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/* ../../../dependencies/lapack/src/slarzt.f -- translated by f2c (version 20061008).
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 real c_b8 = 0.f;
static integer c__1 = 1;
/* Subroutine */ int slarzt_(char *direct, char *storev, integer *n, integer *
k, real *v, integer *ldv, real *tau, real *t, integer *ldt, ftnlen
direct_len, ftnlen storev_len)
{
/* System generated locals */
integer t_dim1, t_offset, v_dim1, v_offset, i__1;
real r__1;
/* Local variables */
static integer i__, j, info;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *,
ftnlen), strmv_(char *, char *, char *, integer *, real *,
integer *, real *, integer *, ftnlen, ftnlen, ftnlen), xerbla_(
char *, integer *, ftnlen);
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLARZT 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' */
/* 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 * V */
/* Currently, only STOREV = 'R' and DIRECT = 'B' are supported. */
/* Arguments */
/* ========= */
/* DIRECT (input) 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, not supported yet) */
/* = 'B': H = H(k) . . . H(2) H(1) (Backward) */
/* STOREV (input) CHARACTER*1 */
/* Specifies how the vectors which define the elementary */
/* reflectors are stored (see also Further Details): */
/* = 'C': columnwise (not supported yet) */
/* = 'R': rowwise */
/* N (input) INTEGER */
/* The order of the block reflector H. N >= 0. */
/* K (input) INTEGER */
/* The order of the triangular factor T (= the number of */
/* elementary reflectors). K >= 1. */
/* V (input/output) REAL array, dimension */
/* (LDV,K) if STOREV = 'C' */
/* (LDV,N) if STOREV = 'R' */
/* The matrix V. See further details. */
/* LDV (input) INTEGER */
/* The leading dimension of the array V. */
/* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */
/* TAU (input) REAL array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i). */
/* T (output) REAL 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. */
/* LDT (input) INTEGER */
/* The leading dimension of the array T. LDT >= K. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA */
/* 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; the corresponding */
/* array elements are modified but restored on exit. The rest of the */
/* array is not used. */
/* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */
/* ______V_____ */
/* ( v1 v2 v3 ) / \ */
/* ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 ) */
/* V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 ) */
/* ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 ) */
/* ( v1 v2 v3 ) */
/* . . . */
/* . . . */
/* 1 . . */
/* 1 . */
/* 1 */
/* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */
/* ______V_____ */
/* 1 / \ */
/* . 1 ( 1 . . . . v1 v1 v1 v1 v1 ) */
/* . . 1 ( . 1 . . . v2 v2 v2 v2 v2 ) */
/* . . . ( . . 1 . . v3 v3 v3 v3 v3 ) */
/* . . . */
/* ( v1 v2 v3 ) */
/* ( v1 v2 v3 ) */
/* V = ( v1 v2 v3 ) */
/* ( v1 v2 v3 ) */
/* ( v1 v2 v3 ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Check for currently supported options */
/* 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 */
info = 0;
if (! lsame_(direct, "B", (ftnlen)1, (ftnlen)1)) {
info = -1;
} else if (! lsame_(storev, "R", (ftnlen)1, (ftnlen)1)) {
info = -2;
}
if (info != 0) {
i__1 = -info;
xerbla_("SLARZT", &i__1, (ftnlen)6);
return 0;
}
for (i__ = *k; i__ >= 1; --i__) {
if (tau[i__] == 0.f) {
/* H(i) = I */
i__1 = *k;
for (j = i__; j <= i__1; ++j) {
t[j + i__ * t_dim1] = 0.f;
/* L10: */
}
} else {
/* general case */
if (i__ < *k) {
/* T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)' */
i__1 = *k - i__;
r__1 = -tau[i__];
sgemv_("No transpose", &i__1, n, &r__1, &v[i__ + 1 + v_dim1],
ldv, &v[i__ + v_dim1], ldv, &c_b8, &t[i__ + 1 + i__ *
t_dim1], &c__1, (ftnlen)12);
/* T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i) */
i__1 = *k - i__;
strmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__ + 1
+ (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * t_dim1]
, &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)8);
}
t[i__ + i__ * t_dim1] = tau[i__];
}
/* L20: */
}
return 0;
/* End of SLARZT */
} /* slarzt_ */
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