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/* clabrd.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__1 = 1;
/* Subroutine */ int clabrd_(integer *m, integer *n, integer *nb, complex *a,
integer *lda, real *d__, real *e, complex *tauq, complex *taup,
complex *x, integer *ldx, complex *y, integer *ldy)
{
/* System generated locals */
integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2,
i__3;
complex q__1;
/* Local variables */
integer i__;
complex alpha;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *), cgemv_(char *, integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, complex *,
integer *), clarfg_(integer *, complex *, complex *,
integer *, complex *), clacgv_(integer *, complex *, integer *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLABRD reduces the first NB rows and columns of a complex general */
/* m by n matrix A to upper or lower real bidiagonal form by a unitary */
/* transformation Q' * A * P, and returns the matrices X and Y which */
/* are needed to apply the transformation to the unreduced part of A. */
/* If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower */
/* bidiagonal form. */
/* This is an auxiliary routine called by CGEBRD */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows in the matrix A. */
/* N (input) INTEGER */
/* The number of columns in the matrix A. */
/* NB (input) INTEGER */
/* The number of leading rows and columns of A to be reduced. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the m by n general matrix to be reduced. */
/* On exit, the first NB rows and columns of the matrix are */
/* overwritten; the rest of the array is unchanged. */
/* If m >= n, elements on and below the diagonal in the first NB */
/* columns, with the array TAUQ, represent the unitary */
/* matrix Q as a product of elementary reflectors; and */
/* elements above the diagonal in the first NB rows, with the */
/* array TAUP, represent the unitary matrix P as a product */
/* of elementary reflectors. */
/* If m < n, elements below the diagonal in the first NB */
/* columns, with the array TAUQ, represent the unitary */
/* matrix Q as a product of elementary reflectors, and */
/* elements on and above the diagonal in the first NB rows, */
/* with the array TAUP, represent the unitary matrix P as */
/* a product of elementary reflectors. */
/* See Further Details. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* D (output) REAL array, dimension (NB) */
/* The diagonal elements of the first NB rows and columns of */
/* the reduced matrix. D(i) = A(i,i). */
/* E (output) REAL array, dimension (NB) */
/* The off-diagonal elements of the first NB rows and columns of */
/* the reduced matrix. */
/* TAUQ (output) COMPLEX array dimension (NB) */
/* The scalar factors of the elementary reflectors which */
/* represent the unitary matrix Q. See Further Details. */
/* TAUP (output) COMPLEX array, dimension (NB) */
/* The scalar factors of the elementary reflectors which */
/* represent the unitary matrix P. See Further Details. */
/* X (output) COMPLEX array, dimension (LDX,NB) */
/* The m-by-nb matrix X required to update the unreduced part */
/* of A. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,M). */
/* Y (output) COMPLEX array, dimension (LDY,NB) */
/* The n-by-nb matrix Y required to update the unreduced part */
/* of A. */
/* LDY (input) INTEGER */
/* The leading dimension of the array Y. LDY >= max(1,N). */
/* Further Details */
/* =============== */
/* The matrices Q and P are represented as products of elementary */
/* reflectors: */
/* Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb) */
/* Each H(i) and G(i) has the form: */
/* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */
/* where tauq and taup are complex scalars, and v and u are complex */
/* vectors. */
/* If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in */
/* A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in */
/* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
/* If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in */
/* A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in */
/* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
/* The elements of the vectors v and u together form the m-by-nb matrix */
/* V and the nb-by-n matrix U' which are needed, with X and Y, to apply */
/* the transformation to the unreduced part of the matrix, using a block */
/* update of the form: A := A - V*Y' - X*U'. */
/* The contents of A on exit are illustrated by the following examples */
/* with nb = 2: */
/* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */
/* ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 ) */
/* ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 ) */
/* ( v1 v2 a a a ) ( v1 1 a a a a ) */
/* ( v1 v2 a a a ) ( v1 v2 a a a a ) */
/* ( v1 v2 a a a ) ( v1 v2 a a a a ) */
/* ( v1 v2 a a a ) */
/* where a denotes an element of the original matrix which is unchanged, */
/* vi denotes an element of the vector defining H(i), and ui an element */
/* of the vector defining G(i). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--d__;
--e;
--tauq;
--taup;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1;
y -= y_offset;
/* Function Body */
if (*m <= 0 || *n <= 0) {
return 0;
}
if (*m >= *n) {
/* Reduce to upper bidiagonal form */
i__1 = *nb;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Update A(i:m,i) */
i__2 = i__ - 1;
clacgv_(&i__2, &y[i__ + y_dim1], ldy);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &a[i__ + a_dim1], lda,
&y[i__ + y_dim1], ldy, &c_b2, &a[i__ + i__ * a_dim1], &
c__1);
i__2 = i__ - 1;
clacgv_(&i__2, &y[i__ + y_dim1], ldy);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &x[i__ + x_dim1], ldx,
&a[i__ * a_dim1 + 1], &c__1, &c_b2, &a[i__ + i__ *
a_dim1], &c__1);
/* Generate reflection Q(i) to annihilate A(i+1:m,i) */
i__2 = i__ + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *m - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
clarfg_(&i__2, &alpha, &a[min(i__3, *m)+ i__ * a_dim1], &c__1, &
tauq[i__]);
i__2 = i__;
d__[i__2] = alpha.r;
if (i__ < *n) {
i__2 = i__ + i__ * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
/* Compute Y(i+1:n,i) */
i__2 = *m - i__ + 1;
i__3 = *n - i__;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + (
i__ + 1) * a_dim1], lda, &a[i__ + i__ * a_dim1], &
c__1, &c_b1, &y[i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ +
a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b1, &
y[i__ * y_dim1 + 1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &y[i__ + 1 +
y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b2, &y[
i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &x[i__ +
x_dim1], ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b1, &
y[i__ * y_dim1 + 1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("Conjugate transpose", &i__2, &i__3, &q__1, &a[(i__ +
1) * a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &
c_b2, &y[i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *n - i__;
cscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
/* Update A(i,i+1:n) */
i__2 = *n - i__;
clacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
clacgv_(&i__, &a[i__ + a_dim1], lda);
i__2 = *n - i__;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__, &q__1, &y[i__ + 1 +
y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b2, &a[i__ + (
i__ + 1) * a_dim1], lda);
clacgv_(&i__, &a[i__ + a_dim1], lda);
i__2 = i__ - 1;
clacgv_(&i__2, &x[i__ + x_dim1], ldx);
i__2 = i__ - 1;
i__3 = *n - i__;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("Conjugate transpose", &i__2, &i__3, &q__1, &a[(i__ +
1) * a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b2, &
a[i__ + (i__ + 1) * a_dim1], lda);
i__2 = i__ - 1;
clacgv_(&i__2, &x[i__ + x_dim1], ldx);
/* Generate reflection P(i) to annihilate A(i,i+2:n) */
i__2 = i__ + (i__ + 1) * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *n - i__;
/* Computing MIN */
i__3 = i__ + 2;
clarfg_(&i__2, &alpha, &a[i__ + min(i__3, *n)* a_dim1], lda, &
taup[i__]);
i__2 = i__;
e[i__2] = alpha.r;
i__2 = i__ + (i__ + 1) * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
/* Compute X(i+1:m,i) */
i__2 = *m - i__;
i__3 = *n - i__;
cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i__ + 1 + (i__
+ 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1],
lda, &c_b1, &x[i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *n - i__;
cgemv_("Conjugate transpose", &i__2, &i__, &c_b2, &y[i__ + 1
+ y_dim1], ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &
c_b1, &x[i__ * x_dim1 + 1], &c__1);
i__2 = *m - i__;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__, &q__1, &a[i__ + 1 +
a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b2, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[(i__ + 1) *
a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, &
c_b1, &x[i__ * x_dim1 + 1], &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &x[i__ + 1 +
x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b2, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *m - i__;
cscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *n - i__;
clacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
}
/* L10: */
}
} else {
/* Reduce to lower bidiagonal form */
i__1 = *nb;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Update A(i,i:n) */
i__2 = *n - i__ + 1;
clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
i__2 = i__ - 1;
clacgv_(&i__2, &a[i__ + a_dim1], lda);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &y[i__ + y_dim1], ldy,
&a[i__ + a_dim1], lda, &c_b2, &a[i__ + i__ * a_dim1],
lda);
i__2 = i__ - 1;
clacgv_(&i__2, &a[i__ + a_dim1], lda);
i__2 = i__ - 1;
clacgv_(&i__2, &x[i__ + x_dim1], ldx);
i__2 = i__ - 1;
i__3 = *n - i__ + 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("Conjugate transpose", &i__2, &i__3, &q__1, &a[i__ *
a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b2, &a[i__ +
i__ * a_dim1], lda);
i__2 = i__ - 1;
clacgv_(&i__2, &x[i__ + x_dim1], ldx);
/* Generate reflection P(i) to annihilate A(i,i+1:n) */
i__2 = i__ + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *n - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
clarfg_(&i__2, &alpha, &a[i__ + min(i__3, *n)* a_dim1], lda, &
taup[i__]);
i__2 = i__;
d__[i__2] = alpha.r;
if (i__ < *m) {
i__2 = i__ + i__ * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
/* Compute X(i+1:m,i) */
i__2 = *m - i__;
i__3 = *n - i__ + 1;
cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i__ + 1 + i__ *
a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b1, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &y[i__ +
y_dim1], ldy, &a[i__ + i__ * a_dim1], lda, &c_b1, &x[
i__ * x_dim1 + 1], &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &a[i__ + 1 +
a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b2, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__ + 1;
cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i__ * a_dim1 +
1], lda, &a[i__ + i__ * a_dim1], lda, &c_b1, &x[i__ *
x_dim1 + 1], &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &x[i__ + 1 +
x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b2, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *m - i__;
cscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *n - i__ + 1;
clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
/* Update A(i+1:m,i) */
i__2 = i__ - 1;
clacgv_(&i__2, &y[i__ + y_dim1], ldy);
i__2 = *m - i__;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &a[i__ + 1 +
a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b2, &a[i__ +
1 + i__ * a_dim1], &c__1);
i__2 = i__ - 1;
clacgv_(&i__2, &y[i__ + y_dim1], ldy);
i__2 = *m - i__;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__, &q__1, &x[i__ + 1 +
x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b2, &a[
i__ + 1 + i__ * a_dim1], &c__1);
/* Generate reflection Q(i) to annihilate A(i+2:m,i) */
i__2 = i__ + 1 + i__ * a_dim1;
alpha.r = a[i__2].r, alpha.i = a[i__2].i;
i__2 = *m - i__;
/* Computing MIN */
i__3 = i__ + 2;
clarfg_(&i__2, &alpha, &a[min(i__3, *m)+ i__ * a_dim1], &c__1,
&tauq[i__]);
i__2 = i__;
e[i__2] = alpha.r;
i__2 = i__ + 1 + i__ * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
/* Compute Y(i+1:n,i) */
i__2 = *m - i__;
i__3 = *n - i__;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + 1
+ (i__ + 1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1]
, &c__1, &c_b1, &y[i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + 1
+ a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &
c_b1, &y[i__ * y_dim1 + 1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("No transpose", &i__2, &i__3, &q__1, &y[i__ + 1 +
y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b2, &y[
i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *m - i__;
cgemv_("Conjugate transpose", &i__2, &i__, &c_b2, &x[i__ + 1
+ x_dim1], ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &
c_b1, &y[i__ * y_dim1 + 1], &c__1);
i__2 = *n - i__;
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("Conjugate transpose", &i__, &i__2, &q__1, &a[(i__ + 1)
* a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &
c_b2, &y[i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *n - i__;
cscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
} else {
i__2 = *n - i__ + 1;
clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
}
/* L20: */
}
}
return 0;
/* End of CLABRD */
} /* clabrd_ */
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