/* -- translated by f2c (version 20100827).
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
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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*/
#include "f2c.h"
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
static integer c__65 = 65;
static doublereal c_b25 = -1.;
static doublereal c_b26 = 1.;
/* > \brief \b DGEHRD
=========== DOCUMENTATION ===========
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Definition:
===========
SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER IHI, ILO, INFO, LDA, LWORK, N
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
> \par Purpose:
=============
>
> \verbatim
>
> DGEHRD reduces a real general matrix A to upper Hessenberg form H by
> an orthogonal similarity transformation: Q**T * A * Q = H .
> \endverbatim
Arguments:
==========
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix A. N >= 0.
> \endverbatim
>
> \param[in] ILO
> \verbatim
> ILO is INTEGER
> \endverbatim
>
> \param[in] IHI
> \verbatim
> IHI is INTEGER
>
> It is assumed that A is already upper triangular in rows
> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
> set by a previous call to DGEBAL; otherwise they should be
> set to 1 and N respectively. See Further Details.
> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
> \endverbatim
>
> \param[in,out] A
> \verbatim
> A is DOUBLE PRECISION array, dimension (LDA,N)
> On entry, the N-by-N general matrix to be reduced.
> On exit, the upper triangle and the first subdiagonal of A
> are overwritten with the upper Hessenberg matrix H, and the
> elements below the first subdiagonal, with the array TAU,
> represent the orthogonal matrix Q as a product of elementary
> reflectors. See Further Details.
> \endverbatim
>
> \param[in] LDA
> \verbatim
> LDA is INTEGER
> The leading dimension of the array A. LDA >= max(1,N).
> \endverbatim
>
> \param[out] TAU
> \verbatim
> TAU is DOUBLE PRECISION array, dimension (N-1)
> The scalar factors of the elementary reflectors (see Further
> Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
> zero.
> \endverbatim
>
> \param[out] WORK
> \verbatim
> WORK is DOUBLE PRECISION array, dimension (LWORK)
> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
> \endverbatim
>
> \param[in] LWORK
> \verbatim
> LWORK is INTEGER
> The length of the array WORK. LWORK >= max(1,N).
> For optimum performance LWORK >= N*NB, where NB is the
> optimal blocksize.
>
> If LWORK = -1, then a workspace query is assumed; the routine
> only calculates the optimal size of the WORK array, returns
> this value as the first entry of the WORK array, and no error
> message related to LWORK is issued by XERBLA.
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0: successful exit
> < 0: if INFO = -i, the i-th argument had an illegal value.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date November 2011
> \ingroup doubleGEcomputational
> \par Further Details:
=====================
>
> \verbatim
>
> The matrix Q is represented as a product of (ihi-ilo) elementary
> reflectors
>
> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
>
> Each H(i) has the form
>
> H(i) = I - tau * v * v**T
>
> where tau is a real scalar, and v is a real vector with
> v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
> exit in A(i+2:ihi,i), and tau in TAU(i).
>
> The contents of A are illustrated by the following example, with
> n = 7, ilo = 2 and ihi = 6:
>
> on entry, on exit,
>
> ( a a a a a a a ) ( a a h h h h a )
> ( a a a a a a ) ( a h h h h a )
> ( a a a a a a ) ( h h h h h h )
> ( a a a a a a ) ( v2 h h h h h )
> ( a a a a a a ) ( v2 v3 h h h h )
> ( a a a a a a ) ( v2 v3 v4 h h h )
> ( a ) ( a )
>
> where a denotes an element of the original matrix A, h denotes a
> modified element of the upper Hessenberg matrix H, and vi denotes an
> element of the vector defining H(i).
>
> This file is a slight modification of LAPACK-3.0's DGEHRD
> subroutine incorporating improvements proposed by Quintana-Orti and
> Van de Geijn (2006). (See DLAHR2.)
> \endverbatim
>
=====================================================================
Subroutine */ int igraphdgehrd_(integer *n, integer *ilo, integer *ihi,
doublereal *a, integer *lda, doublereal *tau, doublereal *work,
integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, j;
doublereal t[4160] /* was [65][64] */;
integer ib;
doublereal ei;
integer nb, nh, nx, iws;
extern /* Subroutine */ int igraphdgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
integer nbmin, iinfo;
extern /* Subroutine */ int igraphdtrmm_(char *, char *, char *, char *,
integer *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *), igraphdaxpy_(
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *), igraphdgehd2_(integer *, integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *), igraphdlahr2_(
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *),
igraphdlarfb_(char *, char *, char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *), igraphxerbla_(char *, integer *, ftnlen);
extern integer igraphilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK computational routine (version 3.4.0) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
November 2011
=====================================================================
Test the input parameters
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/* Computing MIN */
i__1 = 64, i__2 = igraphilaenv_(&c__1, "DGEHRD", " ", n, ilo, ihi, &c_n1, (
ftnlen)6, (ftnlen)1);
nb = min(i__1,i__2);
lwkopt = *n * nb;
work[1] = (doublereal) lwkopt;
lquery = *lwork == -1;
if (*n < 0) {
*info = -1;
} else if (*ilo < 1 || *ilo > max(1,*n)) {
*info = -2;
} else if (*ihi < min(*ilo,*n) || *ihi > *n) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*lwork < max(1,*n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
igraphxerbla_("DGEHRD", &i__1, (ftnlen)6);
return 0;
} else if (lquery) {
return 0;
}
/* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
i__1 = *ilo - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
tau[i__] = 0.;
/* L10: */
}
i__1 = *n - 1;
for (i__ = max(1,*ihi); i__ <= i__1; ++i__) {
tau[i__] = 0.;
/* L20: */
}
/* Quick return if possible */
nh = *ihi - *ilo + 1;
if (nh <= 1) {
work[1] = 1.;
return 0;
}
/* Determine the block size
Computing MIN */
i__1 = 64, i__2 = igraphilaenv_(&c__1, "DGEHRD", " ", n, ilo, ihi, &c_n1, (
ftnlen)6, (ftnlen)1);
nb = min(i__1,i__2);
nbmin = 2;
iws = 1;
if (nb > 1 && nb < nh) {
/* Determine when to cross over from blocked to unblocked code
(last block is always handled by unblocked code)
Computing MAX */
i__1 = nb, i__2 = igraphilaenv_(&c__3, "DGEHRD", " ", n, ilo, ihi, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
if (nx < nh) {
/* Determine if workspace is large enough for blocked code */
iws = *n * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: determine the
minimum value of NB, and reduce NB or force use of
unblocked code
Computing MAX */
i__1 = 2, i__2 = igraphilaenv_(&c__2, "DGEHRD", " ", n, ilo, ihi, &
c_n1, (ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
if (*lwork >= *n * nbmin) {
nb = *lwork / *n;
} else {
nb = 1;
}
}
}
}
ldwork = *n;
if (nb < nbmin || nb >= nh) {
/* Use unblocked code below */
i__ = *ilo;
} else {
/* Use blocked code */
i__1 = *ihi - 1 - nx;
i__2 = nb;
for (i__ = *ilo; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = nb, i__4 = *ihi - i__;
ib = min(i__3,i__4);
/* Reduce columns i:i+ib-1 to Hessenberg form, returning the
matrices V and T of the block reflector H = I - V*T*V**T
which performs the reduction, and also the matrix Y = A*V*T */
igraphdlahr2_(ihi, &i__, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], t, &
c__65, &work[1], &ldwork);
/* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the
right, computing A := A - Y * V**T. V(i+ib,ib-1) must be set
to 1 */
ei = a[i__ + ib + (i__ + ib - 1) * a_dim1];
a[i__ + ib + (i__ + ib - 1) * a_dim1] = 1.;
i__3 = *ihi - i__ - ib + 1;
igraphdgemm_("No transpose", "Transpose", ihi, &i__3, &ib, &c_b25, &
work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda, &
c_b26, &a[(i__ + ib) * a_dim1 + 1], lda);
a[i__ + ib + (i__ + ib - 1) * a_dim1] = ei;
/* Apply the block reflector H to A(1:i,i+1:i+ib-1) from the
right */
i__3 = ib - 1;
igraphdtrmm_("Right", "Lower", "Transpose", "Unit", &i__, &i__3, &c_b26,
&a[i__ + 1 + i__ * a_dim1], lda, &work[1], &ldwork);
i__3 = ib - 2;
for (j = 0; j <= i__3; ++j) {
igraphdaxpy_(&i__, &c_b25, &work[ldwork * j + 1], &c__1, &a[(i__ +
j + 1) * a_dim1 + 1], &c__1);
/* L30: */
}
/* Apply the block reflector H to A(i+1:ihi,i+ib:n) from the
left */
i__3 = *ihi - i__;
i__4 = *n - i__ - ib + 1;
igraphdlarfb_("Left", "Transpose", "Forward", "Columnwise", &i__3, &
i__4, &ib, &a[i__ + 1 + i__ * a_dim1], lda, t, &c__65, &a[
i__ + 1 + (i__ + ib) * a_dim1], lda, &work[1], &ldwork);
/* L40: */
}
}
/* Use unblocked code to reduce the rest of the matrix */
igraphdgehd2_(n, &i__, ihi, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
work[1] = (doublereal) iws;
return 0;
/* End of DGEHRD */
} /* igraphdgehrd_ */