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/* lapack/double/dlarft.f -- translated by f2c (version 20050501).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__1 = 1;
static doublereal c_b8 = 0.;
/*< SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) >*/
/* Subroutine */ int dlarft_(char *direct, char *storev, integer *n, integer *
k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t,
integer *ldt, ftnlen direct_len, ftnlen storev_len)
{
/* System generated locals */
integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3;
doublereal d__1;
/* Local variables */
integer i__, j;
doublereal vii;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, ftnlen), dtrmv_(char *,
char *, char *, integer *, doublereal *, integer *, doublereal *,
integer *, ftnlen, ftnlen, ftnlen);
(void)direct_len;
(void)storev_len;
/* -- 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 */
/* .. Scalar Arguments .. */
/*< CHARACTER DIRECT, STOREV >*/
/*< INTEGER K, LDT, LDV, N >*/
/* .. */
/* .. Array Arguments .. */
/*< DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) >*/
/* .. */
/* 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 ) */
/* ===================================================================== */
/* .. Parameters .. */
/*< DOUBLE PRECISION ONE, ZERO >*/
/*< PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER I, J >*/
/*< DOUBLE PRECISION VII >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL DGEMV, DTRMV >*/
/* .. */
/* .. External Functions .. */
/*< LOGICAL LSAME >*/
/*< EXTERNAL LSAME >*/
/* .. */
/* .. 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' ) ) THEN >*/
if (lsame_(direct, "F", (ftnlen)1, (ftnlen)1)) {
/*< DO 20 I = 1, K >*/
i__1 = *k;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< IF( TAU( I ).EQ.ZERO ) THEN >*/
if (tau[i__] == 0.) {
/* H(i) = I */
/*< DO 10 J = 1, I >*/
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
/*< T( J, I ) = ZERO >*/
t[j + i__ * t_dim1] = 0.;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< ELSE >*/
} else {
/* general case */
/*< VII = V( I, I ) >*/
vii = v[i__ + i__ * v_dim1];
/*< V( I, I ) = ONE >*/
v[i__ + i__ * v_dim1] = 1.;
/*< IF( LSAME( STOREV, 'C' ) ) THEN >*/
if (lsame_(storev, "C", (ftnlen)1, (ftnlen)1)) {
/* 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, (ftnlen)9);
/*< ELSE >*/
} 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, (ftnlen)12);
/*< END IF >*/
}
/*< V( I, I ) = VII >*/
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, (ftnlen)
5, (ftnlen)12, (ftnlen)8);
/*< T( I, I ) = TAU( I ) >*/
t[i__ + i__ * t_dim1] = tau[i__];
/*< END IF >*/
}
/*< 20 CONTINUE >*/
/* L20: */
}
/*< ELSE >*/
} else {
/*< DO 40 I = K, 1, -1 >*/
for (i__ = *k; i__ >= 1; --i__) {
/*< IF( TAU( I ).EQ.ZERO ) THEN >*/
if (tau[i__] == 0.) {
/* H(i) = I */
/*< DO 30 J = I, K >*/
i__1 = *k;
for (j = i__; j <= i__1; ++j) {
/*< T( J, I ) = ZERO >*/
t[j + i__ * t_dim1] = 0.;
/*< 30 CONTINUE >*/
/* L30: */
}
/*< ELSE >*/
} else {
/* general case */
/*< IF( I.LT.K ) THEN >*/
if (i__ < *k) {
/*< IF( LSAME( STOREV, 'C' ) ) THEN >*/
if (lsame_(storev, "C", (ftnlen)1, (ftnlen)1)) {
/*< VII = V( N-K+I, I ) >*/
vii = v[*n - *k + i__ + i__ * v_dim1];
/*< V( N-K+I, I ) = ONE >*/
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, (ftnlen)9);
/*< V( N-K+I, I ) = VII >*/
v[*n - *k + i__ + i__ * v_dim1] = vii;
/*< ELSE >*/
} else {
/*< VII = V( I, N-K+I ) >*/
vii = v[i__ + (*n - *k + i__) * v_dim1];
/*< V( I, N-K+I ) = ONE >*/
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, (
ftnlen)12);
/*< V( I, N-K+I ) = VII >*/
v[i__ + (*n - *k + i__) * v_dim1] = vii;
/*< END IF >*/
}
/* 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, (ftnlen)5, (ftnlen)12, (ftnlen)8)
;
/*< END IF >*/
}
/*< T( I, I ) = TAU( I ) >*/
t[i__ + i__ * t_dim1] = tau[i__];
/*< END IF >*/
}
/*< 40 CONTINUE >*/
/* L40: */
}
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of DLARFT */
/*< END >*/
} /* dlarft_ */
#ifdef __cplusplus
}
#endif
|
