/* dlarft.f -- 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
-- 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_b8 = 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 ) */
/* .. Scalar Arguments .. */
/* CHARACTER DIRECT, STOREV */
/* INTEGER K, LDT, LDV, N */
/* .. */
/* .. Array Arguments .. */
/* 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 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* 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. */
lastv = *n;
L14:
if (v[lastv + i__ * v_dim1] != 0.) {
goto L15;
}
if (lastv == i__ + 1) {
goto L15;
}
--lastv;
goto L14;
L15:
/* DO LASTV = N, I+1, -1 */
/* IF( V( LASTV, I ).NE.ZERO ) EXIT */
/* END DO */
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_b8, &t[i__ * t_dim1 + 1], &c__1);
} else {
/* Skip any trailing zeros. */
lastv = *n;
L16:
if (v[i__ + lastv * v_dim1] != 0.) {
goto L17;
}
if (lastv == i__ + 1) {
goto L17;
}
--lastv;
goto L16;
L17:
/* DO LASTV = N, I+1, -1 */
/* IF( V( I, LASTV ).NE.ZERO ) EXIT */
/* END DO */
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_b8, &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. */
lastv = 1;
L34:
if (v[lastv + i__ * v_dim1] != 0.) {
goto L35;
}
if (lastv == i__ - 1) {
goto L35;
}
++lastv;
goto L34;
L35:
/* DO LASTV = 1, I-1 */
/* IF( V( LASTV, I ).NE.ZERO ) EXIT */
/* END DO */
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_b8, &t[i__ + 1 + i__ * t_dim1], &
c__1);
} else {
/* Skip any leading zeros. */
lastv = 1;
/* L36: */
if (v[i__ + lastv * v_dim1] != 0.) {
goto L37;
}
if (lastv == i__ - 1) {
goto L37;
}
++lastv;
L37:
/* DO LASTV = 1, I-1 */
/* IF( V( I, LASTV ).NE.ZERO ) EXIT */
/* END DO */
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_b8, &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 */
} /* dlarft_ */