscr(i__, j); z__1.r = alpha->r * temp.r - alpha->i * temp.i, z__1.i = alpha->r * temp.i + alpha->i * temp.r; b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L110: */ } /* L120: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); temp.r = b[i__3].r, temp.i = b[i__3].i; if (noconj) { if (nounit) { i__3 = a_subscr(i__, i__); z__1.r = temp.r * a[i__3].r - temp.i * a[i__3] .i, z__1.i = temp.r * a[i__3].i + temp.i * a[i__3].r; temp.r = z__1.r, temp.i = z__1.i; } i__3 = *m; for (k = i__ + 1; k <= i__3; ++k) { i__4 = a_subscr(k, i__); i__5 = b_subscr(k, j); z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5].i, z__2.i = a[i__4].r * b[ i__5].i + a[i__4].i * b[i__5].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L130: */ } } else { if (nounit) { d_cnjg(&z__2, &a_ref(i__, i__)); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__3 = *m; for (k = i__ + 1; k <= i__3; ++k) { d_cnjg(&z__3, &a_ref(k, i__)); i__4 = b_subscr(k, j); z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4] .i, z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L140: */ } } i__3 = b_subscr(i__, j); z__1.r = alpha->r * temp.r - alpha->i * temp.i, z__1.i = alpha->r * temp.i + alpha->i * temp.r; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L150: */ } /* L160: */ } } } } else { if (lsame_(transa, "N")) { /* Form B := alpha*B*A. */ if (upper) { for (j = *n; j >= 1; --j) { temp.r = alpha->r, temp.i = alpha->i; if (nounit) { i__1 = a_subscr(j, j); z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, z__1.i = temp.r * a[i__1].i + temp.i * a[i__1] .r; temp.r = z__1.r, temp.i = z__1.i; } i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = b_subscr(i__, j); i__3 = b_subscr(i__, j); z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, z__1.i = temp.r * b[i__3].i + temp.i * b[i__3] .r; b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L170: */ } i__1 = j - 1; for (k = 1; k <= i__1; ++k) { i__2 = a_subscr(k, j); if (a[i__2].r != 0. || a[i__2].i != 0.) { i__2 = a_subscr(k, j); z__1.r = alpha->r * a[i__2].r - alpha->i * a[i__2] .i, z__1.i = alpha->r * a[i__2].i + alpha->i * a[i__2].r; temp.r = z__1.r, temp.i = z__1.i; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); i__4 = b_subscr(i__, j); i__5 = b_subscr(i__, k); z__2.r = temp.r * b[i__5].r - temp.i * b[i__5] .i, z__2.i = temp.r * b[i__5].i + temp.i * b[i__5].r; z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] .i + z__2.i; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L180: */ } } /* L190: */ } /* L200: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { temp.r = alpha->r, temp.i = alpha->i; if (nounit) { i__2 = a_subscr(j, j); z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, z__1.i = temp.r * a[i__2].i + temp.i * a[i__2] .r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); i__4 = b_subscr(i__, j); z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, z__1.i = temp.r * b[i__4].i + temp.i * b[i__4] .r; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L210: */ } i__2 = *n; for (k = j + 1; k <= i__2; ++k) { i__3 = a_subscr(k, j); if (a[i__3].r != 0. || a[i__3].i != 0.) { i__3 = a_subscr(k, j); z__1.r = alpha->r * a[i__3].r - alpha->i * a[i__3] .i, z__1.i = alpha->r * a[i__3].i + alpha->i * a[i__3].r; temp.r = z__1.r, temp.i = z__1.i; i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = b_subscr(i__, j); i__5 = b_subscr(i__, j); i__6 = b_subscr(i__, k); z__2.r = temp.r * b[i__6].r - temp.i * b[i__6] .i, z__2.i = temp.r * b[i__6].i + temp.i * b[i__6].r; z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] .i + z__2.i; b[i__4].r = z__1.r, b[i__4].i = z__1.i; /* L220: */ } } /* L230: */ } /* L240: */ } } } else { /* Form B := alpha*B*A' or B := alpha*B*conjg( A' ). */ if (upper) { i__1 = *n; for (k = 1; k <= i__1; ++k) { i__2 = k - 1; for (j = 1; j <= i__2; ++j) { i__3 = a_subscr(j, k); if (a[i__3].r != 0. || a[i__3].i != 0.) { if (noconj) { i__3 = a_subscr(j, k); z__1.r = alpha->r * a[i__3].r - alpha->i * a[ i__3].i, z__1.i = alpha->r * a[i__3] .i + alpha->i * a[i__3].r; temp.r = z__1.r, temp.i = z__1.i; } else { d_cnjg(&z__2, &a_ref(j, k)); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = b_subscr(i__, j); i__5 = b_subscr(i__, j); i__6 = b_subscr(i__, k); z__2.r = temp.r * b[i__6].r - temp.i * b[i__6] .i, z__2.i = temp.r * b[i__6].i + temp.i * b[i__6].r; z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] .i + z__2.i; b[i__4].r = z__1.r, b[i__4].i = z__1.i; /* L250: */ } } /* L260: */ } temp.r = alpha->r, temp.i = alpha->i; if (nounit) { if (noconj) { i__2 = a_subscr(k, k); z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, z__1.i = temp.r * a[i__2].i + temp.i * a[ i__2].r; temp.r = z__1.r, temp.i = z__1.i; } else { d_cnjg(&z__2, &a_ref(k, k)); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } } if (temp.r != 1. || temp.i != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, k); i__4 = b_subscr(i__, k); z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, z__1.i = temp.r * b[i__4].i + temp.i * b[ i__4].r; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L270: */ } } /* L280: */ } } else { for (k = *n; k >= 1; --k) { i__1 = *n; for (j = k + 1; j <= i__1; ++j) { i__2 = a_subscr(j, k); if (a[i__2].r != 0. || a[i__2].i != 0.) { if (noconj) { i__2 = a_subscr(j, k); z__1.r = alpha->r * a[i__2].r - alpha->i * a[ i__2].i, z__1.i = alpha->r * a[i__2] .i + alpha->i * a[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } else { d_cnjg(&z__2, &a_ref(j, k)); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); i__4 = b_subscr(i__, j); i__5 = b_subscr(i__, k); z__2.r = temp.r * b[i__5].r - temp.i * b[i__5] .i, z__2.i = temp.r * b[i__5].i + temp.i * b[i__5].r; z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] .i + z__2.i; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L290: */ } } /* L300: */ } temp.r = alpha->r, temp.i = alpha->i; if (nounit) { if (noconj) { i__1 = a_subscr(k, k); z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, z__1.i = temp.r * a[i__1].i + temp.i * a[ i__1].r; temp.r = z__1.r, temp.i = z__1.i; } else { d_cnjg(&z__2, &a_ref(k, k)); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } } if (temp.r != 1. || temp.i != 0.) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = b_subscr(i__, k); i__3 = b_subscr(i__, k); z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, z__1.i = temp.r * b[i__3].i + temp.i * b[ i__3].r; b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L310: */ } } /* L320: */ } } } } return 0; /* End of ZTRMM . */ } /* ztrmm_ */ #undef b_ref #undef b_subscr #undef a_ref #undef a_subscr /* Subroutine */ int ztrmv_(char *uplo, char *trans, char *diag, integer *n, doublecomplex *a, integer *lda, doublecomplex *x, integer *incx) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2, z__3; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static doublecomplex temp; static integer i__, j; extern logical lsame_(char *, char *); static integer ix, jx, kx; extern /* Subroutine */ int xerbla_(char *, integer *); static logical noconj, nounit; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] /* Purpose ======= ZTRMV performs one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix. Parameters ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. Unchanged on exit. TRANS - CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' x := A*x. TRANS = 'T' or 't' x := A'*x. TRANS = 'C' or 'c' x := conjg( A' )*x. Unchanged on exit. DIAG - CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. Unchanged on exit. N - INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). Unchanged on exit. X - COMPLEX*16 array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the tranformed vector x. INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --x; /* Function Body */ info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { info = 1; } else if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")) { info = 2; } else if (! lsame_(diag, "U") && ! lsame_(diag, "N")) { info = 3; } else if (*n < 0) { info = 4; } else if (*lda < max(1,*n)) { info = 6; } else if (*incx == 0) { info = 8; } if (info != 0) { xerbla_("ZTRMV ", &info); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } noconj = lsame_(trans, "T"); nounit = lsame_(diag, "N"); /* Set up the start point in X if the increment is not unity. This will be ( N - 1 )*INCX too small for descending loops. */ if (*incx <= 0) { kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { kx = 1; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through A. */ if (lsame_(trans, "N")) { /* Form x := A*x. */ if (lsame_(uplo, "U")) { if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; if (x[i__2].r != 0. || x[i__2].i != 0.) { i__2 = j; temp.r = x[i__2].r, temp.i = x[i__2].i; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = a_subscr(i__, j); z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = temp.r * a[i__5].i + temp.i * a[ i__5].r; z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + z__2.i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; /* L10: */ } if (nounit) { i__2 = j; i__3 = j; i__4 = a_subscr(j, j); z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[ i__4].i, z__1.i = x[i__3].r * a[i__4].i + x[i__3].i * a[i__4].r; x[i__2].r = z__1.r, x[i__2].i = z__1.i; } } /* L20: */ } } else { jx = kx; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; if (x[i__2].r != 0. || x[i__2].i != 0.) { i__2 = jx; temp.r = x[i__2].r, temp.i = x[i__2].i; ix = kx; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = ix; i__4 = ix; i__5 = a_subscr(i__, j); z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = temp.r * a[i__5].i + temp.i * a[ i__5].r; z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + z__2.i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; ix += *incx; /* L30: */ } if (nounit) { i__2 = jx; i__3 = jx; i__4 = a_subscr(j, j); z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[ i__4].i, z__1.i = x[i__3].r * a[i__4].i + x[i__3].i * a[i__4].r; x[i__2].r = z__1.r, x[i__2].i = z__1.i; } } jx += *incx; /* L40: */ } } } else { if (*incx == 1) { for (j = *n; j >= 1; --j) { i__1 = j; if (x[i__1].r != 0. || x[i__1].i != 0.) { i__1 = j; temp.r = x[i__1].r, temp.i = x[i__1].i; i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { i__2 = i__; i__3 = i__; i__4 = a_subscr(i__, j); z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i, z__2.i = temp.r * a[i__4].i + temp.i * a[ i__4].r; z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + z__2.i; x[i__2].r = z__1.r, x[i__2].i = z__1.i; /* L50: */ } if (nounit) { i__1 = j; i__2 = j; i__3 = a_subscr(j, j); z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[ i__3].i, z__1.i = x[i__2].r * a[i__3].i + x[i__2].i * a[i__3].r; x[i__1].r = z__1.r, x[i__1].i = z__1.i; } } /* L60: */ } } else { kx += (*n - 1) * *incx; jx = kx; for (j = *n; j >= 1; --j) { i__1 = jx; if (x[i__1].r != 0. || x[i__1].i != 0.) { i__1 = jx; temp.r = x[i__1].r, temp.i = x[i__1].i; ix = kx; i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { i__2 = ix; i__3 = ix; i__4 = a_subscr(i__, j); z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i, z__2.i = temp.r * a[i__4].i + temp.i * a[ i__4].r; z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + z__2.i; x[i__2].r = z__1.r, x[i__2].i = z__1.i; ix -= *incx; /* L70: */ } if (nounit) { i__1 = jx; i__2 = jx; i__3 = a_subscr(j, j); z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[ i__3].i, z__1.i = x[i__2].r * a[i__3].i + x[i__2].i * a[i__3].r; x[i__1].r = z__1.r, x[i__1].i = z__1.i; } } jx -= *incx; /* L80: */ } } } } else { /* Form x := A'*x or x := conjg( A' )*x. */ if (lsame_(uplo, "U")) { if (*incx == 1) { for (j = *n; j >= 1; --j) { i__1 = j; temp.r = x[i__1].r, temp.i = x[i__1].i; if (noconj) { if (nounit) { i__1 = a_subscr(j, j); z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, z__1.i = temp.r * a[i__1].i + temp.i * a[ i__1].r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { i__1 = a_subscr(i__, j); i__2 = i__; z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[ i__2].i, z__2.i = a[i__1].r * x[i__2].i + a[i__1].i * x[i__2].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L90: */ } } else { if (nounit) { d_cnjg(&z__2, &a_ref(j, j)); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { d_cnjg(&z__3, &a_ref(i__, j)); i__1 = i__; z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, z__2.i = z__3.r * x[i__1].i + z__3.i * x[ i__1].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L100: */ } } i__1 = j; x[i__1].r = temp.r, x[i__1].i = temp.i; /* L110: */ } } else { jx = kx + (*n - 1) * *incx; for (j = *n; j >= 1; --j) { i__1 = jx; temp.r = x[i__1].r, temp.i = x[i__1].i; ix = jx; if (noconj) { if (nounit) { i__1 = a_subscr(j, j); z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, z__1.i = temp.r * a[i__1].i + temp.i * a[ i__1].r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { ix -= *incx; i__1 = a_subscr(i__, j); i__2 = ix; z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[ i__2].i, z__2.i = a[i__1].r * x[i__2].i + a[i__1].i * x[i__2].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L120: */ } } else { if (nounit) { d_cnjg(&z__2, &a_ref(j, j)); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { ix -= *incx; d_cnjg(&z__3, &a_ref(i__, j)); i__1 = ix; z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, z__2.i = z__3.r * x[i__1].i + z__3.i * x[ i__1].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L130: */ } } i__1 = jx; x[i__1].r = temp.r, x[i__1].i = temp.i; jx -= *incx; /* L140: */ } } } else { if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; temp.r = x[i__2].r, temp.i = x[i__2].i; if (noconj) { if (nounit) { i__2 = a_subscr(j, j); z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, z__1.i = temp.r * a[i__2].i + temp.i * a[ i__2].r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); i__4 = i__; z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ i__4].i, z__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[i__4].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L150: */ } } else { if (nounit) { d_cnjg(&z__2, &a_ref(j, j)); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { d_cnjg(&z__3, &a_ref(i__, j)); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[ i__3].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L160: */ } } i__2 = j; x[i__2].r = temp.r, x[i__2].i = temp.i; /* L170: */ } } else { jx = kx; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; temp.r = x[i__2].r, temp.i = x[i__2].i; ix = jx; if (noconj) { if (nounit) { i__2 = a_subscr(j, j); z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, z__1.i = temp.r * a[i__2].i + temp.i * a[ i__2].r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { ix += *incx; i__3 = a_subscr(i__, j); i__4 = ix; z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ i__4].i, z__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[i__4].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L180: */ } } else { if (nounit) { d_cnjg(&z__2, &a_ref(j, j)); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { ix += *incx; d_cnjg(&z__3, &a_ref(i__, j)); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[ i__3].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L190: */ } } i__2 = jx; x[i__2].r = temp.r, x[i__2].i = temp.i; jx += *incx; /* L200: */ } } } } return 0; /* End of ZTRMV . */ } /* ztrmv_ */ #undef a_ref #undef a_subscr /* Subroutine */ int ztrsm_(char *side, char *uplo, char *transa, char *diag, integer *m, integer *n, doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb) { /* Table of constant values */ static doublecomplex c_b1 = {1.,0.}; /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7; doublecomplex z__1, z__2, z__3; /* Builtin functions */ void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg( doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static doublecomplex temp; static integer i__, j, k; static logical lside; extern logical lsame_(char *, char *); static integer nrowa; static logical upper; extern /* Subroutine */ int xerbla_(char *, integer *); static logical noconj, nounit; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] #define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1 #define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)] /* Purpose ======= ZTRSM solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ). The matrix X is overwritten on B. Parameters ========== SIDE - CHARACTER*1. On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = 'L' or 'l' op( A )*X = alpha*B. SIDE = 'R' or 'r' X*op( A ) = alpha*B. Unchanged on exit. UPLO - CHARACTER*1. On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. Unchanged on exit. TRANSA - CHARACTER*1. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n' op( A ) = A. TRANSA = 'T' or 't' op( A ) = A'. TRANSA = 'C' or 'c' op( A ) = conjg( A' ). Unchanged on exit. DIAG - CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. Unchanged on exit. M - INTEGER. On entry, M specifies the number of rows of B. M must be at least zero. Unchanged on exit. N - INTEGER. On entry, N specifies the number of columns of B. N must be at least zero. Unchanged on exit. ALPHA - COMPLEX*16 . On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, k ), where k is m when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ). Unchanged on exit. B - COMPLEX*16 array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X. LDB - INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ). Unchanged on exit. Level 3 Blas routine. -- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; /* Function Body */ lside = lsame_(side, "L"); if (lside) { nrowa = *m; } else { nrowa = *n; } noconj = lsame_(transa, "T"); nounit = lsame_(diag, "N"); upper = lsame_(uplo, "U"); info = 0; if (! lside && ! lsame_(side, "R")) { info = 1; } else if (! upper && ! lsame_(uplo, "L")) { info = 2; } else if (! lsame_(transa, "N") && ! lsame_(transa, "T") && ! lsame_(transa, "C")) { info = 3; } else if (! lsame_(diag, "U") && ! lsame_(diag, "N")) { info = 4; } else if (*m < 0) { info = 5; } else if (*n < 0) { info = 6; } else if (*lda < max(1,nrowa)) { info = 9; } else if (*ldb < max(1,*m)) { info = 11; } if (info != 0) { xerbla_("ZTRSM ", &info); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } /* And when alpha.eq.zero. */ if (alpha->r == 0. && alpha->i == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); b[i__3].r = 0., b[i__3].i = 0.; /* L10: */ } /* L20: */ } return 0; } /* Start the operations. */ if (lside) { if (lsame_(transa, "N")) { /* Form B := alpha*inv( A )*B. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (alpha->r != 1. || alpha->i != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); i__4 = b_subscr(i__, j); z__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4] .i, z__1.i = alpha->r * b[i__4].i + alpha->i * b[i__4].r; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L30: */ } } for (k = *m; k >= 1; --k) { i__2 = b_subscr(k, j); if (b[i__2].r != 0. || b[i__2].i != 0.) { if (nounit) { i__2 = b_subscr(k, j); z_div(&z__1, &b_ref(k, j), &a_ref(k, k)); b[i__2].r = z__1.r, b[i__2].i = z__1.i; } i__2 = k - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); i__4 = b_subscr(i__, j); i__5 = b_subscr(k, j); i__6 = a_subscr(i__, k); z__2.r = b[i__5].r * a[i__6].r - b[i__5].i * a[i__6].i, z__2.i = b[i__5].r * a[ i__6].i + b[i__5].i * a[i__6].r; z__1.r = b[i__4].r - z__2.r, z__1.i = b[i__4] .i - z__2.i; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L40: */ } } /* L50: */ } /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (alpha->r != 1. || alpha->i != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); i__4 = b_subscr(i__, j); z__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4] .i, z__1.i = alpha->r * b[i__4].i + alpha->i * b[i__4].r; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L70: */ } } i__2 = *m; for (k = 1; k <= i__2; ++k) { i__3 = b_subscr(k, j); if (b[i__3].r != 0. || b[i__3].i != 0.) { if (nounit) { i__3 = b_subscr(k, j); z_div(&z__1, &b_ref(k, j), &a_ref(k, k)); b[i__3].r = z__1.r, b[i__3].i = z__1.i; } i__3 = *m; for (i__ = k + 1; i__ <= i__3; ++i__) { i__4 = b_subscr(i__, j); i__5 = b_subscr(i__, j); i__6 = b_subscr(k, j); i__7 = a_subscr(i__, k); z__2.r = b[i__6].r * a[i__7].r - b[i__6].i * a[i__7].i, z__2.i = b[i__6].r * a[ i__7].i + b[i__6].i * a[i__7].r; z__1.r = b[i__5].r - z__2.r, z__1.i = b[i__5] .i - z__2.i; b[i__4].r = z__1.r, b[i__4].i = z__1.i; /* L80: */ } } /* L90: */ } /* L100: */ } } } else { /* Form B := alpha*inv( A' )*B or B := alpha*inv( conjg( A' ) )*B. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, z__1.i = alpha->r * b[i__3].i + alpha->i * b[ i__3].r; temp.r = z__1.r, temp.i = z__1.i; if (noconj) { i__3 = i__ - 1; for (k = 1; k <= i__3; ++k) { i__4 = a_subscr(k, i__); i__5 = b_subscr(k, j); z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5].i, z__2.i = a[i__4].r * b[ i__5].i + a[i__4].i * b[i__5].r; z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L110: */ } if (nounit) { z_div(&z__1, &temp, &a_ref(i__, i__)); temp.r = z__1.r, temp.i = z__1.i; } } else { i__3 = i__ - 1; for (k = 1; k <= i__3; ++k) { d_cnjg(&z__3, &a_ref(k, i__)); i__4 = b_subscr(k, j); z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4] .i, z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4].r; z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L120: */ } if (nounit) { d_cnjg(&z__2, &a_ref(i__, i__)); z_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } i__3 = b_subscr(i__, j); b[i__3].r = temp.r, b[i__3].i = temp.i; /* L130: */ } /* L140: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { for (i__ = *m; i__ >= 1; --i__) { i__2 = b_subscr(i__, j); z__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2].i, z__1.i = alpha->r * b[i__2].i + alpha->i * b[ i__2].r; temp.r = z__1.r, temp.i = z__1.i; if (noconj) { i__2 = *m; for (k = i__ + 1; k <= i__2; ++k) { i__3 = a_subscr(k, i__); i__4 = b_subscr(k, j); z__2.r = a[i__3].r * b[i__4].r - a[i__3].i * b[i__4].i, z__2.i = a[i__3].r * b[ i__4].i + a[i__3].i * b[i__4].r; z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L150: */ } if (nounit) { z_div(&z__1, &temp, &a_ref(i__, i__)); temp.r = z__1.r, temp.i = z__1.i; } } else { i__2 = *m; for (k = i__ + 1; k <= i__2; ++k) { d_cnjg(&z__3, &a_ref(k, i__)); i__3 = b_subscr(k, j); z__2.r = z__3.r * b[i__3].r - z__3.i * b[i__3] .i, z__2.i = z__3.r * b[i__3].i + z__3.i * b[i__3].r; z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L160: */ } if (nounit) { d_cnjg(&z__2, &a_ref(i__, i__)); z_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } i__2 = b_subscr(i__, j); b[i__2].r = temp.r, b[i__2].i = temp.i; /* L170: */ } /* L180: */ } } } } else { if (lsame_(transa, "N")) { /* Form B := alpha*B*inv( A ). */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (alpha->r != 1. || alpha->i != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); i__4 = b_subscr(i__, j); z__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4] .i, z__1.i = alpha->r * b[i__4].i + alpha->i * b[i__4].r; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L190: */ } } i__2 = j - 1; for (k = 1; k <= i__2; ++k) { i__3 = a_subscr(k, j); if (a[i__3].r != 0. || a[i__3].i != 0.) { i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = b_subscr(i__, j); i__5 = b_subscr(i__, j); i__6 = a_subscr(k, j); i__7 = b_subscr(i__, k); z__2.r = a[i__6].r * b[i__7].r - a[i__6].i * b[i__7].i, z__2.i = a[i__6].r * b[ i__7].i + a[i__6].i * b[i__7].r; z__1.r = b[i__5].r - z__2.r, z__1.i = b[i__5] .i - z__2.i; b[i__4].r = z__1.r, b[i__4].i = z__1.i; /* L200: */ } } /* L210: */ } if (nounit) { z_div(&z__1, &c_b1, &a_ref(j, j)); temp.r = z__1.r, temp.i = z__1.i; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); i__4 = b_subscr(i__, j); z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, z__1.i = temp.r * b[i__4].i + temp.i * b[ i__4].r; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L220: */ } } /* L230: */ } } else { for (j = *n; j >= 1; --j) { if (alpha->r != 1. || alpha->i != 0.) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = b_subscr(i__, j); i__3 = b_subscr(i__, j); z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3] .i, z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3].r; b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L240: */ } } i__1 = *n; for (k = j + 1; k <= i__1; ++k) { i__2 = a_subscr(k, j); if (a[i__2].r != 0. || a[i__2].i != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); i__4 = b_subscr(i__, j); i__5 = a_subscr(k, j); i__6 = b_subscr(i__, k); z__2.r = a[i__5].r * b[i__6].r - a[i__5].i * b[i__6].i, z__2.i = a[i__5].r * b[ i__6].i + a[i__5].i * b[i__6].r; z__1.r = b[i__4].r - z__2.r, z__1.i = b[i__4] .i - z__2.i; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L250: */ } } /* L260: */ } if (nounit) { z_div(&z__1, &c_b1, &a_ref(j, j)); temp.r = z__1.r, temp.i = z__1.i; i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = b_subscr(i__, j); i__3 = b_subscr(i__, j); z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, z__1.i = temp.r * b[i__3].i + temp.i * b[ i__3].r; b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L270: */ } } /* L280: */ } } } else { /* Form B := alpha*B*inv( A' ) or B := alpha*B*inv( conjg( A' ) ). */ if (upper) { for (k = *n; k >= 1; --k) { if (nounit) { if (noconj) { z_div(&z__1, &c_b1, &a_ref(k, k)); temp.r = z__1.r, temp.i = z__1.i; } else { d_cnjg(&z__2, &a_ref(k, k)); z_div(&z__1, &c_b1, &z__2); temp.r = z__1.r, temp.i = z__1.i; } i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = b_subscr(i__, k); i__3 = b_subscr(i__, k); z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, z__1.i = temp.r * b[i__3].i + temp.i * b[ i__3].r; b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L290: */ } } i__1 = k - 1; for (j = 1; j <= i__1; ++j) { i__2 = a_subscr(j, k); if (a[i__2].r != 0. || a[i__2].i != 0.) { if (noconj) { i__2 = a_subscr(j, k); temp.r = a[i__2].r, temp.i = a[i__2].i; } else { d_cnjg(&z__1, &a_ref(j, k)); temp.r = z__1.r, temp.i = z__1.i; } i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, j); i__4 = b_subscr(i__, j); i__5 = b_subscr(i__, k); z__2.r = temp.r * b[i__5].r - temp.i * b[i__5] .i, z__2.i = temp.r * b[i__5].i + temp.i * b[i__5].r; z__1.r = b[i__4].r - z__2.r, z__1.i = b[i__4] .i - z__2.i; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L300: */ } } /* L310: */ } if (alpha->r != 1. || alpha->i != 0.) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = b_subscr(i__, k); i__3 = b_subscr(i__, k); z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3] .i, z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3].r; b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L320: */ } } /* L330: */ } } else { i__1 = *n; for (k = 1; k <= i__1; ++k) { if (nounit) { if (noconj) { z_div(&z__1, &c_b1, &a_ref(k, k)); temp.r = z__1.r, temp.i = z__1.i; } else { d_cnjg(&z__2, &a_ref(k, k)); z_div(&z__1, &c_b1, &z__2); temp.r = z__1.r, temp.i = z__1.i; } i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, k); i__4 = b_subscr(i__, k); z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, z__1.i = temp.r * b[i__4].i + temp.i * b[ i__4].r; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L340: */ } } i__2 = *n; for (j = k + 1; j <= i__2; ++j) { i__3 = a_subscr(j, k); if (a[i__3].r != 0. || a[i__3].i != 0.) { if (noconj) { i__3 = a_subscr(j, k); temp.r = a[i__3].r, temp.i = a[i__3].i; } else { d_cnjg(&z__1, &a_ref(j, k)); temp.r = z__1.r, temp.i = z__1.i; } i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = b_subscr(i__, j); i__5 = b_subscr(i__, j); i__6 = b_subscr(i__, k); z__2.r = temp.r * b[i__6].r - temp.i * b[i__6] .i, z__2.i = temp.r * b[i__6].i + temp.i * b[i__6].r; z__1.r = b[i__5].r - z__2.r, z__1.i = b[i__5] .i - z__2.i; b[i__4].r = z__1.r, b[i__4].i = z__1.i; /* L350: */ } } /* L360: */ } if (alpha->r != 1. || alpha->i != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = b_subscr(i__, k); i__4 = b_subscr(i__, k); z__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4] .i, z__1.i = alpha->r * b[i__4].i + alpha->i * b[i__4].r; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L370: */ } } /* L380: */ } } } } return 0; /* End of ZTRSM . */ } /* ztrsm_ */ #undef b_ref #undef b_subscr #undef a_ref #undef a_subscr /* Subroutine */ int ztrsv_(char *uplo, char *trans, char *diag, integer *n, doublecomplex *a, integer *lda, doublecomplex *x, integer *incx) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2, z__3; /* Builtin functions */ void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg( doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static doublecomplex temp; static integer i__, j; extern logical lsame_(char *, char *); static integer ix, jx, kx; extern /* Subroutine */ int xerbla_(char *, integer *); static logical noconj, nounit; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] /* Purpose ======= ZTRSV solves one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. Parameters ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. Unchanged on exit. TRANS - CHARACTER*1. On entry, TRANS specifies the equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' A'*x = b. TRANS = 'C' or 'c' conjg( A' )*x = b. Unchanged on exit. DIAG - CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. Unchanged on exit. N - INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). Unchanged on exit. X - COMPLEX*16 array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element right-hand side vector b. On exit, X is overwritten with the solution vector x. INCX - INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. Level 2 Blas routine. -- Written on 22-October-1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --x; /* Function Body */ info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { info = 1; } else if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")) { info = 2; } else if (! lsame_(diag, "U") && ! lsame_(diag, "N")) { info = 3; } else if (*n < 0) { info = 4; } else if (*lda < max(1,*n)) { info = 6; } else if (*incx == 0) { info = 8; } if (info != 0) { xerbla_("ZTRSV ", &info); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } noconj = lsame_(trans, "T"); nounit = lsame_(diag, "N"); /* Set up the start point in X if the increment is not unity. This will be ( N - 1 )*INCX too small for descending loops. */ if (*incx <= 0) { kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { kx = 1; } /* Start the operations. In this version the elements of A are accessed sequentially with one pass through A. */ if (lsame_(trans, "N")) { /* Form x := inv( A )*x. */ if (lsame_(uplo, "U")) { if (*incx == 1) { for (j = *n; j >= 1; --j) { i__1 = j; if (x[i__1].r != 0. || x[i__1].i != 0.) { if (nounit) { i__1 = j; z_div(&z__1, &x[j], &a_ref(j, j)); x[i__1].r = z__1.r, x[i__1].i = z__1.i; } i__1 = j; temp.r = x[i__1].r, temp.i = x[i__1].i; for (i__ = j - 1; i__ >= 1; --i__) { i__1 = i__; i__2 = i__; i__3 = a_subscr(i__, j); z__2.r = temp.r * a[i__3].r - temp.i * a[i__3].i, z__2.i = temp.r * a[i__3].i + temp.i * a[ i__3].r; z__1.r = x[i__2].r - z__2.r, z__1.i = x[i__2].i - z__2.i; x[i__1].r = z__1.r, x[i__1].i = z__1.i; /* L10: */ } } /* L20: */ } } else { jx = kx + (*n - 1) * *incx; for (j = *n; j >= 1; --j) { i__1 = jx; if (x[i__1].r != 0. || x[i__1].i != 0.) { if (nounit) { i__1 = jx; z_div(&z__1, &x[jx], &a_ref(j, j)); x[i__1].r = z__1.r, x[i__1].i = z__1.i; } i__1 = jx; temp.r = x[i__1].r, temp.i = x[i__1].i; ix = jx; for (i__ = j - 1; i__ >= 1; --i__) { ix -= *incx; i__1 = ix; i__2 = ix; i__3 = a_subscr(i__, j); z__2.r = temp.r * a[i__3].r - temp.i * a[i__3].i, z__2.i = temp.r * a[i__3].i + temp.i * a[ i__3].r; z__1.r = x[i__2].r - z__2.r, z__1.i = x[i__2].i - z__2.i; x[i__1].r = z__1.r, x[i__1].i = z__1.i; /* L30: */ } } jx -= *incx; /* L40: */ } } } else { if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; if (x[i__2].r != 0. || x[i__2].i != 0.) { if (nounit) { i__2 = j; z_div(&z__1, &x[j], &a_ref(j, j)); x[i__2].r = z__1.r, x[i__2].i = z__1.i; } i__2 = j; temp.r = x[i__2].r, temp.i = x[i__2].i; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = a_subscr(i__, j); z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = temp.r * a[i__5].i + temp.i * a[ i__5].r; z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i - z__2.i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; /* L50: */ } } /* L60: */ } } else { jx = kx; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; if (x[i__2].r != 0. || x[i__2].i != 0.) { if (nounit) { i__2 = jx; z_div(&z__1, &x[jx], &a_ref(j, j)); x[i__2].r = z__1.r, x[i__2].i = z__1.i; } i__2 = jx; temp.r = x[i__2].r, temp.i = x[i__2].i; ix = jx; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { ix += *incx; i__3 = ix; i__4 = ix; i__5 = a_subscr(i__, j); z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = temp.r * a[i__5].i + temp.i * a[ i__5].r; z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i - z__2.i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; /* L70: */ } } jx += *incx; /* L80: */ } } } } else { /* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. */ if (lsame_(uplo, "U")) { if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; temp.r = x[i__2].r, temp.i = x[i__2].i; if (noconj) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); i__4 = i__; z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ i__4].i, z__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[i__4].r; z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L90: */ } if (nounit) { z_div(&z__1, &temp, &a_ref(j, j)); temp.r = z__1.r, temp.i = z__1.i; } } else { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { d_cnjg(&z__3, &a_ref(i__, j)); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[ i__3].r; z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L100: */ } if (nounit) { d_cnjg(&z__2, &a_ref(j, j)); z_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } i__2 = j; x[i__2].r = temp.r, x[i__2].i = temp.i; /* L110: */ } } else { jx = kx; i__1 = *n; for (j = 1; j <= i__1; ++j) { ix = kx; i__2 = jx; temp.r = x[i__2].r, temp.i = x[i__2].i; if (noconj) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = a_subscr(i__, j); i__4 = ix; z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ i__4].i, z__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[i__4].r; z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix += *incx; /* L120: */ } if (nounit) { z_div(&z__1, &temp, &a_ref(j, j)); temp.r = z__1.r, temp.i = z__1.i; } } else { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { d_cnjg(&z__3, &a_ref(i__, j)); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[ i__3].r; z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix += *incx; /* L130: */ } if (nounit) { d_cnjg(&z__2, &a_ref(j, j)); z_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } i__2 = jx; x[i__2].r = temp.r, x[i__2].i = temp.i; jx += *incx; /* L140: */ } } } else { if (*incx == 1) { for (j = *n; j >= 1; --j) { i__1 = j; temp.r = x[i__1].r, temp.i = x[i__1].i; if (noconj) { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { i__2 = a_subscr(i__, j); i__3 = i__; z__2.r = a[i__2].r * x[i__3].r - a[i__2].i * x[ i__3].i, z__2.i = a[i__2].r * x[i__3].i + a[i__2].i * x[i__3].r; z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L150: */ } if (nounit) { z_div(&z__1, &temp, &a_ref(j, j)); temp.r = z__1.r, temp.i = z__1.i; } } else { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { d_cnjg(&z__3, &a_ref(i__, j)); i__2 = i__; z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, z__2.i = z__3.r * x[i__2].i + z__3.i * x[ i__2].r; z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L160: */ } if (nounit) { d_cnjg(&z__2, &a_ref(j, j)); z_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } i__1 = j; x[i__1].r = temp.r, x[i__1].i = temp.i; /* L170: */ } } else { kx += (*n - 1) * *incx; jx = kx; for (j = *n; j >= 1; --j) { ix = kx; i__1 = jx; temp.r = x[i__1].r, temp.i = x[i__1].i; if (noconj) { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { i__2 = a_subscr(i__, j); i__3 = ix; z__2.r = a[i__2].r * x[i__3].r - a[i__2].i * x[ i__3].i, z__2.i = a[i__2].r * x[i__3].i + a[i__2].i * x[i__3].r; z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix -= *incx; /* L180: */ } if (nounit) { z_div(&z__1, &temp, &a_ref(j, j)); temp.r = z__1.r, temp.i = z__1.i; } } else { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { d_cnjg(&z__3, &a_ref(i__, j)); i__2 = ix; z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, z__2.i = z__3.r * x[i__2].i + z__3.i * x[ i__2].r; z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix -= *incx; /* L190: */ } if (nounit) { d_cnjg(&z__2, &a_ref(j, j)); z_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } i__1 = jx; x[i__1].r = temp.r, x[i__1].i = temp.i; jx -= *incx; /* L200: */ } } } } return 0; /* End of ZTRSV . */ } /* ztrsv_ */ #undef a_ref #undef a_subscr logical lsame_(char *ca, char *cb) { /* -- LAPACK auxiliary routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= LSAME returns .TRUE. if CA is the same letter as CB regardless of case. Arguments ========= CA (input) CHARACTER*1 CB (input) CHARACTER*1 CA and CB specify the single characters to be compared. ===================================================================== Test if the characters are equal */ /* System generated locals */ logical ret_val; /* Local variables */ static integer inta, intb, zcode; ret_val = *(unsigned char *)ca == *(unsigned char *)cb; if (ret_val) { return ret_val; } /* Now test for equivalence if both characters are alphabetic. */ zcode = 'Z'; /* Use 'Z' rather than 'A' so that ASCII can be detected on Prime machines, on which ICHAR returns a value with bit 8 set. ICHAR('A') on Prime machines returns 193 which is the same as ICHAR('A') on an EBCDIC machine. */ inta = *(unsigned char *)ca; intb = *(unsigned char *)cb; if (zcode == 90 || zcode == 122) { /* ASCII is assumed - ZCODE is the ASCII code of either lower o r upper case 'Z'. */ if (inta >= 97 && inta <= 122) { inta += -32; } if (intb >= 97 && intb <= 122) { intb += -32; } } else if (zcode == 233 || zcode == 169) { /* EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or upper case 'Z'. */ if (inta >= 129 && inta <= 137 || inta >= 145 && inta <= 153 || inta >= 162 && inta <= 169) { inta += 64; } if (intb >= 129 && intb <= 137 || intb >= 145 && intb <= 153 || intb >= 162 && intb <= 169) { intb += 64; } } else if (zcode == 218 || zcode == 250) { /* ASCII is assumed, on Prime machines - ZCODE is the ASCII cod e plus 128 of either lower or upper case 'Z'. */ if (inta >= 225 && inta <= 250) { inta += -32; } if (intb >= 225 && intb <= 250) { intb += -32; } } ret_val = inta == intb; /* RETURN End of LSAME */ return ret_val; } /* lsame_ */ /* Subroutine */ int dsyrk_(char *uplo, char *trans, integer *n, integer *k, doublereal *alpha, doublereal *a, integer *lda, doublereal *beta, doublereal *c__, integer *ldc) { /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3; /* Local variables */ static integer info; static doublereal temp; static integer i__, j, l; extern logical lsame_(char *, char *); static integer nrowa; static logical upper; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] #define c___ref(a_1,a_2) c__[(a_2)*c_dim1 + a_1] /* Purpose ======= DSYRK performs one of the symmetric rank k operations C := alpha*A*A' + beta*C, or C := alpha*A'*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case. Parameters ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced. Unchanged on exit. TRANS - CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*A' + beta*C. TRANS = 'T' or 't' C := alpha*A'*A + beta*C. TRANS = 'C' or 'c' C := alpha*A'*A + beta*C. Unchanged on exit. N - INTEGER. On entry, N specifies the order of the matrix C. N must be at least zero. Unchanged on exit. K - INTEGER. On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrix A, and on entry with TRANS = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrix A. K must be at least zero. Unchanged on exit. ALPHA - DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ). Unchanged on exit. BETA - DOUBLE PRECISION. On entry, BETA specifies the scalar beta. Unchanged on exit. C - DOUBLE PRECISION array of DIMENSION ( LDC, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. LDC - INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, n ). Unchanged on exit. Level 3 Blas routine. -- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; /* Function Body */ if (lsame_(trans, "N")) { nrowa = *n; } else { nrowa = *k; } upper = lsame_(uplo, "U"); info = 0; if (! upper && ! lsame_(uplo, "L")) { info = 1; } else if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")) { info = 2; } else if (*n < 0) { info = 3; } else if (*k < 0) { info = 4; } else if (*lda < max(1,nrowa)) { info = 7; } else if (*ldc < max(1,*n)) { info = 10; } if (info != 0) { xerbla_("DSYRK ", &info); return 0; } /* Quick return if possible. */ if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { return 0; } /* And when alpha.eq.zero. */ if (*alpha == 0.) { if (upper) { if (*beta == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = 0.; /* L10: */ } /* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = *beta * c___ref(i__, j); /* L30: */ } /* L40: */ } } } else { if (*beta == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c___ref(i__, j) = 0.; /* L50: */ } /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c___ref(i__, j) = *beta * c___ref(i__, j); /* L70: */ } /* L80: */ } } } return 0; } /* Start the operations. */ if (lsame_(trans, "N")) { /* Form C := alpha*A*A' + beta*C. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = 0.; /* L90: */ } } else if (*beta != 1.) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c___ref(i__, j) = *beta * c___ref(i__, j); /* L100: */ } } i__2 = *k; for (l = 1; l <= i__2; ++l) { if (a_ref(j, l) != 0.) { temp = *alpha * a_ref(j, l); i__3 = j; for (i__ = 1; i__ <= i__3; ++i__) { c___ref(i__, j) = c___ref(i__, j) + temp * a_ref( i__, l); /* L110: */ } } /* L120: */ } /* L130: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c___ref(i__, j) = 0.; /* L140: */ } } else if (*beta != 1.) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c___ref(i__, j) = *beta * c___ref(i__, j); /* L150: */ } } i__2 = *k; for (l = 1; l <= i__2; ++l) { if (a_ref(j, l) != 0.) { temp = *alpha * a_ref(j, l); i__3 = *n; for (i__ = j; i__ <= i__3; ++i__) { c___ref(i__, j) = c___ref(i__, j) + temp * a_ref( i__, l); /* L160: */ } } /* L170: */ } /* L180: */ } } } else { /* Form C := alpha*A'*A + beta*C. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { temp = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { temp += a_ref(l, i__) * a_ref(l, j); /* L190: */ } if (*beta == 0.) { c___ref(i__, j) = *alpha * temp; } else { c___ref(i__, j) = *alpha * temp + *beta * c___ref(i__, j); } /* L200: */ } /* L210: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { temp = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { temp += a_ref(l, i__) * a_ref(l, j); /* L220: */ } if (*beta == 0.) { c___ref(i__, j) = *alpha * temp; } else { c___ref(i__, j) = *alpha * temp + *beta * c___ref(i__, j); } /* L230: */ } /* L240: */ } } } return 0; /* End of DSYRK . */ } /* dsyrk_ */ #undef c___ref #undef a_ref /* Subroutine */ int zherk_(char *uplo, char *trans, integer *n, integer *k, doublereal *alpha, doublecomplex *a, integer *lda, doublereal *beta, doublecomplex *c__, integer *ldc) { /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublereal d__1; doublecomplex z__1, z__2, z__3; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static doublecomplex temp; static integer i__, j, l; extern logical lsame_(char *, char *); static integer nrowa; static doublereal rtemp; static logical upper; extern /* Subroutine */ int xerbla_(char *, integer *); #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] #define c___subscr(a_1,a_2) (a_2)*c_dim1 + a_1 #define c___ref(a_1,a_2) c__[c___subscr(a_1,a_2)] /* Purpose ======= ZHERK performs one of the hermitian rank k operations C := alpha*A*conjg( A' ) + beta*C, or C := alpha*conjg( A' )*A + beta*C, where alpha and beta are real scalars, C is an n by n hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case. Parameters ========== UPLO - CHARACTER*1. On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced. Unchanged on exit. TRANS - CHARACTER*1. On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*conjg( A' ) + beta*C. TRANS = 'C' or 'c' C := alpha*conjg( A' )*A + beta*C. Unchanged on exit. N - INTEGER. On entry, N specifies the order of the matrix C. N must be at least zero. Unchanged on exit. K - INTEGER. On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrix A, and on entry with TRANS = 'C' or 'c', K specifies the number of rows of the matrix A. K must be at least zero. Unchanged on exit. ALPHA - DOUBLE PRECISION . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A. Unchanged on exit. LDA - INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ). Unchanged on exit. BETA - DOUBLE PRECISION. On entry, BETA specifies the scalar beta. Unchanged on exit. C - COMPLEX*16 array of DIMENSION ( LDC, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. LDC - INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, n ). Unchanged on exit. Level 3 Blas routine. -- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd. -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. Ed Anderson, Cray Research Inc. Test the input parameters. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; /* Function Body */ if (lsame_(trans, "N")) { nrowa = *n; } else { nrowa = *k; } upper = lsame_(uplo, "U"); info = 0; if (! upper && ! lsame_(uplo, "L")) { info = 1; } else if (! lsame_(trans, "N") && ! lsame_(trans, "C")) { info = 2; } else if (*n < 0) { info = 3; } else if (*k < 0) { info = 4; } else if (*lda < max(1,nrowa)) { info = 7; } else if (*ldc < max(1,*n)) { info = 10; } if (info != 0) { xerbla_("ZHERK ", &info); return 0; } /* Quick return if possible. */ if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { return 0; } /* And when alpha.eq.zero. */ if (*alpha == 0.) { if (upper) { if (*beta == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); c__[i__3].r = 0., c__[i__3].i = 0.; /* L10: */ } /* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ i__4].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L30: */ } i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = *beta * c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; /* L40: */ } } } else { if (*beta == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); c__[i__3].r = 0., c__[i__3].i = 0.; /* L50: */ } /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = *beta * c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ i__4].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L70: */ } /* L80: */ } } } return 0; } /* Start the operations. */ if (lsame_(trans, "N")) { /* Form C := alpha*A*conjg( A' ) + beta*C. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); c__[i__3].r = 0., c__[i__3].i = 0.; /* L90: */ } } else if (*beta != 1.) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ i__4].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L100: */ } i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = *beta * c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; } else { i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; } i__2 = *k; for (l = 1; l <= i__2; ++l) { i__3 = a_subscr(j, l); if (a[i__3].r != 0. || a[i__3].i != 0.) { d_cnjg(&z__2, &a_ref(j, l)); z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; temp.r = z__1.r, temp.i = z__1.i; i__3 = j - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = c___subscr(i__, j); i__5 = c___subscr(i__, j); i__6 = a_subscr(i__, l); z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, z__2.i = temp.r * a[i__6].i + temp.i * a[ i__6].r; z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5] .i + z__2.i; c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; /* L110: */ } i__3 = c___subscr(j, j); i__4 = c___subscr(j, j); i__5 = a_subscr(i__, l); z__1.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__1.i = temp.r * a[i__5].i + temp.i * a[i__5] .r; d__1 = c__[i__4].r + z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } /* L120: */ } /* L130: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); c__[i__3].r = 0., c__[i__3].i = 0.; /* L140: */ } } else if (*beta != 1.) { i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = *beta * c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = c___subscr(i__, j); i__4 = c___subscr(i__, j); z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ i__4].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L150: */ } } else { i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; } i__2 = *k; for (l = 1; l <= i__2; ++l) { i__3 = a_subscr(j, l); if (a[i__3].r != 0. || a[i__3].i != 0.) { d_cnjg(&z__2, &a_ref(j, l)); z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; temp.r = z__1.r, temp.i = z__1.i; i__3 = c___subscr(j, j); i__4 = c___subscr(j, j); i__5 = a_subscr(j, l); z__1.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__1.i = temp.r * a[i__5].i + temp.i * a[i__5] .r; d__1 = c__[i__4].r + z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; i__3 = *n; for (i__ = j + 1; i__ <= i__3; ++i__) { i__4 = c___subscr(i__, j); i__5 = c___subscr(i__, j); i__6 = a_subscr(i__, l); z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, z__2.i = temp.r * a[i__6].i + temp.i * a[ i__6].r; z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5] .i + z__2.i; c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; /* L160: */ } } /* L170: */ } /* L180: */ } } } else { /* Form C := alpha*conjg( A' )*A + beta*C. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { temp.r = 0., temp.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { d_cnjg(&z__3, &a_ref(l, i__)); i__4 = a_subscr(l, j); z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] .r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L190: */ } if (*beta == 0.) { i__3 = c___subscr(i__, j); z__1.r = *alpha * temp.r, z__1.i = *alpha * temp.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = c___subscr(i__, j); z__2.r = *alpha * temp.r, z__2.i = *alpha * temp.i; i__4 = c___subscr(i__, j); z__3.r = *beta * c__[i__4].r, z__3.i = *beta * c__[ i__4].i; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } /* L200: */ } rtemp = 0.; i__2 = *k; for (l = 1; l <= i__2; ++l) { d_cnjg(&z__3, &a_ref(l, j)); i__3 = a_subscr(l, j); z__2.r = z__3.r * a[i__3].r - z__3.i * a[i__3].i, z__2.i = z__3.r * a[i__3].i + z__3.i * a[i__3].r; z__1.r = rtemp + z__2.r, z__1.i = z__2.i; rtemp = z__1.r; /* L210: */ } if (*beta == 0.) { i__2 = c___subscr(j, j); d__1 = *alpha * rtemp; c__[i__2].r = d__1, c__[i__2].i = 0.; } else { i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = *alpha * rtemp + *beta * c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; } /* L220: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { rtemp = 0.; i__2 = *k; for (l = 1; l <= i__2; ++l) { d_cnjg(&z__3, &a_ref(l, j)); i__3 = a_subscr(l, j); z__2.r = z__3.r * a[i__3].r - z__3.i * a[i__3].i, z__2.i = z__3.r * a[i__3].i + z__3.i * a[i__3].r; z__1.r = rtemp + z__2.r, z__1.i = z__2.i; rtemp = z__1.r; /* L230: */ } if (*beta == 0.) { i__2 = c___subscr(j, j); d__1 = *alpha * rtemp; c__[i__2].r = d__1, c__[i__2].i = 0.; } else { i__2 = c___subscr(j, j); i__3 = c___subscr(j, j); d__1 = *alpha * rtemp + *beta * c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { temp.r = 0., temp.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { d_cnjg(&z__3, &a_ref(l, i__)); i__4 = a_subscr(l, j); z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] .r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L240: */ } if (*beta == 0.) { i__3 = c___subscr(i__, j); z__1.r = *alpha * temp.r, z__1.i = *alpha * temp.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = c___subscr(i__, j); z__2.r = *alpha * temp.r, z__2.i = *alpha * temp.i; i__4 = c___subscr(i__, j); z__3.r = *beta * c__[i__4].r, z__3.i = *beta * c__[ i__4].i; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } /* L250: */ } /* L260: */ } } } return 0; /* End of ZHERK . */ } /* zherk_ */ #undef c___ref #undef c___subscr #undef a_ref #undef a_subscr