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agent_compositor_test/references/igraph-1.0.1/vendor/lapack/dlarft.c
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Abdelrahman Said a11edf0c53 Add graph references
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/* -- translated by f2c (version 20240504).
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"
/* Table of constant values */
static integer c__1 = 1;
static doublereal c_b7 = 1.;
/* > \brief \b DLARFT forms the triangular factor T of a block reflector H = I - vtvH
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DLARFT + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarft.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarft.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarft.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
CHARACTER DIRECT, STOREV
INTEGER K, LDT, LDV, N
DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
> \par Purpose:
=============
>
> \verbatim
>
> DLARFT forms the triangular factor T of a real block reflector H
> of order n, which is defined as a product of k elementary reflectors.
>
> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
>
> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
>
> If STOREV = 'C', the vector which defines the elementary reflector
> H(i) is stored in the i-th column of the array V, and
>
> H = I - V * T * V**T
>
> If STOREV = 'R', the vector which defines the elementary reflector
> H(i) is stored in the i-th row of the array V, and
>
> H = I - V**T * T * V
> \endverbatim
Arguments:
==========
> \param[in] DIRECT
> \verbatim
> DIRECT is CHARACTER*1
> Specifies the order in which the elementary reflectors are
> multiplied to form the block reflector:
> = 'F': H = H(1) H(2) . . . H(k) (Forward)
> = 'B': H = H(k) . . . H(2) H(1) (Backward)
> \endverbatim
>
> \param[in] STOREV
> \verbatim
> STOREV is CHARACTER*1
> Specifies how the vectors which define the elementary
> reflectors are stored (see also Further Details):
> = 'C': columnwise
> = 'R': rowwise
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the block reflector H. N >= 0.
> \endverbatim
>
> \param[in] K
> \verbatim
> K is INTEGER
> The order of the triangular factor T (= the number of
> elementary reflectors). K >= 1.
> \endverbatim
>
> \param[in] V
> \verbatim
> V is DOUBLE PRECISION array, dimension
> (LDV,K) if STOREV = 'C'
> (LDV,N) if STOREV = 'R'
> The matrix V. See further details.
> \endverbatim
>
> \param[in] LDV
> \verbatim
> LDV is INTEGER
> The leading dimension of the array V.
> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
> \endverbatim
>
> \param[in] TAU
> \verbatim
> TAU is DOUBLE PRECISION array, dimension (K)
> TAU(i) must contain the scalar factor of the elementary
> reflector H(i).
> \endverbatim
>
> \param[out] T
> \verbatim
> T is DOUBLE PRECISION array, dimension (LDT,K)
> The k by k triangular factor T of the block reflector.
> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
> lower triangular. The rest of the array is not used.
> \endverbatim
>
> \param[in] LDT
> \verbatim
> LDT is INTEGER
> The leading dimension of the array T. LDT >= K.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup doubleOTHERauxiliary
> \par Further Details:
=====================
>
> \verbatim
>
> The shape of the matrix V and the storage of the vectors which define
> the H(i) is best illustrated by the following example with n = 5 and
> k = 3. The elements equal to 1 are not stored.
>
> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
>
> V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
> ( v1 1 ) ( 1 v2 v2 v2 )
> ( v1 v2 1 ) ( 1 v3 v3 )
> ( v1 v2 v3 )
> ( v1 v2 v3 )
>
> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
>
> V = ( v1 v2 v3 ) V = ( v1 v1 1 )
> ( v1 v2 v3 ) ( v2 v2 v2 1 )
> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
> ( 1 v3 )
> ( 1 )
> \endverbatim
>
=====================================================================
Subroutine */ int igraphdlarft_(char *direct, char *storev, integer *n, integer *
k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t,
integer *ldt)
{
/* System generated locals */
integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3;
doublereal d__1;
/* Local variables */
integer i__, j, prevlastv;
extern logical igraphlsame_(char *, char *);
extern /* Subroutine */ int igraphdgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *);
integer lastv;
extern /* Subroutine */ int igraphdtrmv_(char *, char *, char *, integer *,
doublereal *, integer *, doublereal *, integer *);
/* -- LAPACK auxiliary routine (version 3.4.2) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
September 2012
=====================================================================
Quick return if possible
Parameter adjustments */
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
--tau;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
/* Function Body */
if (*n == 0) {
return 0;
}
if (igraphlsame_(direct, "F")) {
prevlastv = *n;
i__1 = *k;
for (i__ = 1; i__ <= i__1; ++i__) {
prevlastv = max(i__,prevlastv);
if (tau[i__] == 0.) {
/* H(i) = I */
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
t[j + i__ * t_dim1] = 0.;
}
} else {
/* general case */
if (igraphlsame_(storev, "C")) {
/* Skip any trailing zeros. */
i__2 = i__ + 1;
for (lastv = *n; lastv >= i__2; --lastv) {
if (v[lastv + i__ * v_dim1] != 0.) {
goto L11;
}
}
L11:
i__2 = i__ - 1;
for (j = 1; j <= i__2; ++j) {
t[j + i__ * t_dim1] = -tau[i__] * v[i__ + j * v_dim1];
}
j = min(lastv,prevlastv);
/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) */
i__2 = j - i__;
i__3 = i__ - 1;
d__1 = -tau[i__];
igraphdgemv_("Transpose", &i__2, &i__3, &d__1, &v[i__ + 1 +
v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], &c__1, &
c_b7, &t[i__ * t_dim1 + 1], &c__1);
} else {
/* Skip any trailing zeros. */
i__2 = i__ + 1;
for (lastv = *n; lastv >= i__2; --lastv) {
if (v[i__ + lastv * v_dim1] != 0.) {
goto L21;
}
}
L21:
i__2 = i__ - 1;
for (j = 1; j <= i__2; ++j) {
t[j + i__ * t_dim1] = -tau[i__] * v[j + i__ * v_dim1];
}
j = min(lastv,prevlastv);
/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T */
i__2 = i__ - 1;
i__3 = j - i__;
d__1 = -tau[i__];
igraphdgemv_("No transpose", &i__2, &i__3, &d__1, &v[(i__ + 1) *
v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1],
ldv, &c_b7, &t[i__ * t_dim1 + 1], &c__1);
}
/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */
i__2 = i__ - 1;
igraphdtrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[
t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1);
t[i__ + i__ * t_dim1] = tau[i__];
if (i__ > 1) {
prevlastv = max(prevlastv,lastv);
} else {
prevlastv = lastv;
}
}
}
} else {
prevlastv = 1;
for (i__ = *k; i__ >= 1; --i__) {
if (tau[i__] == 0.) {
/* H(i) = I */
i__1 = *k;
for (j = i__; j <= i__1; ++j) {
t[j + i__ * t_dim1] = 0.;
}
} else {
/* general case */
if (i__ < *k) {
if (igraphlsame_(storev, "C")) {
/* Skip any leading zeros. */
i__1 = i__ - 1;
for (lastv = 1; lastv <= i__1; ++lastv) {
if (v[lastv + i__ * v_dim1] != 0.) {
goto L31;
}
}
L31:
i__1 = *k;
for (j = i__ + 1; j <= i__1; ++j) {
t[j + i__ * t_dim1] = -tau[i__] * v[*n - *k + i__
+ j * v_dim1];
}
j = max(lastv,prevlastv);
/* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) */
i__1 = *n - *k + i__ - j;
i__2 = *k - i__;
d__1 = -tau[i__];
igraphdgemv_("Transpose", &i__1, &i__2, &d__1, &v[j + (i__
+ 1) * v_dim1], ldv, &v[j + i__ * v_dim1], &
c__1, &c_b7, &t[i__ + 1 + i__ * t_dim1], &
c__1);
} else {
/* Skip any leading zeros. */
i__1 = i__ - 1;
for (lastv = 1; lastv <= i__1; ++lastv) {
if (v[i__ + lastv * v_dim1] != 0.) {
goto L41;
}
}
L41:
i__1 = *k;
for (j = i__ + 1; j <= i__1; ++j) {
t[j + i__ * t_dim1] = -tau[i__] * v[j + (*n - *k
+ i__) * v_dim1];
}
j = max(lastv,prevlastv);
/* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T */
i__1 = *k - i__;
i__2 = *n - *k + i__ - j;
d__1 = -tau[i__];
igraphdgemv_("No transpose", &i__1, &i__2, &d__1, &v[i__ +
1 + j * v_dim1], ldv, &v[i__ + j * v_dim1],
ldv, &c_b7, &t[i__ + 1 + i__ * t_dim1], &c__1);
}
/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */
i__1 = *k - i__;
igraphdtrmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__
+ 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ *
t_dim1], &c__1)
;
if (i__ > 1) {
prevlastv = min(prevlastv,lastv);
} else {
prevlastv = lastv;
}
}
t[i__ + i__ * t_dim1] = tau[i__];
}
}
}
return 0;
/* End of DLARFT */
} /* igraphdlarft_ */
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