zlarft.c
来自「InsightToolkit-1.4.0(有大量的优化算法程序)」· C语言 代码 · 共 248 行
C
248 行
#include "f2c.h"
#include "netlib.h"
/* Modified by Peter Vanroose, June 2001: manual optimisation and clean-up */
/* Table of constant values */
static doublecomplex c_b4 = {0.,0.};
static integer c__1 = 1;
/* Subroutine */ void zlarft_(direct, storev, n, k, v, ldv, tau, t, ldt)
const char *direct, *storev;
const integer *n, *k;
doublecomplex *v;
const integer *ldv;
const doublecomplex *tau;
doublecomplex *t;
integer *ldt;
{
/* System generated locals */
integer i__1, i__2;
doublecomplex z__1;
/* Local variables */
static integer i, j;
static doublecomplex vii;
/* -- LAPACK auxiliary routine (version 2.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* September 30, 1994 */
/* ===================================================================== */
/* */
/* Purpose */
/* ======= */
/* */
/* ZLARFT forms the triangular factor T of a complex 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) COMPLEX*16 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) COMPLEX*16 array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i). */
/* */
/* T (output) COMPLEX*16 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 ) */
/* */
/* ===================================================================== */
/* Quick return if possible */
if (*n == 0) {
return;
}
if (lsame_(direct, "F")) {
for (i = 0; i < *k; ++i) {
if (tau[i].r == 0. && tau[i].i == 0.) {
/* H(i) = I */
for (j = 0; j <= i; ++j) {
i__1 = j + i * *ldt;
t[i__1].r = 0., t[i__1].i = 0.;
}
} else {
/* general case */
i__2 = i + i * *ldv;
vii.r = v[i__2].r, vii.i = v[i__2].i;
i__2 = i + i * *ldv;
v[i__2].r = 1., v[i__2].i = 0.;
if (lsame_(storev, "C")) {
/* T(1:i-1,i) := - tau(i) * V(i:n,1:i-1)' * V(i:n,i) */
z__1.r = -tau[i].r, z__1.i = -tau[i].i;
i__1 = *n - i;
zgemv_("Conjugate transpose", &i__1, &i, &z__1,
&v[i], ldv, &v[i + i * *ldv], &c__1, &c_b4,
&t[i * *ldt], &c__1);
} else {
/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:n) * V(i,i:n)' */
if (i < *n-1) {
i__2 = *n-1 - i;
zlacgv_(&i__2, &v[i + (i + 1) * *ldv], ldv);
}
z__1.r = -tau[i].r, z__1.i = -tau[i].i;
i__2 = *n - i;
zgemv_("No transpose", &i, &i__2, &z__1, &v[i* *ldv], ldv,
&v[i+i* *ldv], ldv, &c_b4, &t[i* *ldt], &c__1);
if (i < *n-1) {
i__2 = *n-1 - i;
zlacgv_(&i__2, &v[i + (i + 1) * *ldv], ldv);
}
}
i__2 = i + i * *ldv;
v[i__2].r = vii.r, v[i__2].i = vii.i;
/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */
ztrmv_("Upper", "No transpose", "Non-unit", &i, t, ldt, &t[i * *ldt], &c__1);
i__2 = i + i * *ldt;
t[i__2].r = tau[i].r, t[i__2].i = tau[i].i;
}
}
} else {
for (i = *k-1; i >= 0; --i) {
if (tau[i].r == 0. && tau[i].i == 0.) {
/* H(i) = I */
for (j = i; j < *k; ++j) {
i__2 = j + i * *ldt;
t[i__2].r = 0., t[i__2].i = 0.;
}
} else {
/* general case */
if (i < *k-1) {
if (lsame_(storev, "C")) {
i__1 = *n - *k + i + i * *ldv;
vii.r = v[i__1].r, vii.i = v[i__1].i;
v[i__1].r = 1., v[i__1].i = 0.;
/* T(i+1:k,i) := */
/* - tau(i) * V(1:n-k+i,i+1:k)' * V(1:n-k+i,i) */
z__1.r = -tau[i].r, z__1.i = -tau[i].i;
i__1 = *n - *k + i + 1;
i__2 = *k - i - 1;
zgemv_("Conjugate transpose", &i__1, &i__2, &z__1,
&v[(i + 1) * *ldv], ldv, &v[i * *ldv], &c__1,
&c_b4, &t[i + 1 + i * *ldt], &c__1);
i__1 = *n - *k + i + i * *ldv;
v[i__1].r = vii.r, v[i__1].i = vii.i;
} else {
i__1 = i + (*n - *k + i) * *ldv;
vii.r = v[i__1].r, vii.i = v[i__1].i;
v[i__1].r = 1., v[i__1].i = 0.;
/* T(i+1:k,i) := */
/* - tau(i) * V(i+1:k,1:n-k+i) * V(i,1:n-k+i)' */
i__1 = *n - *k + i;
zlacgv_(&i__1, &v[i], ldv);
z__1.r = -tau[i].r, z__1.i = -tau[i].i;
i__1 = *k - i - 1;
i__2 = *n - *k + i + 1;
zgemv_("No transpose", &i__1, &i__2, &z__1, &v[i+1], ldv,
&v[i], ldv, &c_b4, &t[i+1 + i* *ldt], &c__1);
i__1 = *n - *k + i;
zlacgv_(&i__1, &v[i], ldv);
i__1 = i + (*n - *k + i) * *ldv;
v[i__1].r = vii.r, v[i__1].i = vii.i;
}
/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */
i__1 = *k - i - 1;
ztrmv_("Lower", "No transpose", "Non-unit", &i__1,
&t[i + 1 + (i + 1) * *ldt], ldt,
&t[i + 1 + i * *ldt], &c__1);
}
i__1 = i + i * *ldt;
t[i__1].r = tau[i].r, t[i__1].i = tau[i].i;
}
}
}
} /* zlarft_ */
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