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/* dlabrd.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 doublereal c_b4 = -1.;
static doublereal c_b5 = 1.;
static integer c__1 = 1;
static doublereal c_b16 = 0.;
/* Subroutine */ int dlabrd_(integer *m, integer *n, integer *nb, doublereal *
a, integer *lda, doublereal *d__, doublereal *e, doublereal *tauq,
doublereal *taup, doublereal *x, integer *ldx, doublereal *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;
/* Local variables */
integer i__;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *), dgemv_(char *, integer *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *), dlarfg_(integer *, doublereal *,
doublereal *, integer *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLABRD reduces the first NB rows and columns of a real general */
/* m by n matrix A to upper or lower bidiagonal form by an orthogonal */
/* 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 DGEBRD */
/* 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) DOUBLE PRECISION 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 orthogonal */
/* matrix Q as a product of elementary reflectors; and */
/* elements above the diagonal in the first NB rows, with the */
/* array TAUP, represent the orthogonal 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 orthogonal */
/* 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 orthogonal 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) DOUBLE PRECISION array, dimension (NB) */
/* The diagonal elements of the first NB rows and columns of */
/* the reduced matrix. D(i) = A(i,i). */
/* E (output) DOUBLE PRECISION array, dimension (NB) */
/* The off-diagonal elements of the first NB rows and columns of */
/* the reduced matrix. */
/* TAUQ (output) DOUBLE PRECISION array dimension (NB) */
/* The scalar factors of the elementary reflectors which */
/* represent the orthogonal matrix Q. See Further Details. */
/* TAUP (output) DOUBLE PRECISION array, dimension (NB) */
/* The scalar factors of the elementary reflectors which */
/* represent the orthogonal matrix P. See Further Details. */
/* X (output) DOUBLE PRECISION 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 >= M. */
/* Y (output) DOUBLE PRECISION 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 >= 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 real scalars, and v and u are real 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 = *m - i__ + 1;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda,
&y[i__ + y_dim1], ldy, &c_b5, &a[i__ + i__ * a_dim1], &
c__1);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx,
&a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + i__ *
a_dim1], &c__1);
/* Generate reflection Q(i) to annihilate A(i+1:m,i) */
i__2 = *m - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3, *m)+ i__ *
a_dim1], &c__1, &tauq[i__]);
d__[i__] = a[i__ + i__ * a_dim1];
if (i__ < *n) {
a[i__ + i__ * a_dim1] = 1.;
/* Compute Y(i+1:n,i) */
i__2 = *m - i__ + 1;
i__3 = *n - i__;
dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) *
a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &
y[i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1],
lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ *
y_dim1 + 1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 +
y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[
i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
dgemv_("Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1],
ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ *
y_dim1 + 1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
dgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) *
a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5,
&y[i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *n - i__;
dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
/* Update A(i,i+1:n) */
i__2 = *n - i__;
dgemv_("No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 +
y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b5, &a[i__ + (
i__ + 1) * a_dim1], lda);
i__2 = i__ - 1;
i__3 = *n - i__;
dgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) *
a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b5, &a[
i__ + (i__ + 1) * a_dim1], lda);
/* Generate reflection P(i) to annihilate A(i,i+2:n) */
i__2 = *n - i__;
/* Computing MIN */
i__3 = i__ + 2;
dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min(
i__3, *n)* a_dim1], lda, &taup[i__]);
e[i__] = a[i__ + (i__ + 1) * a_dim1];
a[i__ + (i__ + 1) * a_dim1] = 1.;
/* Compute X(i+1:m,i) */
i__2 = *m - i__;
i__3 = *n - i__;
dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__
+ 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1],
lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *n - i__;
dgemv_("Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1],
ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[
i__ * x_dim1 + 1], &c__1);
i__2 = *m - i__;
dgemv_("No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 +
a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) *
a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, &
c_b16, &x[i__ * x_dim1 + 1], &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 +
x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *m - i__;
dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
}
/* 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;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy,
&a[i__ + a_dim1], lda, &c_b5, &a[i__ + i__ * a_dim1],
lda);
i__2 = i__ - 1;
i__3 = *n - i__ + 1;
dgemv_("Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1],
lda, &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + i__ * a_dim1],
lda);
/* Generate reflection P(i) to annihilate A(i,i+1:n) */
i__2 = *n - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3, *n)*
a_dim1], lda, &taup[i__]);
d__[i__] = a[i__ + i__ * a_dim1];
if (i__ < *m) {
a[i__ + i__ * a_dim1] = 1.;
/* Compute X(i+1:m,i) */
i__2 = *m - i__;
i__3 = *n - i__ + 1;
dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + i__ *
a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &
x[i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
dgemv_("Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1],
ldy, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ *
x_dim1 + 1], &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 +
a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = i__ - 1;
i__3 = *n - i__ + 1;
dgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ * a_dim1 +
1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ *
x_dim1 + 1], &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 +
x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
i__ + 1 + i__ * x_dim1], &c__1);
i__2 = *m - i__;
dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
/* Update A(i+1:m,i) */
i__2 = *m - i__;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 +
a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b5, &a[i__ +
1 + i__ * a_dim1], &c__1);
i__2 = *m - i__;
dgemv_("No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 +
x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[
i__ + 1 + i__ * a_dim1], &c__1);
/* Generate reflection Q(i) to annihilate A(i+2:m,i) */
i__2 = *m - i__;
/* Computing MIN */
i__3 = i__ + 2;
dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *m)+
i__ * a_dim1], &c__1, &tauq[i__]);
e[i__] = a[i__ + 1 + i__ * a_dim1];
a[i__ + 1 + i__ * a_dim1] = 1.;
/* Compute Y(i+1:n,i) */
i__2 = *m - i__;
i__3 = *n - i__;
dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ +
1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1,
&c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
dgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1],
lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[
i__ * y_dim1 + 1], &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 +
y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[
i__ + 1 + i__ * y_dim1], &c__1);
i__2 = *m - i__;
dgemv_("Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1],
ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[
i__ * y_dim1 + 1], &c__1);
i__2 = *n - i__;
dgemv_("Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1
+ 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__
+ 1 + i__ * y_dim1], &c__1);
i__2 = *n - i__;
dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
}
/* L20: */
}
}
return 0;
/* End of DLABRD */
} /* dlabrd_ */
|
