264 lines
7.7 KiB
C
264 lines
7.7 KiB
C
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#include "clapack.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static real c_b8 = 0.f;
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/* Subroutine */ int slarft_(char *direct, char *storev, integer *n, integer *
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k, real *v, integer *ldv, real *tau, real *t, integer *ldt)
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{
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/* System generated locals */
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integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3;
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real r__1;
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/* Local variables */
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integer i__, j;
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real vii;
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extern logical lsame_(char *, char *);
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extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *,
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real *, integer *, real *, integer *, real *, real *, integer *), strmv_(char *, char *, char *, integer *, real *,
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integer *, real *, integer *);
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/* -- LAPACK auxiliary routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* SLARFT forms the triangular factor T of a real block reflector H */
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/* of order n, which is defined as a product of k elementary reflectors. */
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/* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */
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/* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */
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/* If STOREV = 'C', the vector which defines the elementary reflector */
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/* H(i) is stored in the i-th column of the array V, and */
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/* H = I - V * T * V' */
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/* If STOREV = 'R', the vector which defines the elementary reflector */
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/* H(i) is stored in the i-th row of the array V, and */
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/* H = I - V' * T * V */
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/* Arguments */
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/* ========= */
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/* DIRECT (input) CHARACTER*1 */
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/* Specifies the order in which the elementary reflectors are */
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/* multiplied to form the block reflector: */
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/* = 'F': H = H(1) H(2) . . . H(k) (Forward) */
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/* = 'B': H = H(k) . . . H(2) H(1) (Backward) */
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/* STOREV (input) CHARACTER*1 */
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/* Specifies how the vectors which define the elementary */
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/* reflectors are stored (see also Further Details): */
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/* = 'C': columnwise */
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/* = 'R': rowwise */
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/* N (input) INTEGER */
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/* The order of the block reflector H. N >= 0. */
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/* K (input) INTEGER */
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/* The order of the triangular factor T (= the number of */
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/* elementary reflectors). K >= 1. */
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/* V (input/output) REAL array, dimension */
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/* (LDV,K) if STOREV = 'C' */
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/* (LDV,N) if STOREV = 'R' */
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/* The matrix V. See further details. */
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/* LDV (input) INTEGER */
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/* The leading dimension of the array V. */
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/* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */
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/* TAU (input) REAL array, dimension (K) */
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/* TAU(i) must contain the scalar factor of the elementary */
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/* reflector H(i). */
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/* T (output) REAL array, dimension (LDT,K) */
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/* The k by k triangular factor T of the block reflector. */
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/* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */
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/* lower triangular. The rest of the array is not used. */
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/* LDT (input) INTEGER */
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/* The leading dimension of the array T. LDT >= K. */
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/* Further Details */
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/* =============== */
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/* The shape of the matrix V and the storage of the vectors which define */
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/* the H(i) is best illustrated by the following example with n = 5 and */
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/* k = 3. The elements equal to 1 are not stored; the corresponding */
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/* array elements are modified but restored on exit. The rest of the */
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/* array is not used. */
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/* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */
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/* V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */
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/* ( v1 1 ) ( 1 v2 v2 v2 ) */
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/* ( v1 v2 1 ) ( 1 v3 v3 ) */
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/* ( v1 v2 v3 ) */
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/* ( v1 v2 v3 ) */
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/* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */
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/* V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */
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/* ( v1 v2 v3 ) ( v2 v2 v2 1 ) */
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/* ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */
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/* ( 1 v3 ) */
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/* ( 1 ) */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Quick return if possible */
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/* Parameter adjustments */
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v_dim1 = *ldv;
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v_offset = 1 + v_dim1;
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v -= v_offset;
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--tau;
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t_dim1 = *ldt;
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t_offset = 1 + t_dim1;
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t -= t_offset;
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/* Function Body */
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if (*n == 0) {
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return 0;
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}
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if (lsame_(direct, "F")) {
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i__1 = *k;
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for (i__ = 1; i__ <= i__1; ++i__) {
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if (tau[i__] == 0.f) {
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/* H(i) = I */
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i__2 = i__;
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for (j = 1; j <= i__2; ++j) {
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t[j + i__ * t_dim1] = 0.f;
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/* L10: */
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}
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} else {
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/* general case */
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vii = v[i__ + i__ * v_dim1];
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v[i__ + i__ * v_dim1] = 1.f;
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if (lsame_(storev, "C")) {
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/* T(1:i-1,i) := - tau(i) * V(i:n,1:i-1)' * V(i:n,i) */
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i__2 = *n - i__ + 1;
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i__3 = i__ - 1;
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r__1 = -tau[i__];
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sgemv_("Transpose", &i__2, &i__3, &r__1, &v[i__ + v_dim1],
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ldv, &v[i__ + i__ * v_dim1], &c__1, &c_b8, &t[
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i__ * t_dim1 + 1], &c__1);
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} else {
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/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:n) * V(i,i:n)' */
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i__2 = i__ - 1;
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i__3 = *n - i__ + 1;
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r__1 = -tau[i__];
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sgemv_("No transpose", &i__2, &i__3, &r__1, &v[i__ *
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v_dim1 + 1], ldv, &v[i__ + i__ * v_dim1], ldv, &
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c_b8, &t[i__ * t_dim1 + 1], &c__1);
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}
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v[i__ + i__ * v_dim1] = vii;
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/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */
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i__2 = i__ - 1;
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strmv_("Upper", "No transpose", "Non-unit", &i__2, &t[
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t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1);
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t[i__ + i__ * t_dim1] = tau[i__];
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}
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/* L20: */
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}
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} else {
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for (i__ = *k; i__ >= 1; --i__) {
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if (tau[i__] == 0.f) {
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/* H(i) = I */
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i__1 = *k;
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for (j = i__; j <= i__1; ++j) {
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t[j + i__ * t_dim1] = 0.f;
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/* L30: */
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}
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} else {
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/* general case */
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if (i__ < *k) {
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if (lsame_(storev, "C")) {
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vii = v[*n - *k + i__ + i__ * v_dim1];
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v[*n - *k + i__ + i__ * v_dim1] = 1.f;
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/* T(i+1:k,i) := */
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/* - tau(i) * V(1:n-k+i,i+1:k)' * V(1:n-k+i,i) */
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i__1 = *n - *k + i__;
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i__2 = *k - i__;
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r__1 = -tau[i__];
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sgemv_("Transpose", &i__1, &i__2, &r__1, &v[(i__ + 1)
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* v_dim1 + 1], ldv, &v[i__ * v_dim1 + 1], &
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c__1, &c_b8, &t[i__ + 1 + i__ * t_dim1], &
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c__1);
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v[*n - *k + i__ + i__ * v_dim1] = vii;
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} else {
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vii = v[i__ + (*n - *k + i__) * v_dim1];
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v[i__ + (*n - *k + i__) * v_dim1] = 1.f;
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/* T(i+1:k,i) := */
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/* - tau(i) * V(i+1:k,1:n-k+i) * V(i,1:n-k+i)' */
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i__1 = *k - i__;
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i__2 = *n - *k + i__;
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r__1 = -tau[i__];
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sgemv_("No transpose", &i__1, &i__2, &r__1, &v[i__ +
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1 + v_dim1], ldv, &v[i__ + v_dim1], ldv, &
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c_b8, &t[i__ + 1 + i__ * t_dim1], &c__1);
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v[i__ + (*n - *k + i__) * v_dim1] = vii;
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}
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/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */
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i__1 = *k - i__;
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strmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__
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+ 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ *
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t_dim1], &c__1)
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;
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}
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t[i__ + i__ * t_dim1] = tau[i__];
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}
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/* L40: */
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}
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}
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return 0;
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/* End of SLARFT */
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} /* slarft_ */
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