/* clarft.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"
#include "blaswrap.h"
/* Table of constant values */
static complex c_b2 = {0.f,0.f};
static integer c__1 = 1;
/* Subroutine */ int clarft_(char *direct, char *storev, integer *n, integer *
k, complex *v, integer *ldv, complex *tau, complex *t, integer *ldt)
{
/* System generated locals */
integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4;
complex q__1;
/* Local variables */
integer i__, j, prevlastv;
complex vii;
extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *);
extern logical lsame_(char *, char *);
integer lastv;
extern /* Subroutine */ int ctrmv_(char *, char *, char *, integer *,
complex *, integer *, complex *, integer *), clacgv_(integer *, complex *, integer *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLARFT 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 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 array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i). */
/* T (output) COMPLEX 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 ) */
/* ===================================================================== */
/* .. 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 (lsame_(direct, "F")) {
prevlastv = *n;
i__1 = *k;
for (i__ = 1; i__ <= i__1; ++i__) {
prevlastv = max(prevlastv,i__);
i__2 = i__;
if (tau[i__2].r == 0.f && tau[i__2].i == 0.f) {
/* H(i) = I */
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
i__3 = j + i__ * t_dim1;
t[i__3].r = 0.f, t[i__3].i = 0.f;
/* L10: */
}
} else {
/* general case */
i__2 = i__ + i__ * v_dim1;
vii.r = v[i__2].r, vii.i = v[i__2].i;
i__2 = i__ + i__ * v_dim1;
v[i__2].r = 1.f, v[i__2].i = 0.f;
if (lsame_(storev, "C")) {
/* Skip any trailing zeros. */
i__2 = i__ + 1;
for (lastv = *n; lastv >= i__2; --lastv) {
i__3 = lastv + i__ * v_dim1;
if (v[i__3].r != 0.f || v[i__3].i != 0.f) {
break;
}
}
j = min(lastv,prevlastv);
/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)' * V(i:j,i) */
i__2 = j - i__ + 1;
i__3 = i__ - 1;
i__4 = i__;
q__1.r = -tau[i__4].r, q__1.i = -tau[i__4].i;
cgemv_("Conjugate transpose", &i__2, &i__3, &q__1, &v[i__
+ v_dim1], ldv, &v[i__ + i__ * v_dim1], &c__1, &
c_b2, &t[i__ * t_dim1 + 1], &c__1);
} else {
/* Skip any trailing zeros. */
i__2 = i__ + 1;
for (lastv = *n; lastv >= i__2; --lastv) {
i__3 = i__ + lastv * v_dim1;
if (v[i__3].r != 0.f || v[i__3].i != 0.f) {
break;
}
}
j = min(lastv,prevlastv);
/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)' */
if (i__ < j) {
i__2 = j - i__;
clacgv_(&i__2, &v[i__ + (i__ + 1) * v_dim1], ldv);
}
i__2 = i__ - 1;
i__3 = j - i__ + 1;
i__4 = i__;
q__1.r = -tau[i__4].r, q__1.i = -tau[i__4].i;
cgemv_("No transpose", &i__2, &i__3, &q__1, &v[i__ *
v_dim1 + 1], ldv, &v[i__ + i__ * v_dim1], ldv, &
c_b2, &t[i__ * t_dim1 + 1], &c__1);
if (i__ < j) {
i__2 = j - i__;
clacgv_(&i__2, &v[i__ + (i__ + 1) * v_dim1], ldv);
}
}
i__2 = i__ + i__ * v_dim1;
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) */
i__2 = i__ - 1;
ctrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[
t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1);
i__2 = i__ + i__ * t_dim1;
i__3 = i__;
t[i__2].r = tau[i__3].r, t[i__2].i = tau[i__3].i;
if (i__ > 1) {
prevlastv = max(prevlastv,lastv);
} else {
prevlastv = lastv;
}
}
/* L20: */
}
} else {
prevlastv = 1;
for (i__ = *k; i__ >= 1; --i__) {
i__1 = i__;
if (tau[i__1].r == 0.f && tau[i__1].i == 0.f) {
/* H(i) = I */
i__1 = *k;
for (j = i__; j <= i__1; ++j) {
i__2 = j + i__ * t_dim1;
t[i__2].r = 0.f, t[i__2].i = 0.f;
/* L30: */
}
} else {
/* general case */
if (i__ < *k) {
if (lsame_(storev, "C")) {
i__1 = *n - *k + i__ + i__ * v_dim1;
vii.r = v[i__1].r, vii.i = v[i__1].i;
i__1 = *n - *k + i__ + i__ * v_dim1;
v[i__1].r = 1.f, v[i__1].i = 0.f;
/* Skip any leading zeros. */
i__1 = i__ - 1;
for (lastv = 1; lastv <= i__1; ++lastv) {
i__2 = lastv + i__ * v_dim1;
if (v[i__2].r != 0.f || v[i__2].i != 0.f) {
break;
}
}
j = max(lastv,prevlastv);
/* T(i+1:k,i) := */
/* - tau(i) * V(j:n-k+i,i+1:k)' * V(j:n-k+i,i) */
i__1 = *n - *k + i__ - j + 1;
i__2 = *k - i__;
i__3 = i__;
q__1.r = -tau[i__3].r, q__1.i = -tau[i__3].i;
cgemv_("Conjugate transpose", &i__1, &i__2, &q__1, &v[
j + (i__ + 1) * v_dim1], ldv, &v[j + i__ *
v_dim1], &c__1, &c_b2, &t[i__ + 1 + i__ *
t_dim1], &c__1);
i__1 = *n - *k + i__ + i__ * v_dim1;
v[i__1].r = vii.r, v[i__1].i = vii.i;
} else {
i__1 = i__ + (*n - *k + i__) * v_dim1;
vii.r = v[i__1].r, vii.i = v[i__1].i;
i__1 = i__ + (*n - *k + i__) * v_dim1;
v[i__1].r = 1.f, v[i__1].i = 0.f;
/* Skip any leading zeros. */
i__1 = i__ - 1;
for (lastv = 1; lastv <= i__1; ++lastv) {
i__2 = i__ + lastv * v_dim1;
if (v[i__2].r != 0.f || v[i__2].i != 0.f) {
break;
}
}
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)' */
i__1 = *n - *k + i__ - 1 - j + 1;
clacgv_(&i__1, &v[i__ + j * v_dim1], ldv);
i__1 = *k - i__;
i__2 = *n - *k + i__ - j + 1;
i__3 = i__;
q__1.r = -tau[i__3].r, q__1.i = -tau[i__3].i;
cgemv_("No transpose", &i__1, &i__2, &q__1, &v[i__ +
1 + j * v_dim1], ldv, &v[i__ + j * v_dim1],
ldv, &c_b2, &t[i__ + 1 + i__ * t_dim1], &c__1);
i__1 = *n - *k + i__ - 1 - j + 1;
clacgv_(&i__1, &v[i__ + j * v_dim1], ldv);
i__1 = i__ + (*n - *k + i__) * v_dim1;
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__;
ctrmv_("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;
}
}
i__1 = i__ + i__ * t_dim1;
i__2 = i__;
t[i__1].r = tau[i__2].r, t[i__1].i = tau[i__2].i;
}
/* L40: */
}
}
return 0;
/* End of CLARFT */
} /* clarft_ */