509 lines
13 KiB
C
509 lines
13 KiB
C
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/* -- translated by f2c (version 19940927).
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You must link the resulting object file with the libraries:
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-lf2c -lm (in that order)
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*/
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#include "f2c.h"
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/* Subroutine */ int ctrsv_(char *uplo, char *trans, char *diag, integer *n,
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complex *a, integer *lda, complex *x, integer *incx)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
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complex q__1, q__2, q__3;
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/* Builtin functions */
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void c_div(complex *, complex *, complex *), r_cnjg(complex *, complex *);
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/* Local variables */
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static integer info;
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static complex temp;
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static integer i, j;
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extern logical lsame_(char *, char *);
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static integer ix, jx, kx;
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extern /* Subroutine */ int xerbla_(char *, integer *);
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static logical noconj, nounit;
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/* Purpose
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=======
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CTRSV solves one of the systems of equations
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A*x = b, or A'*x = b, or conjg( A' )*x = b,
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where b and x are n element vectors and A is an n by n unit, or
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non-unit, upper or lower triangular matrix.
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No test for singularity or near-singularity is included in this
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routine. Such tests must be performed before calling this routine.
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Parameters
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==========
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UPLO - CHARACTER*1.
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On entry, UPLO specifies whether the matrix is an upper or
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lower triangular matrix as follows:
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UPLO = 'U' or 'u' A is an upper triangular matrix.
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UPLO = 'L' or 'l' A is a lower triangular matrix.
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Unchanged on exit.
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TRANS - CHARACTER*1.
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On entry, TRANS specifies the equations to be solved as
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follows:
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TRANS = 'N' or 'n' A*x = b.
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TRANS = 'T' or 't' A'*x = b.
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TRANS = 'C' or 'c' conjg( A' )*x = b.
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Unchanged on exit.
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DIAG - CHARACTER*1.
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On entry, DIAG specifies whether or not A is unit
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triangular as follows:
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DIAG = 'U' or 'u' A is assumed to be unit triangular.
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DIAG = 'N' or 'n' A is not assumed to be unit
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triangular.
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Unchanged on exit.
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N - INTEGER.
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On entry, N specifies the order of the matrix A.
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N must be at least zero.
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Unchanged on exit.
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A - COMPLEX array of DIMENSION ( LDA, n ).
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Before entry with UPLO = 'U' or 'u', the leading n by n
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upper triangular part of the array A must contain the upper
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triangular matrix and the strictly lower triangular part of
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A is not referenced.
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Before entry with UPLO = 'L' or 'l', the leading n by n
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lower triangular part of the array A must contain the lower
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triangular matrix and the strictly upper triangular part of
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A is not referenced.
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Note that when DIAG = 'U' or 'u', the diagonal elements of
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A are not referenced either, but are assumed to be unity.
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Unchanged on exit.
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LDA - INTEGER.
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On entry, LDA specifies the first dimension of A as declared
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in the calling (sub) program. LDA must be at least
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max( 1, n ).
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Unchanged on exit.
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X - COMPLEX array of dimension at least
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( 1 + ( n - 1 )*abs( INCX ) ).
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Before entry, the incremented array X must contain the n
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element right-hand side vector b. On exit, X is overwritten
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with the solution vector x.
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INCX - INTEGER.
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On entry, INCX specifies the increment for the elements of
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X. INCX must not be zero.
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Unchanged on exit.
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Level 2 Blas routine.
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-- Written on 22-October-1986.
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Jack Dongarra, Argonne National Lab.
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Jeremy Du Croz, Nag Central Office.
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Sven Hammarling, Nag Central Office.
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Richard Hanson, Sandia National Labs.
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Test the input parameters.
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Parameter adjustments
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Function Body */
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#define X(I) x[(I)-1]
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#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
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info = 0;
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if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
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info = 1;
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} else if (! lsame_(trans, "N") && ! lsame_(trans, "T") &&
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! lsame_(trans, "C")) {
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info = 2;
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} else if (! lsame_(diag, "U") && ! lsame_(diag, "N")) {
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info = 3;
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} else if (*n < 0) {
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info = 4;
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} else if (*lda < max(1,*n)) {
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info = 6;
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} else if (*incx == 0) {
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info = 8;
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}
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if (info != 0) {
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xerbla_("CTRSV ", &info);
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return 0;
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}
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/* Quick return if possible. */
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if (*n == 0) {
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return 0;
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}
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noconj = lsame_(trans, "T");
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nounit = lsame_(diag, "N");
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/* Set up the start point in X if the increment is not unity. This
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will be ( N - 1 )*INCX too small for descending loops. */
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if (*incx <= 0) {
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kx = 1 - (*n - 1) * *incx;
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} else if (*incx != 1) {
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kx = 1;
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}
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/* Start the operations. In this version the elements of A are
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accessed sequentially with one pass through A. */
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if (lsame_(trans, "N")) {
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/* Form x := inv( A )*x. */
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if (lsame_(uplo, "U")) {
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if (*incx == 1) {
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for (j = *n; j >= 1; --j) {
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i__1 = j;
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if (X(j).r != 0.f || X(j).i != 0.f) {
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if (nounit) {
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i__1 = j;
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c_div(&q__1, &X(j), &A(j,j));
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X(j).r = q__1.r, X(j).i = q__1.i;
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}
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i__1 = j;
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temp.r = X(j).r, temp.i = X(j).i;
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for (i = j - 1; i >= 1; --i) {
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i__1 = i;
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i__2 = i;
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i__3 = i + j * a_dim1;
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q__2.r = temp.r * A(i,j).r - temp.i * A(i,j).i,
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q__2.i = temp.r * A(i,j).i + temp.i * A(i,j).r;
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q__1.r = X(i).r - q__2.r, q__1.i = X(i).i -
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q__2.i;
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X(i).r = q__1.r, X(i).i = q__1.i;
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/* L10: */
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}
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}
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/* L20: */
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}
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} else {
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jx = kx + (*n - 1) * *incx;
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for (j = *n; j >= 1; --j) {
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i__1 = jx;
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if (X(jx).r != 0.f || X(jx).i != 0.f) {
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if (nounit) {
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i__1 = jx;
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c_div(&q__1, &X(jx), &A(j,j));
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X(jx).r = q__1.r, X(jx).i = q__1.i;
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}
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i__1 = jx;
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temp.r = X(jx).r, temp.i = X(jx).i;
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ix = jx;
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for (i = j - 1; i >= 1; --i) {
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ix -= *incx;
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i__1 = ix;
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i__2 = ix;
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i__3 = i + j * a_dim1;
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q__2.r = temp.r * A(i,j).r - temp.i * A(i,j).i,
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q__2.i = temp.r * A(i,j).i + temp.i * A(i,j).r;
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q__1.r = X(ix).r - q__2.r, q__1.i = X(ix).i -
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q__2.i;
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X(ix).r = q__1.r, X(ix).i = q__1.i;
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/* L30: */
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}
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}
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jx -= *incx;
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/* L40: */
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}
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}
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} else {
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if (*incx == 1) {
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i__1 = *n;
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for (j = 1; j <= *n; ++j) {
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i__2 = j;
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if (X(j).r != 0.f || X(j).i != 0.f) {
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if (nounit) {
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i__2 = j;
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c_div(&q__1, &X(j), &A(j,j));
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X(j).r = q__1.r, X(j).i = q__1.i;
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}
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i__2 = j;
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temp.r = X(j).r, temp.i = X(j).i;
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i__2 = *n;
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for (i = j + 1; i <= *n; ++i) {
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i__3 = i;
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i__4 = i;
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i__5 = i + j * a_dim1;
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q__2.r = temp.r * A(i,j).r - temp.i * A(i,j).i,
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q__2.i = temp.r * A(i,j).i + temp.i * A(i,j).r;
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q__1.r = X(i).r - q__2.r, q__1.i = X(i).i -
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q__2.i;
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X(i).r = q__1.r, X(i).i = q__1.i;
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/* L50: */
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}
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}
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/* L60: */
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}
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} else {
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jx = kx;
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i__1 = *n;
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for (j = 1; j <= *n; ++j) {
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i__2 = jx;
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if (X(jx).r != 0.f || X(jx).i != 0.f) {
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if (nounit) {
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i__2 = jx;
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c_div(&q__1, &X(jx), &A(j,j));
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X(jx).r = q__1.r, X(jx).i = q__1.i;
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}
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i__2 = jx;
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temp.r = X(jx).r, temp.i = X(jx).i;
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ix = jx;
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i__2 = *n;
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for (i = j + 1; i <= *n; ++i) {
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ix += *incx;
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i__3 = ix;
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i__4 = ix;
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i__5 = i + j * a_dim1;
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q__2.r = temp.r * A(i,j).r - temp.i * A(i,j).i,
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q__2.i = temp.r * A(i,j).i + temp.i * A(i,j).r;
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q__1.r = X(ix).r - q__2.r, q__1.i = X(ix).i -
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q__2.i;
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X(ix).r = q__1.r, X(ix).i = q__1.i;
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/* L70: */
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}
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}
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jx += *incx;
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/* L80: */
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}
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}
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}
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} else {
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/* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. */
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if (lsame_(uplo, "U")) {
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if (*incx == 1) {
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i__1 = *n;
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for (j = 1; j <= *n; ++j) {
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i__2 = j;
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temp.r = X(j).r, temp.i = X(j).i;
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if (noconj) {
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i__2 = j - 1;
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for (i = 1; i <= j-1; ++i) {
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i__3 = i + j * a_dim1;
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i__4 = i;
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q__2.r = A(i,j).r * X(i).r - A(i,j).i * X(
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i).i, q__2.i = A(i,j).r * X(i).i +
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A(i,j).i * X(i).r;
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q__1.r = temp.r - q__2.r, q__1.i = temp.i -
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q__2.i;
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temp.r = q__1.r, temp.i = q__1.i;
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/* L90: */
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}
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if (nounit) {
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c_div(&q__1, &temp, &A(j,j));
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temp.r = q__1.r, temp.i = q__1.i;
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}
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} else {
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i__2 = j - 1;
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for (i = 1; i <= j-1; ++i) {
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r_cnjg(&q__3, &A(i,j));
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i__3 = i;
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q__2.r = q__3.r * X(i).r - q__3.i * X(i).i,
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q__2.i = q__3.r * X(i).i + q__3.i * X(
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i).r;
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q__1.r = temp.r - q__2.r, q__1.i = temp.i -
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q__2.i;
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temp.r = q__1.r, temp.i = q__1.i;
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/* L100: */
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}
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if (nounit) {
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r_cnjg(&q__2, &A(j,j));
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c_div(&q__1, &temp, &q__2);
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temp.r = q__1.r, temp.i = q__1.i;
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}
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}
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i__2 = j;
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X(j).r = temp.r, X(j).i = temp.i;
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/* L110: */
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}
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} else {
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jx = kx;
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i__1 = *n;
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for (j = 1; j <= *n; ++j) {
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ix = kx;
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i__2 = jx;
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temp.r = X(jx).r, temp.i = X(jx).i;
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if (noconj) {
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i__2 = j - 1;
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for (i = 1; i <= j-1; ++i) {
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i__3 = i + j * a_dim1;
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i__4 = ix;
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q__2.r = A(i,j).r * X(ix).r - A(i,j).i * X(
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ix).i, q__2.i = A(i,j).r * X(ix).i +
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A(i,j).i * X(ix).r;
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q__1.r = temp.r - q__2.r, q__1.i = temp.i -
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q__2.i;
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temp.r = q__1.r, temp.i = q__1.i;
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ix += *incx;
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/* L120: */
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}
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if (nounit) {
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c_div(&q__1, &temp, &A(j,j));
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temp.r = q__1.r, temp.i = q__1.i;
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}
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} else {
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i__2 = j - 1;
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for (i = 1; i <= j-1; ++i) {
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r_cnjg(&q__3, &A(i,j));
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i__3 = ix;
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q__2.r = q__3.r * X(ix).r - q__3.i * X(ix).i,
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q__2.i = q__3.r * X(ix).i + q__3.i * X(
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ix).r;
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q__1.r = temp.r - q__2.r, q__1.i = temp.i -
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q__2.i;
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temp.r = q__1.r, temp.i = q__1.i;
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ix += *incx;
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/* L130: */
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}
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if (nounit) {
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r_cnjg(&q__2, &A(j,j));
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c_div(&q__1, &temp, &q__2);
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temp.r = q__1.r, temp.i = q__1.i;
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}
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}
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i__2 = jx;
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X(jx).r = temp.r, X(jx).i = temp.i;
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jx += *incx;
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/* L140: */
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}
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}
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} else {
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if (*incx == 1) {
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for (j = *n; j >= 1; --j) {
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i__1 = j;
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temp.r = X(j).r, temp.i = X(j).i;
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if (noconj) {
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i__1 = j + 1;
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for (i = *n; i >= j+1; --i) {
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i__2 = i + j * a_dim1;
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i__3 = i;
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q__2.r = A(i,j).r * X(i).r - A(i,j).i * X(
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i).i, q__2.i = A(i,j).r * X(i).i +
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A(i,j).i * X(i).r;
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q__1.r = temp.r - q__2.r, q__1.i = temp.i -
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q__2.i;
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temp.r = q__1.r, temp.i = q__1.i;
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/* L150: */
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}
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if (nounit) {
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c_div(&q__1, &temp, &A(j,j));
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temp.r = q__1.r, temp.i = q__1.i;
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}
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} else {
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i__1 = j + 1;
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for (i = *n; i >= j+1; --i) {
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r_cnjg(&q__3, &A(i,j));
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i__2 = i;
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q__2.r = q__3.r * X(i).r - q__3.i * X(i).i,
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q__2.i = q__3.r * X(i).i + q__3.i * X(
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i).r;
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q__1.r = temp.r - q__2.r, q__1.i = temp.i -
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q__2.i;
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temp.r = q__1.r, temp.i = q__1.i;
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/* L160: */
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}
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if (nounit) {
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r_cnjg(&q__2, &A(j,j));
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c_div(&q__1, &temp, &q__2);
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temp.r = q__1.r, temp.i = q__1.i;
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}
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}
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i__1 = j;
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X(j).r = temp.r, X(j).i = temp.i;
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/* L170: */
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}
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} else {
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kx += (*n - 1) * *incx;
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jx = kx;
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for (j = *n; j >= 1; --j) {
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ix = kx;
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i__1 = jx;
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temp.r = X(jx).r, temp.i = X(jx).i;
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if (noconj) {
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i__1 = j + 1;
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for (i = *n; i >= j+1; --i) {
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i__2 = i + j * a_dim1;
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i__3 = ix;
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q__2.r = A(i,j).r * X(ix).r - A(i,j).i * X(
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ix).i, q__2.i = A(i,j).r * X(ix).i +
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A(i,j).i * X(ix).r;
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q__1.r = temp.r - q__2.r, q__1.i = temp.i -
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q__2.i;
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temp.r = q__1.r, temp.i = q__1.i;
|
|
ix -= *incx;
|
|
/* L180: */
|
|
}
|
|
if (nounit) {
|
|
c_div(&q__1, &temp, &A(j,j));
|
|
temp.r = q__1.r, temp.i = q__1.i;
|
|
}
|
|
} else {
|
|
i__1 = j + 1;
|
|
for (i = *n; i >= j+1; --i) {
|
|
r_cnjg(&q__3, &A(i,j));
|
|
i__2 = ix;
|
|
q__2.r = q__3.r * X(ix).r - q__3.i * X(ix).i,
|
|
q__2.i = q__3.r * X(ix).i + q__3.i * X(
|
|
ix).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));
|
|
c_div(&q__1, &temp, &q__2);
|
|
temp.r = q__1.r, temp.i = q__1.i;
|
|
}
|
|
}
|
|
i__1 = jx;
|
|
X(jx).r = temp.r, X(jx).i = temp.i;
|
|
jx -= *incx;
|
|
/* L200: */
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of CTRSV . */
|
|
|
|
} /* ctrsv_ */
|
|
|