#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int ctrsv_(char *uplo, char *trans, char *diag, integer *n, complex *a, integer *lda, complex *x, integer *incx) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; 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, ix, jx, kx, info; static complex temp; extern logical lsame_(char *, char *); extern /* Subroutine */ int xerbla_(char *, integer *); static logical noconj, nounit; /* Purpose ======= CTRSV 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. Arguments ========== 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 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 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; 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_("CTRSV ", &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.f || x[i__1].i != 0.f) { if (nounit) { i__1 = j; c_div(&q__1, &x[j], &a[j + j * a_dim1]); x[i__1].r = q__1.r, x[i__1].i = q__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 = i__ + j * a_dim1; q__2.r = temp.r * a[i__3].r - temp.i * a[i__3].i, q__2.i = temp.r * a[i__3].i + temp.i * a[ i__3].r; q__1.r = x[i__2].r - q__2.r, q__1.i = x[i__2].i - q__2.i; x[i__1].r = q__1.r, x[i__1].i = q__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.f || x[i__1].i != 0.f) { if (nounit) { i__1 = jx; c_div(&q__1, &x[jx], &a[j + j * a_dim1]); x[i__1].r = q__1.r, x[i__1].i = q__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 = i__ + j * a_dim1; q__2.r = temp.r * a[i__3].r - temp.i * a[i__3].i, q__2.i = temp.r * a[i__3].i + temp.i * a[ i__3].r; q__1.r = x[i__2].r - q__2.r, q__1.i = x[i__2].i - q__2.i; x[i__1].r = q__1.r, x[i__1].i = q__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.f || x[i__2].i != 0.f) { if (nounit) { i__2 = j; c_div(&q__1, &x[j], &a[j + j * a_dim1]); x[i__2].r = q__1.r, x[i__2].i = q__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 = i__ + j * a_dim1; q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, q__2.i = temp.r * a[i__5].i + temp.i * a[ i__5].r; q__1.r = x[i__4].r - q__2.r, q__1.i = x[i__4].i - q__2.i; x[i__3].r = q__1.r, x[i__3].i = q__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.f || x[i__2].i != 0.f) { if (nounit) { i__2 = jx; c_div(&q__1, &x[jx], &a[j + j * a_dim1]); x[i__2].r = q__1.r, x[i__2].i = q__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 = i__ + j * a_dim1; q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, q__2.i = temp.r * a[i__5].i + temp.i * a[ i__5].r; q__1.r = x[i__4].r - q__2.r, q__1.i = x[i__4].i - q__2.i; x[i__3].r = q__1.r, x[i__3].i = q__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 = i__ + j * a_dim1; i__4 = i__; q__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ i__4].i, q__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[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; /* L90: */ } if (nounit) { c_div(&q__1, &temp, &a[j + j * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; } } else { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { r_cnjg(&q__3, &a[i__ + j * a_dim1]); i__3 = i__; q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i = q__3.r * x[i__3].i + q__3.i * x[ 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; /* L100: */ } if (nounit) { r_cnjg(&q__2, &a[j + j * a_dim1]); c_div(&q__1, &temp, &q__2); temp.r = q__1.r, temp.i = q__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 = i__ + j * a_dim1; i__4 = ix; q__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ i__4].i, q__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[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; ix += *incx; /* L120: */ } if (nounit) { c_div(&q__1, &temp, &a[j + j * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; } } else { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { r_cnjg(&q__3, &a[i__ + j * a_dim1]); i__3 = ix; q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i = q__3.r * x[i__3].i + q__3.i * x[ 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; ix += *incx; /* L130: */ } if (nounit) { r_cnjg(&q__2, &a[j + j * a_dim1]); c_div(&q__1, &temp, &q__2); temp.r = q__1.r, temp.i = q__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 = i__ + j * a_dim1; i__3 = i__; q__2.r = a[i__2].r * x[i__3].r - a[i__2].i * x[ i__3].i, q__2.i = a[i__2].r * x[i__3].i + a[i__2].i * x[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; /* L150: */ } if (nounit) { c_div(&q__1, &temp, &a[j + j * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; } } else { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { r_cnjg(&q__3, &a[i__ + j * a_dim1]); i__2 = i__; q__2.r = q__3.r * x[i__2].r - q__3.i * x[i__2].i, q__2.i = q__3.r * x[i__2].i + q__3.i * x[ i__2].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[j + j * a_dim1]); c_div(&q__1, &temp, &q__2); temp.r = q__1.r, temp.i = q__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 = i__ + j * a_dim1; i__3 = ix; q__2.r = a[i__2].r * x[i__3].r - a[i__2].i * x[ i__3].i, q__2.i = a[i__2].r * x[i__3].i + a[i__2].i * x[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; ix -= *incx; /* L180: */ } if (nounit) { c_div(&q__1, &temp, &a[j + j * a_dim1]); temp.r = q__1.r, temp.i = q__1.i; } } else { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { r_cnjg(&q__3, &a[i__ + j * a_dim1]); i__2 = ix; q__2.r = q__3.r * x[i__2].r - q__3.i * x[i__2].i, q__2.i = q__3.r * x[i__2].i + q__3.i * x[ i__2].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; ix -= *incx; /* L190: */ } if (nounit) { r_cnjg(&q__2, &a[j + j * a_dim1]); c_div(&q__1, &temp, &q__2); temp.r = q__1.r, temp.i = q__1.i; } } i__1 = jx; x[i__1].r = temp.r, x[i__1].i = temp.i; jx -= *incx; /* L200: */ } } } } return 0; /* End of CTRSV . */ } /* ctrsv_ */