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hypre/lapack/dgebd2.c
falgout e3181f26b1 Added 64 bit feature using HYPRE_Int (see tracker [issue489] for details). 
Changed MPI routines to hypre_MPI routines.
Added hypre_printf, etc. routines.
Added AUTOTEST tests to look for 'int' and 'MPI_' calls.
Added a new approach for the Fortran interface (not implemented everywhere yet).
2010-12-20 19:27:44 +00:00

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#include "hypre_lapack.h"
#include "f2c.h"
/* Subroutine */ HYPRE_Int dgebd2_(integer *m, integer *n, doublereal *a, integer *
lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal *
taup, doublereal *work, integer *info)
{
/* -- LAPACK 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
=======
DGEBD2 reduces a real general m by n matrix A to upper or lower
bidiagonal form B by an orthogonal transformation: Q' * A * P = B.
If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
Arguments
=========
M (input) INTEGER
The number of rows in the matrix A. M >= 0.
N (input) INTEGER
The number of columns in the matrix A. N >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the m by n general matrix to be reduced.
On exit,
if m >= n, the diagonal and the first superdiagonal are
overwritten with the upper bidiagonal matrix B; the
elements below the diagonal, with the array TAUQ, represent
the orthogonal matrix Q as a product of elementary
reflectors, and the elements above the first superdiagonal,
with the array TAUP, represent the orthogonal matrix P as
a product of elementary reflectors;
if m < n, the diagonal and the first subdiagonal are
overwritten with the lower bidiagonal matrix B; the
elements below the first subdiagonal, with the array TAUQ,
represent the orthogonal matrix Q as a product of
elementary reflectors, and the elements above the diagonal,
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 (min(M,N))
The diagonal elements of the bidiagonal matrix B:
D(i) = A(i,i).
E (output) DOUBLE PRECISION array, dimension (min(M,N)-1)
The off-diagonal elements of the bidiagonal matrix B:
if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
TAUQ (output) DOUBLE PRECISION array dimension (min(M,N))
The scalar factors of the elementary reflectors which
represent the orthogonal matrix Q. See Further Details.
TAUP (output) DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors which
represent the orthogonal matrix P. See Further Details.
WORK (workspace) DOUBLE PRECISION array, dimension (max(M,N))
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
The matrices Q and P are represented as products of elementary
reflectors:
If m >= n,
Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1)
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;
v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);
u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n);
tauq is stored in TAUQ(i) and taup in TAUP(i).
If m < n,
Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m)
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;
v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
u(1:i-1) = 0, u(i) = 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).
The contents of A on exit are illustrated by the following examples:
m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):
( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 )
( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 )
( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 )
( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 )
( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 )
( v1 v2 v3 v4 v5 )
where d and e denote diagonal and off-diagonal elements of B, vi
denotes an element of the vector defining H(i), and ui an element of
the vector defining G(i).
=====================================================================
Test the input parameters
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i__;
extern /* Subroutine */ HYPRE_Int dlarf_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *), dlarfg_(integer *, doublereal *,
doublereal *, integer *, doublereal *), xerbla_(char *, integer *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--d__;
--e;
--tauq;
--taup;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("DGEBD2", &i__1);
return 0;
}
if (*m >= *n) {
/* Reduce to upper bidiagonal form */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Generate elementary reflector H(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__);
a_ref(i__, i__) = 1.;
/* Apply H(i) to A(i:m,i+1:n) from the left */
i__2 = *m - i__ + 1;
i__3 = *n - i__;
dlarf_("Left", &i__2, &i__3, &a_ref(i__, i__), &c__1, &tauq[i__],
&a_ref(i__, i__ + 1), lda, &work[1]);
a_ref(i__, i__) = d__[i__];
if (i__ < *n) {
/* Generate elementary reflector G(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.;
/* Apply G(i) to A(i+1:m,i+1:n) from the right */
i__2 = *m - i__;
i__3 = *n - i__;
dlarf_("Right", &i__2, &i__3, &a_ref(i__, i__ + 1), lda, &
taup[i__], &a_ref(i__ + 1, i__ + 1), lda, &work[1]);
a_ref(i__, i__ + 1) = e[i__];
} else {
taup[i__] = 0.;
}
/* L10: */
}
} else {
/* Reduce to lower bidiagonal form */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Generate elementary reflector G(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__);
a_ref(i__, i__) = 1.;
/* Apply G(i) to A(i+1:m,i:n) from the right
Computing MIN */
i__2 = i__ + 1;
i__3 = *m - i__;
i__4 = *n - i__ + 1;
dlarf_("Right", &i__3, &i__4, &a_ref(i__, i__), lda, &taup[i__], &
a_ref(min(i__2,*m), i__), lda, &work[1]);
a_ref(i__, i__) = d__[i__];
if (i__ < *m) {
/* Generate elementary reflector H(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.;
/* Apply H(i) to A(i+1:m,i+1:n) from the left */
i__2 = *m - i__;
i__3 = *n - i__;
dlarf_("Left", &i__2, &i__3, &a_ref(i__ + 1, i__), &c__1, &
tauq[i__], &a_ref(i__ + 1, i__ + 1), lda, &work[1]);
a_ref(i__ + 1, i__) = e[i__];
} else {
tauq[i__] = 0.;
}
/* L20: */
}
}
return 0;
/* End of DGEBD2 */
} /* dgebd2_ */
#undef a_ref
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