#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int ctrsm_(char *side, char *uplo, char *transa, char *diag, integer *m, integer *n, complex *alpha, complex *a, integer *lda, complex *b, integer *ldb) { /* Table of constant values */ static complex c_b1 = {1.f,0.f}; /* 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; complex q__1, q__2, q__3; /* Builtin functions */ void c_div(complex *, complex *, complex *), r_cnjg(complex *, complex *); /* Local variables */ static integer i__, j, k, info; static complex temp; extern logical lsame_(char *, char *); static logical lside; static integer nrowa; static logical upper; extern /* Subroutine */ int xerbla_(char *, integer *); static logical noconj, nounit; /* Purpose ======= CTRSM 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. Arguments ========== 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 . 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 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 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; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; 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_("CTRSM ", &info); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } /* And when alpha.eq.zero. */ if (alpha->r == 0.f && alpha->i == 0.f) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; b[i__3].r = 0.f, b[i__3].i = 0.f; /* 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.f || alpha->i != 0.f) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__ + j * b_dim1; q__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4] .i, q__1.i = alpha->r * b[i__4].i + alpha->i * b[i__4].r; b[i__3].r = q__1.r, b[i__3].i = q__1.i; /* L30: */ } } for (k = *m; k >= 1; --k) { i__2 = k + j * b_dim1; if (b[i__2].r != 0.f || b[i__2].i != 0.f) { if (nounit) { i__2 = k + j * b_dim1; c_div(&q__1, &b[k + j * b_dim1], &a[k + k * a_dim1]); b[i__2].r = q__1.r, b[i__2].i = q__1.i; } i__2 = k - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__ + j * b_dim1; i__5 = k + j * b_dim1; i__6 = i__ + k * a_dim1; q__2.r = b[i__5].r * a[i__6].r - b[i__5].i * a[i__6].i, q__2.i = b[i__5].r * a[ i__6].i + b[i__5].i * a[i__6].r; q__1.r = b[i__4].r - q__2.r, q__1.i = b[i__4] .i - q__2.i; b[i__3].r = q__1.r, b[i__3].i = q__1.i; /* L40: */ } } /* L50: */ } /* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (alpha->r != 1.f || alpha->i != 0.f) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__ + j * b_dim1; q__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4] .i, q__1.i = alpha->r * b[i__4].i + alpha->i * b[i__4].r; b[i__3].r = q__1.r, b[i__3].i = q__1.i; /* L70: */ } } i__2 = *m; for (k = 1; k <= i__2; ++k) { i__3 = k + j * b_dim1; if (b[i__3].r != 0.f || b[i__3].i != 0.f) { if (nounit) { i__3 = k + j * b_dim1; c_div(&q__1, &b[k + j * b_dim1], &a[k + k * a_dim1]); b[i__3].r = q__1.r, b[i__3].i = q__1.i; } i__3 = *m; for (i__ = k + 1; i__ <= i__3; ++i__) { i__4 = i__ + j * b_dim1; i__5 = i__ + j * b_dim1; i__6 = k + j * b_dim1; i__7 = i__ + k * a_dim1; q__2.r = b[i__6].r * a[i__7].r - b[i__6].i * a[i__7].i, q__2.i = b[i__6].r * a[ i__7].i + b[i__6].i * a[i__7].r; q__1.r = b[i__5].r - q__2.r, q__1.i = b[i__5] .i - q__2.i; b[i__4].r = q__1.r, b[i__4].i = q__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 = i__ + j * b_dim1; q__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, q__1.i = alpha->r * b[i__3].i + alpha->i * b[ i__3].r; temp.r = q__1.r, temp.i = q__1.i; if (noconj) { i__3 = i__ - 1; for (k = 1; k <= i__3; ++k) { i__4 = k + i__ * a_dim1; i__5 = k + j * b_dim1; q__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5].i, q__2.i = a[i__4].r * b[ i__5].i + a[i__4].i * b[i__5].r; q__1.r = temp.r - q__2.r, q__1.i = temp.i - q__2.i; temp.r = q__1.r, temp.i = q__1.i; /* L110: */ } if (nounit) { c_div(&q__1, &temp, &a[i__ + i__ * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; } } else { i__3 = i__ - 1; for (k = 1; k <= i__3; ++k) { r_cnjg(&q__3, &a[k + i__ * a_dim1]); i__4 = k + j * b_dim1; q__2.r = q__3.r * b[i__4].r - q__3.i * b[i__4] .i, q__2.i = q__3.r * b[i__4].i + q__3.i * b[i__4].r; q__1.r = temp.r - q__2.r, q__1.i = temp.i - q__2.i; temp.r = q__1.r, temp.i = q__1.i; /* L120: */ } if (nounit) { r_cnjg(&q__2, &a[i__ + i__ * a_dim1]); c_div(&q__1, &temp, &q__2); temp.r = q__1.r, temp.i = q__1.i; } } i__3 = i__ + j * b_dim1; 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 = i__ + j * b_dim1; q__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2].i, q__1.i = alpha->r * b[i__2].i + alpha->i * b[ i__2].r; temp.r = q__1.r, temp.i = q__1.i; if (noconj) { i__2 = *m; for (k = i__ + 1; k <= i__2; ++k) { i__3 = k + i__ * a_dim1; i__4 = k + j * b_dim1; q__2.r = a[i__3].r * b[i__4].r - a[i__3].i * b[i__4].i, q__2.i = a[i__3].r * b[ i__4].i + a[i__3].i * b[i__4].r; q__1.r = temp.r - q__2.r, q__1.i = temp.i - q__2.i; temp.r = q__1.r, temp.i = q__1.i; /* L150: */ } if (nounit) { c_div(&q__1, &temp, &a[i__ + i__ * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; } } else { i__2 = *m; for (k = i__ + 1; k <= i__2; ++k) { r_cnjg(&q__3, &a[k + i__ * a_dim1]); i__3 = k + j * b_dim1; q__2.r = q__3.r * b[i__3].r - q__3.i * b[i__3] .i, q__2.i = q__3.r * b[i__3].i + q__3.i * b[i__3].r; q__1.r = temp.r - q__2.r, q__1.i = temp.i - q__2.i; temp.r = q__1.r, temp.i = q__1.i; /* L160: */ } if (nounit) { r_cnjg(&q__2, &a[i__ + i__ * a_dim1]); c_div(&q__1, &temp, &q__2); temp.r = q__1.r, temp.i = q__1.i; } } i__2 = i__ + j * b_dim1; 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.f || alpha->i != 0.f) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__ + j * b_dim1; q__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4] .i, q__1.i = alpha->r * b[i__4].i + alpha->i * b[i__4].r; b[i__3].r = q__1.r, b[i__3].i = q__1.i; /* L190: */ } } i__2 = j - 1; for (k = 1; k <= i__2; ++k) { i__3 = k + j * a_dim1; if (a[i__3].r != 0.f || a[i__3].i != 0.f) { i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__ + j * b_dim1; i__5 = i__ + j * b_dim1; i__6 = k + j * a_dim1; i__7 = i__ + k * b_dim1; q__2.r = a[i__6].r * b[i__7].r - a[i__6].i * b[i__7].i, q__2.i = a[i__6].r * b[ i__7].i + a[i__6].i * b[i__7].r; q__1.r = b[i__5].r - q__2.r, q__1.i = b[i__5] .i - q__2.i; b[i__4].r = q__1.r, b[i__4].i = q__1.i; /* L200: */ } } /* L210: */ } if (nounit) { c_div(&q__1, &c_b1, &a[j + j * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__ + j * b_dim1; q__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, q__1.i = temp.r * b[i__4].i + temp.i * b[ i__4].r; b[i__3].r = q__1.r, b[i__3].i = q__1.i; /* L220: */ } } /* L230: */ } } else { for (j = *n; j >= 1; --j) { if (alpha->r != 1.f || alpha->i != 0.f) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + j * b_dim1; i__3 = i__ + j * b_dim1; q__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3] .i, q__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3].r; b[i__2].r = q__1.r, b[i__2].i = q__1.i; /* L240: */ } } i__1 = *n; for (k = j + 1; k <= i__1; ++k) { i__2 = k + j * a_dim1; if (a[i__2].r != 0.f || a[i__2].i != 0.f) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__ + j * b_dim1; i__5 = k + j * a_dim1; i__6 = i__ + k * b_dim1; q__2.r = a[i__5].r * b[i__6].r - a[i__5].i * b[i__6].i, q__2.i = a[i__5].r * b[ i__6].i + a[i__5].i * b[i__6].r; q__1.r = b[i__4].r - q__2.r, q__1.i = b[i__4] .i - q__2.i; b[i__3].r = q__1.r, b[i__3].i = q__1.i; /* L250: */ } } /* L260: */ } if (nounit) { c_div(&q__1, &c_b1, &a[j + j * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + j * b_dim1; i__3 = i__ + j * b_dim1; q__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, q__1.i = temp.r * b[i__3].i + temp.i * b[ i__3].r; b[i__2].r = q__1.r, b[i__2].i = q__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) { c_div(&q__1, &c_b1, &a[k + k * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; } else { r_cnjg(&q__2, &a[k + k * a_dim1]); c_div(&q__1, &c_b1, &q__2); temp.r = q__1.r, temp.i = q__1.i; } i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + k * b_dim1; i__3 = i__ + k * b_dim1; q__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, q__1.i = temp.r * b[i__3].i + temp.i * b[ i__3].r; b[i__2].r = q__1.r, b[i__2].i = q__1.i; /* L290: */ } } i__1 = k - 1; for (j = 1; j <= i__1; ++j) { i__2 = j + k * a_dim1; if (a[i__2].r != 0.f || a[i__2].i != 0.f) { if (noconj) { i__2 = j + k * a_dim1; temp.r = a[i__2].r, temp.i = a[i__2].i; } else { r_cnjg(&q__1, &a[j + k * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; } i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__ + j * b_dim1; i__5 = i__ + k * b_dim1; q__2.r = temp.r * b[i__5].r - temp.i * b[i__5] .i, q__2.i = temp.r * b[i__5].i + temp.i * b[i__5].r; q__1.r = b[i__4].r - q__2.r, q__1.i = b[i__4] .i - q__2.i; b[i__3].r = q__1.r, b[i__3].i = q__1.i; /* L300: */ } } /* L310: */ } if (alpha->r != 1.f || alpha->i != 0.f) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + k * b_dim1; i__3 = i__ + k * b_dim1; q__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3] .i, q__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3].r; b[i__2].r = q__1.r, b[i__2].i = q__1.i; /* L320: */ } } /* L330: */ } } else { i__1 = *n; for (k = 1; k <= i__1; ++k) { if (nounit) { if (noconj) { c_div(&q__1, &c_b1, &a[k + k * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; } else { r_cnjg(&q__2, &a[k + k * a_dim1]); c_div(&q__1, &c_b1, &q__2); temp.r = q__1.r, temp.i = q__1.i; } i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + k * b_dim1; i__4 = i__ + k * b_dim1; q__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, q__1.i = temp.r * b[i__4].i + temp.i * b[ i__4].r; b[i__3].r = q__1.r, b[i__3].i = q__1.i; /* L340: */ } } i__2 = *n; for (j = k + 1; j <= i__2; ++j) { i__3 = j + k * a_dim1; if (a[i__3].r != 0.f || a[i__3].i != 0.f) { if (noconj) { i__3 = j + k * a_dim1; temp.r = a[i__3].r, temp.i = a[i__3].i; } else { r_cnjg(&q__1, &a[j + k * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; } i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__ + j * b_dim1; i__5 = i__ + j * b_dim1; i__6 = i__ + k * b_dim1; q__2.r = temp.r * b[i__6].r - temp.i * b[i__6] .i, q__2.i = temp.r * b[i__6].i + temp.i * b[i__6].r; q__1.r = b[i__5].r - q__2.r, q__1.i = b[i__5] .i - q__2.i; b[i__4].r = q__1.r, b[i__4].i = q__1.i; /* L350: */ } } /* L360: */ } if (alpha->r != 1.f || alpha->i != 0.f) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + k * b_dim1; i__4 = i__ + k * b_dim1; q__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4] .i, q__1.i = alpha->r * b[i__4].i + alpha->i * b[i__4].r; b[i__3].r = q__1.r, b[i__3].i = q__1.i; /* L370: */ } } /* L380: */ } } } } return 0; /* End of CTRSM . */ } /* ctrsm_ */