📄 dlarft.c
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#include "f2c.h"
#include "netlib.h"
/* Table of constant values */
static integer c__1 = 1;
static doublereal c_b8 = 0.;
/* Subroutine */ void dlarft_(direct, storev, n, k, v, ldv, tau, t, ldt)
const char *direct, *storev;
const integer *n, *k;
doublereal *v;
const integer *ldv;
const doublereal *tau;
doublereal *t;
const 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 */
static integer i, j;
static doublereal vii;
/* -- LAPACK auxiliary 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 */
/* ======= */
/* */
/* 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' */
/* */
/* 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 */
/* */
/* 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) */
/* = '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 */
/* = '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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i). */
/* */
/* T (output) 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. */
/* */
/* LDT (input) INTEGER */
/* The leading dimension of the array T. LDT >= K. */
/* */
/* Further Details */
/* =============== */
/* */
/* 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 = ( 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 ) */
/* */
/* ===================================================================== */
/* Parameter adjustments */
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
--tau;
t_dim1 = *ldt;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
/* Quick return if possible */
if (*n == 0) {
return;
}
if (lsame_(direct, "F")) {
i__1 = *k;
for (i = 1; i <= i__1; ++i) {
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 */
vii = v[i + i * v_dim1];
v[i + i * v_dim1] = 1.;
if (lsame_(storev, "C")) {
/* T(1:i-1,i) := - tau(i) * V(i:n,1:i-1)' * V(i:n,i) */
i__2 = *n - i + 1;
i__3 = i - 1;
d__1 = -tau[i];
dgemv_("Transpose", &i__2, &i__3, &d__1, &v[i + v_dim1], ldv,
&v[i + i * v_dim1], &c__1, &c_b8, &t[i * t_dim1 + 1], &c__1);
} else {
/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:n) * V(i,i:n)' */
i__2 = i - 1;
i__3 = *n - i + 1;
d__1 = -tau[i];
dgemv_("No transpose", &i__2, &i__3, &d__1, &v[i * v_dim1 + 1], ldv,
&v[i + i * v_dim1], ldv, &c_b8, &t[i * t_dim1 + 1], &c__1);
}
v[i + i * v_dim1] = vii;
/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */
i__2 = i - 1;
dtrmv_("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];
}
}
} else {
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 (lsame_(storev, "C")) {
vii = v[*n - *k + i + i * v_dim1];
v[*n - *k + i + i * v_dim1] = 1.;
/* T(i+1:k,i) := */
/* - tau(i) * V(1:n-k+i,i+1:k)' * V(1:n-k+i,i) */
i__1 = *n - *k + i;
i__2 = *k - i;
d__1 = -tau[i];
dgemv_("Transpose", &i__1, &i__2, &d__1, &v[(i + 1) * v_dim1 + 1], ldv,
&v[i * v_dim1 + 1], &c__1, &c_b8, &t[i + 1 + i * t_dim1], &c__1);
v[*n - *k + i + i * v_dim1] = vii;
} else {
vii = v[i + (*n - *k + i) * v_dim1];
v[i + (*n - *k + i) * v_dim1] = 1.;
/* T(i+1:k,i) := */
/* - tau(i) * V(i+1:k,1:n-k+i) * V(i,1:n-k+i)' */
i__1 = *k - i;
i__2 = *n - *k + i;
d__1 = -tau[i];
dgemv_("No transpose", &i__1, &i__2, &d__1, &v[i + 1 + v_dim1], ldv,
&v[i + v_dim1], ldv, &c_b8, &t[i + 1 + i * t_dim1], &c__1);
v[i + (*n - *k + i) * v_dim1] = vii;
}
/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */
i__1 = *k - i;
dtrmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i+1+(i+1)*t_dim1], ldt, &t[i+1+i*t_dim1], &c__1);
}
t[i + i * t_dim1] = tau[i];
}
}
}
} /* dlarft_ */
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