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hypre/lapack/dlabrd.c

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/*BHEADER**********************************************************************
* Copyright (c) 2006 The Regents of the University of California.
* Produced at the Lawrence Livermore National Laboratory.
* Written by the HYPRE team. UCRL-CODE-222953.
* All rights reserved.
*
* This file is part of HYPRE (see http://www.llnl.gov/CASC/hypre/).
* Please see the COPYRIGHT_and_LICENSE file for the copyright notice,
* disclaimer, contact information and the GNU Lesser General Public License.
*
* HYPRE is free software; you can redistribute it and/or modify it under the
* terms of the GNU General Public License (as published by the Free Software
* Foundation) version 2.1 dated February 1999.
*
* HYPRE is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the IMPLIED WARRANTY OF MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the terms and conditions of the GNU General
* Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
* $Revision$
***********************************************************************EHEADER*/
#include "../blas/hypre_blas.h"
#include "hypre_lapack.h"
#include "f2c.h"
/* 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)
{
/* -- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
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 (output) 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).
=====================================================================
Quick return if possible
Parameter adjustments */
/* Table of constant values */
static doublereal c_b4 = -1.;
static doublereal c_b5 = 1.;
static integer c__1 = 1;
static doublereal c_b16 = 0.;
/* System generated locals */
integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2,
i__3;
/* Local variables */
static 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 *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define x_ref(a_1,a_2) x[(a_2)*x_dim1 + a_1]
#define y_ref(a_1,a_2) y[(a_2)*y_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--d__;
--e;
--tauq;
--taup;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1 * 1;
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_ref(i__, 1), lda, &
y_ref(i__, 1), ldy, &c_b5, &a_ref(i__, i__), &c__1);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &x_ref(i__, 1), ldx, &
a_ref(1, i__), &c__1, &c_b5, &a_ref(i__, i__), &c__1);
/* Generate reflection Q(i) to annihilate A(i+1:m,i)
Computing MIN */
i__2 = i__ + 1;
i__3 = *m - i__ + 1;
dlarfg_(&i__3, &a_ref(i__, i__), &a_ref(min(i__2,*m), i__), &c__1,
&tauq[i__]);
d__[i__] = a_ref(i__, i__);
if (i__ < *n) {
a_ref(i__, i__) = 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_ref(i__, i__ + 1),
lda, &a_ref(i__, i__), &c__1, &c_b16, &y_ref(i__ + 1,
i__), &c__1);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
dgemv_("Transpose", &i__2, &i__3, &c_b5, &a_ref(i__, 1), lda,
&a_ref(i__, i__), &c__1, &c_b16, &y_ref(1, i__), &
c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &y_ref(i__ + 1, 1)
, ldy, &y_ref(1, i__), &c__1, &c_b5, &y_ref(i__ + 1,
i__), &c__1);
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
dgemv_("Transpose", &i__2, &i__3, &c_b5, &x_ref(i__, 1), ldx,
&a_ref(i__, i__), &c__1, &c_b16, &y_ref(1, i__), &
c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
dgemv_("Transpose", &i__2, &i__3, &c_b4, &a_ref(1, i__ + 1),
lda, &y_ref(1, i__), &c__1, &c_b5, &y_ref(i__ + 1,
i__), &c__1);
i__2 = *n - i__;
dscal_(&i__2, &tauq[i__], &y_ref(i__ + 1, i__), &c__1);
/* Update A(i,i+1:n) */
i__2 = *n - i__;
dgemv_("No transpose", &i__2, &i__, &c_b4, &y_ref(i__ + 1, 1),
ldy, &a_ref(i__, 1), lda, &c_b5, &a_ref(i__, i__ + 1)
, lda);
i__2 = i__ - 1;
i__3 = *n - i__;
dgemv_("Transpose", &i__2, &i__3, &c_b4, &a_ref(1, i__ + 1),
lda, &x_ref(i__, 1), ldx, &c_b5, &a_ref(i__, i__ + 1),
lda);
/* Generate reflection P(i) to annihilate A(i,i+2:n)
Computing MIN */
i__2 = i__ + 2;
i__3 = *n - i__;
dlarfg_(&i__3, &a_ref(i__, i__ + 1), &a_ref(i__, min(i__2,*n))
, lda, &taup[i__]);
e[i__] = a_ref(i__, i__ + 1);
a_ref(i__, i__ + 1) = 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_ref(i__ + 1,
i__ + 1), lda, &a_ref(i__, i__ + 1), lda, &c_b16, &
x_ref(i__ + 1, i__), &c__1);
i__2 = *n - i__;
dgemv_("Transpose", &i__2, &i__, &c_b5, &y_ref(i__ + 1, 1),
ldy, &a_ref(i__, i__ + 1), lda, &c_b16, &x_ref(1, i__)
, &c__1);
i__2 = *m - i__;
dgemv_("No transpose", &i__2, &i__, &c_b4, &a_ref(i__ + 1, 1),
lda, &x_ref(1, i__), &c__1, &c_b5, &x_ref(i__ + 1,
i__), &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
dgemv_("No transpose", &i__2, &i__3, &c_b5, &a_ref(1, i__ + 1)
, lda, &a_ref(i__, i__ + 1), lda, &c_b16, &x_ref(1,
i__), &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &x_ref(i__ + 1, 1)
, ldx, &x_ref(1, i__), &c__1, &c_b5, &x_ref(i__ + 1,
i__), &c__1);
i__2 = *m - i__;
dscal_(&i__2, &taup[i__], &x_ref(i__ + 1, i__), &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_ref(i__, 1), ldy, &
a_ref(i__, 1), lda, &c_b5, &a_ref(i__, i__), lda);
i__2 = i__ - 1;
i__3 = *n - i__ + 1;
dgemv_("Transpose", &i__2, &i__3, &c_b4, &a_ref(1, i__), lda, &
x_ref(i__, 1), ldx, &c_b5, &a_ref(i__, i__), lda);
/* Generate reflection P(i) to annihilate A(i,i+1:n)
Computing MIN */
i__2 = i__ + 1;
i__3 = *n - i__ + 1;
dlarfg_(&i__3, &a_ref(i__, i__), &a_ref(i__, min(i__2,*n)), lda, &
taup[i__]);
d__[i__] = a_ref(i__, i__);
if (i__ < *m) {
a_ref(i__, i__) = 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_ref(i__ + 1,
i__), lda, &a_ref(i__, i__), lda, &c_b16, &x_ref(i__
+ 1, i__), &c__1);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
dgemv_("Transpose", &i__2, &i__3, &c_b5, &y_ref(i__, 1), ldy,
&a_ref(i__, i__), lda, &c_b16, &x_ref(1, i__), &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &a_ref(i__ + 1, 1)
, lda, &x_ref(1, i__), &c__1, &c_b5, &x_ref(i__ + 1,
i__), &c__1);
i__2 = i__ - 1;
i__3 = *n - i__ + 1;
dgemv_("No transpose", &i__2, &i__3, &c_b5, &a_ref(1, i__),
lda, &a_ref(i__, i__), lda, &c_b16, &x_ref(1, i__), &
c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &x_ref(i__ + 1, 1)
, ldx, &x_ref(1, i__), &c__1, &c_b5, &x_ref(i__ + 1,
i__), &c__1);
i__2 = *m - i__;
dscal_(&i__2, &taup[i__], &x_ref(i__ + 1, i__), &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_ref(i__ + 1, 1)
, lda, &y_ref(i__, 1), ldy, &c_b5, &a_ref(i__ + 1,
i__), &c__1);
i__2 = *m - i__;
dgemv_("No transpose", &i__2, &i__, &c_b4, &x_ref(i__ + 1, 1),
ldx, &a_ref(1, i__), &c__1, &c_b5, &a_ref(i__ + 1,
i__), &c__1);
/* Generate reflection Q(i) to annihilate A(i+2:m,i)
Computing MIN */
i__2 = i__ + 2;
i__3 = *m - i__;
dlarfg_(&i__3, &a_ref(i__ + 1, i__), &a_ref(min(i__2,*m), i__)
, &c__1, &tauq[i__]);
e[i__] = a_ref(i__ + 1, i__);
a_ref(i__ + 1, i__) = 1.;
/* Compute Y(i+1:n,i) */
i__2 = *m - i__;
i__3 = *n - i__;
dgemv_("Transpose", &i__2, &i__3, &c_b5, &a_ref(i__ + 1, i__
+ 1), lda, &a_ref(i__ + 1, i__), &c__1, &c_b16, &
y_ref(i__ + 1, i__), &c__1);
i__2 = *m - i__;
i__3 = i__ - 1;
dgemv_("Transpose", &i__2, &i__3, &c_b5, &a_ref(i__ + 1, 1),
lda, &a_ref(i__ + 1, i__), &c__1, &c_b16, &y_ref(1,
i__), &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
dgemv_("No transpose", &i__2, &i__3, &c_b4, &y_ref(i__ + 1, 1)
, ldy, &y_ref(1, i__), &c__1, &c_b5, &y_ref(i__ + 1,
i__), &c__1);
i__2 = *m - i__;
dgemv_("Transpose", &i__2, &i__, &c_b5, &x_ref(i__ + 1, 1),
ldx, &a_ref(i__ + 1, i__), &c__1, &c_b16, &y_ref(1,
i__), &c__1);
i__2 = *n - i__;
dgemv_("Transpose", &i__, &i__2, &c_b4, &a_ref(1, i__ + 1),
lda, &y_ref(1, i__), &c__1, &c_b5, &y_ref(i__ + 1,
i__), &c__1);
i__2 = *n - i__;
dscal_(&i__2, &tauq[i__], &y_ref(i__ + 1, i__), &c__1);
}
/* L20: */
}
}
return 0;
/* End of DLABRD */
} /* dlabrd_ */
#undef y_ref
#undef x_ref
#undef a_ref
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