464 lines
13 KiB
C
464 lines
13 KiB
C
/* -- 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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/* Table of constant values */
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static complex c_b1 = {0.f,0.f};
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static complex c_b2 = {1.f,0.f};
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static integer c__3 = 3;
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static integer c__1 = 1;
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/* Subroutine */ int clagge_(integer *m, integer *n, integer *kl, integer *ku,
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real *d, complex *a, integer *lda, integer *iseed, complex *work,
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integer *info)
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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;
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doublereal d__1;
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complex q__1;
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/* Builtin functions */
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double c_abs(complex *);
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void c_div(complex *, complex *, complex *);
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/* Local variables */
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static integer i, j;
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extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
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complex *, integer *, complex *, integer *, complex *, integer *),
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cscal_(integer *, complex *, complex *, integer *), cgemv_(char *
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, integer *, integer *, complex *, complex *, integer *, complex *
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, integer *, complex *, complex *, integer *);
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extern real scnrm2_(integer *, complex *, integer *);
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static complex wa, wb;
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extern /* Subroutine */ int clacgv_(integer *, complex *, integer *);
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static real wn;
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extern /* Subroutine */ int xerbla_(char *, integer *), clarnv_(
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integer *, integer *, integer *, complex *);
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static complex tau;
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/* -- LAPACK auxiliary test routine (version 2.0) --
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Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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Courant Institute, Argonne National Lab, and Rice University
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September 30, 1994
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Purpose
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=======
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CLAGGE generates a complex general m by n matrix A, by pre- and post-
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multiplying a real diagonal matrix D with random unitary matrices:
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A = U*D*V. The lower and upper bandwidths may then be reduced to
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kl and ku by additional unitary transformations.
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Arguments
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=========
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M (input) INTEGER
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The number of rows of the matrix A. M >= 0.
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N (input) INTEGER
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The number of columns of the matrix A. N >= 0.
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KL (input) INTEGER
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The number of nonzero subdiagonals within the band of A.
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0 <= KL <= M-1.
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KU (input) INTEGER
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The number of nonzero superdiagonals within the band of A.
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0 <= KU <= N-1.
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D (input) REAL array, dimension (min(M,N))
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The diagonal elements of the diagonal matrix D.
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A (output) COMPLEX array, dimension (LDA,N)
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The generated m by n matrix A.
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LDA (input) INTEGER
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The leading dimension of the array A. LDA >= M.
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ISEED (input/output) INTEGER array, dimension (4)
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On entry, the seed of the random number generator; the array
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elements must be between 0 and 4095, and ISEED(4) must be
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odd.
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On exit, the seed is updated.
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WORK (workspace) COMPLEX array, dimension (M+N)
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INFO (output) INTEGER
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= 0: successful exit
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< 0: if INFO = -i, the i-th argument had an illegal value
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=====================================================================
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Test the input arguments
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Parameter adjustments */
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--d;
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a_dim1 = *lda;
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a_offset = a_dim1 + 1;
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a -= a_offset;
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--iseed;
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--work;
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/* Function Body */
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*info = 0;
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if (*m < 0) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*kl < 0 || *kl > *m - 1) {
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*info = -3;
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} else if (*ku < 0 || *ku > *n - 1) {
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*info = -4;
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} else if (*lda < max(1,*m)) {
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*info = -7;
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}
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if (*info < 0) {
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i__1 = -(*info);
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xerbla_("CLAGGE", &i__1);
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return 0;
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}
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/* initialize A to diagonal matrix */
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m;
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for (i = 1; i <= i__2; ++i) {
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i__3 = i + j * a_dim1;
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a[i__3].r = 0.f, a[i__3].i = 0.f;
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/* L10: */
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}
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/* L20: */
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}
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i__1 = min(*m,*n);
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for (i = 1; i <= i__1; ++i) {
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i__2 = i + i * a_dim1;
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i__3 = i;
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a[i__2].r = d[i__3], a[i__2].i = 0.f;
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/* L30: */
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}
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/* pre- and post-multiply A by random unitary matrices */
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for (i = min(*m,*n); i >= 1; --i) {
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if (i < *m) {
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/* generate random reflection */
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i__1 = *m - i + 1;
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clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
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i__1 = *m - i + 1;
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wn = scnrm2_(&i__1, &work[1], &c__1);
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d__1 = wn / c_abs(&work[1]);
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q__1.r = d__1 * work[1].r, q__1.i = d__1 * work[1].i;
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wa.r = q__1.r, wa.i = q__1.i;
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if (wn == 0.f) {
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tau.r = 0.f, tau.i = 0.f;
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} else {
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q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
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wb.r = q__1.r, wb.i = q__1.i;
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i__1 = *m - i;
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c_div(&q__1, &c_b2, &wb);
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cscal_(&i__1, &q__1, &work[2], &c__1);
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work[1].r = 1.f, work[1].i = 0.f;
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c_div(&q__1, &wb, &wa);
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d__1 = q__1.r;
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tau.r = d__1, tau.i = 0.f;
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}
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/* multiply A(i:m,i:n) by random reflection from the lef
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t */
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i__1 = *m - i + 1;
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i__2 = *n - i + 1;
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cgemv_("Conjugate transpose", &i__1, &i__2, &c_b2, &a[i + i *
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a_dim1], lda, &work[1], &c__1, &c_b1, &work[*m + 1], &
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c__1);
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i__1 = *m - i + 1;
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i__2 = *n - i + 1;
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q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
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cgerc_(&i__1, &i__2, &q__1, &work[1], &c__1, &work[*m + 1], &c__1,
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&a[i + i * a_dim1], lda);
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}
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if (i < *n) {
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/* generate random reflection */
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i__1 = *n - i + 1;
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clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
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i__1 = *n - i + 1;
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wn = scnrm2_(&i__1, &work[1], &c__1);
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d__1 = wn / c_abs(&work[1]);
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q__1.r = d__1 * work[1].r, q__1.i = d__1 * work[1].i;
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wa.r = q__1.r, wa.i = q__1.i;
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if (wn == 0.f) {
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tau.r = 0.f, tau.i = 0.f;
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} else {
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q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
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wb.r = q__1.r, wb.i = q__1.i;
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i__1 = *n - i;
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c_div(&q__1, &c_b2, &wb);
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cscal_(&i__1, &q__1, &work[2], &c__1);
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work[1].r = 1.f, work[1].i = 0.f;
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c_div(&q__1, &wb, &wa);
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d__1 = q__1.r;
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tau.r = d__1, tau.i = 0.f;
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}
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/* multiply A(i:m,i:n) by random reflection from the rig
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ht */
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i__1 = *m - i + 1;
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i__2 = *n - i + 1;
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cgemv_("No transpose", &i__1, &i__2, &c_b2, &a[i + i * a_dim1],
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lda, &work[1], &c__1, &c_b1, &work[*n + 1], &c__1);
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i__1 = *m - i + 1;
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i__2 = *n - i + 1;
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q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
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cgerc_(&i__1, &i__2, &q__1, &work[*n + 1], &c__1, &work[1], &c__1,
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&a[i + i * a_dim1], lda);
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}
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/* L40: */
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}
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/* Reduce number of subdiagonals to KL and number of superdiagonals
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to KU
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Computing MAX */
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i__2 = *m - 1 - *kl, i__3 = *n - 1 - *ku;
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i__1 = max(i__2,i__3);
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for (i = 1; i <= i__1; ++i) {
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if (*kl <= *ku) {
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/* annihilate subdiagonal elements first (necessary if K
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L = 0)
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Computing MIN */
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i__2 = *m - 1 - *kl;
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if (i <= min(i__2,*n)) {
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/* generate reflection to annihilate A(kl+i+1:m,i
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) */
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i__2 = *m - *kl - i + 1;
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wn = scnrm2_(&i__2, &a[*kl + i + i * a_dim1], &c__1);
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d__1 = wn / c_abs(&a[*kl + i + i * a_dim1]);
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i__2 = *kl + i + i * a_dim1;
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q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
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wa.r = q__1.r, wa.i = q__1.i;
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if (wn == 0.f) {
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tau.r = 0.f, tau.i = 0.f;
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} else {
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i__2 = *kl + i + i * a_dim1;
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q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
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wb.r = q__1.r, wb.i = q__1.i;
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i__2 = *m - *kl - i;
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c_div(&q__1, &c_b2, &wb);
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cscal_(&i__2, &q__1, &a[*kl + i + 1 + i * a_dim1], &c__1);
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i__2 = *kl + i + i * a_dim1;
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a[i__2].r = 1.f, a[i__2].i = 0.f;
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c_div(&q__1, &wb, &wa);
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d__1 = q__1.r;
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tau.r = d__1, tau.i = 0.f;
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}
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/* apply reflection to A(kl+i:m,i+1:n) from the l
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eft */
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i__2 = *m - *kl - i + 1;
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i__3 = *n - i;
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cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*kl + i
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+ (i + 1) * a_dim1], lda, &a[*kl + i + i * a_dim1], &
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c__1, &c_b1, &work[1], &c__1);
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i__2 = *m - *kl - i + 1;
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i__3 = *n - i;
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q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
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cgerc_(&i__2, &i__3, &q__1, &a[*kl + i + i * a_dim1], &c__1, &
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work[1], &c__1, &a[*kl + i + (i + 1) * a_dim1], lda);
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i__2 = *kl + i + i * a_dim1;
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q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
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a[i__2].r = q__1.r, a[i__2].i = q__1.i;
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}
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/* Computing MIN */
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i__2 = *n - 1 - *ku;
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if (i <= min(i__2,*m)) {
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/* generate reflection to annihilate A(i,ku+i+1:n
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) */
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i__2 = *n - *ku - i + 1;
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wn = scnrm2_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
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d__1 = wn / c_abs(&a[i + (*ku + i) * a_dim1]);
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i__2 = i + (*ku + i) * a_dim1;
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q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
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wa.r = q__1.r, wa.i = q__1.i;
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if (wn == 0.f) {
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tau.r = 0.f, tau.i = 0.f;
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} else {
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i__2 = i + (*ku + i) * a_dim1;
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q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
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wb.r = q__1.r, wb.i = q__1.i;
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i__2 = *n - *ku - i;
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c_div(&q__1, &c_b2, &wb);
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cscal_(&i__2, &q__1, &a[i + (*ku + i + 1) * a_dim1], lda);
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i__2 = i + (*ku + i) * a_dim1;
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a[i__2].r = 1.f, a[i__2].i = 0.f;
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c_div(&q__1, &wb, &wa);
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d__1 = q__1.r;
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tau.r = d__1, tau.i = 0.f;
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}
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/* apply reflection to A(i+1:m,ku+i:n) from the r
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ight */
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i__2 = *n - *ku - i + 1;
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clacgv_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
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i__2 = *m - i;
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i__3 = *n - *ku - i + 1;
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cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i + 1 + (*ku +
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i) * a_dim1], lda, &a[i + (*ku + i) * a_dim1], lda, &
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c_b1, &work[1], &c__1);
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i__2 = *m - i;
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i__3 = *n - *ku - i + 1;
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q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
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cgerc_(&i__2, &i__3, &q__1, &work[1], &c__1, &a[i + (*ku + i)
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* a_dim1], lda, &a[i + 1 + (*ku + i) * a_dim1], lda);
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i__2 = i + (*ku + i) * a_dim1;
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q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
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a[i__2].r = q__1.r, a[i__2].i = q__1.i;
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}
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} else {
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/* annihilate superdiagonal elements first (necessary if
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KU = 0)
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Computing MIN */
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i__2 = *n - 1 - *ku;
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if (i <= min(i__2,*m)) {
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/* generate reflection to annihilate A(i,ku+i+1:n
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) */
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i__2 = *n - *ku - i + 1;
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wn = scnrm2_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
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d__1 = wn / c_abs(&a[i + (*ku + i) * a_dim1]);
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i__2 = i + (*ku + i) * a_dim1;
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q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
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wa.r = q__1.r, wa.i = q__1.i;
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if (wn == 0.f) {
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tau.r = 0.f, tau.i = 0.f;
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} else {
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i__2 = i + (*ku + i) * a_dim1;
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q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
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wb.r = q__1.r, wb.i = q__1.i;
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i__2 = *n - *ku - i;
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c_div(&q__1, &c_b2, &wb);
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cscal_(&i__2, &q__1, &a[i + (*ku + i + 1) * a_dim1], lda);
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i__2 = i + (*ku + i) * a_dim1;
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a[i__2].r = 1.f, a[i__2].i = 0.f;
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c_div(&q__1, &wb, &wa);
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d__1 = q__1.r;
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tau.r = d__1, tau.i = 0.f;
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}
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/* apply reflection to A(i+1:m,ku+i:n) from the r
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ight */
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i__2 = *n - *ku - i + 1;
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clacgv_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
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i__2 = *m - i;
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i__3 = *n - *ku - i + 1;
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cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i + 1 + (*ku +
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i) * a_dim1], lda, &a[i + (*ku + i) * a_dim1], lda, &
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c_b1, &work[1], &c__1);
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i__2 = *m - i;
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i__3 = *n - *ku - i + 1;
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q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
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cgerc_(&i__2, &i__3, &q__1, &work[1], &c__1, &a[i + (*ku + i)
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* a_dim1], lda, &a[i + 1 + (*ku + i) * a_dim1], lda);
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i__2 = i + (*ku + i) * a_dim1;
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q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
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a[i__2].r = q__1.r, a[i__2].i = q__1.i;
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}
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/* Computing MIN */
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i__2 = *m - 1 - *kl;
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if (i <= min(i__2,*n)) {
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/* generate reflection to annihilate A(kl+i+1:m,i
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) */
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i__2 = *m - *kl - i + 1;
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wn = scnrm2_(&i__2, &a[*kl + i + i * a_dim1], &c__1);
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d__1 = wn / c_abs(&a[*kl + i + i * a_dim1]);
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i__2 = *kl + i + i * a_dim1;
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q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
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wa.r = q__1.r, wa.i = q__1.i;
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if (wn == 0.f) {
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tau.r = 0.f, tau.i = 0.f;
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} else {
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i__2 = *kl + i + i * a_dim1;
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q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
|
|
wb.r = q__1.r, wb.i = q__1.i;
|
|
i__2 = *m - *kl - i;
|
|
c_div(&q__1, &c_b2, &wb);
|
|
cscal_(&i__2, &q__1, &a[*kl + i + 1 + i * a_dim1], &c__1);
|
|
i__2 = *kl + i + i * a_dim1;
|
|
a[i__2].r = 1.f, a[i__2].i = 0.f;
|
|
c_div(&q__1, &wb, &wa);
|
|
d__1 = q__1.r;
|
|
tau.r = d__1, tau.i = 0.f;
|
|
}
|
|
|
|
/* apply reflection to A(kl+i:m,i+1:n) from the l
|
|
eft */
|
|
|
|
i__2 = *m - *kl - i + 1;
|
|
i__3 = *n - i;
|
|
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*kl + i
|
|
+ (i + 1) * a_dim1], lda, &a[*kl + i + i * a_dim1], &
|
|
c__1, &c_b1, &work[1], &c__1);
|
|
i__2 = *m - *kl - i + 1;
|
|
i__3 = *n - i;
|
|
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
|
|
cgerc_(&i__2, &i__3, &q__1, &a[*kl + i + i * a_dim1], &c__1, &
|
|
work[1], &c__1, &a[*kl + i + (i + 1) * a_dim1], lda);
|
|
i__2 = *kl + i + i * a_dim1;
|
|
q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
|
|
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
|
|
}
|
|
}
|
|
|
|
i__2 = *m;
|
|
for (j = *kl + i + 1; j <= i__2; ++j) {
|
|
i__3 = j + i * a_dim1;
|
|
a[i__3].r = 0.f, a[i__3].i = 0.f;
|
|
/* L50: */
|
|
}
|
|
|
|
i__2 = *n;
|
|
for (j = *ku + i + 1; j <= i__2; ++j) {
|
|
i__3 = i + j * a_dim1;
|
|
a[i__3].r = 0.f, a[i__3].i = 0.f;
|
|
/* L60: */
|
|
}
|
|
/* L70: */
|
|
}
|
|
return 0;
|
|
|
|
/* End of CLAGGE */
|
|
|
|
} /* clagge_ */
|
|
|