zlarfb.c

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/* lapack/complex16/zlarfb.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 doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;

/*<    >*/
/* Subroutine */ int zlarfb_(char *side, char *trans, char *direct, char *
        storev, integer *m, integer *n, integer *k, doublecomplex *v, integer 
        *ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, integer *
        ldc, doublecomplex *work, integer *ldwork, ftnlen side_len, ftnlen 
        trans_len, ftnlen direct_len, ftnlen storev_len)
{
    /* System generated locals */
    integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, 
            work_offset, i__1, i__2, i__3, i__4, i__5;
    doublecomplex z__1, z__2;

    /* Builtin functions */
    void d_cnjg(doublecomplex *, doublecomplex *);

    /* Local variables */
    integer i__, j;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, 
            integer *, doublecomplex *, doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
            integer *, ftnlen, ftnlen), zcopy_(integer *, doublecomplex *, 
            integer *, doublecomplex *, integer *), ztrmm_(char *, char *, 
            char *, char *, integer *, integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, 
            ftnlen, ftnlen, ftnlen), zlacgv_(integer *, doublecomplex *, 
            integer *);
    char transt[1];
    (void)side_len;
    (void)trans_len;
    (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 */
/*     September 30, 1994 */

/*     .. Scalar Arguments .. */
/*<       CHARACTER          DIRECT, SIDE, STOREV, TRANS >*/
/*<       INTEGER            K, LDC, LDT, LDV, LDWORK, M, N >*/
/*     .. */
/*     .. Array Arguments .. */
/*<    >*/
/*     .. */

/*  Purpose */
/*  ======= */

/*  ZLARFB applies a complex block reflector H or its transpose H' to a */
/*  complex M-by-N matrix C, from either the left or the right. */

/*  Arguments */
/*  ========= */

/*  SIDE    (input) CHARACTER*1 */
/*          = 'L': apply H or H' from the Left */
/*          = 'R': apply H or H' from the Right */

/*  TRANS   (input) CHARACTER*1 */
/*          = 'N': apply H (No transpose) */
/*          = 'C': apply H' (Conjugate transpose) */

/*  DIRECT  (input) CHARACTER*1 */
/*          Indicates how H is formed from a product of elementary */
/*          reflectors */
/*          = 'F': H = H(1) H(2) . . . H(k) (Forward) */
/*          = 'B': H = H(k) . . . H(2) H(1) (Backward) */

/*  STOREV  (input) CHARACTER*1 */
/*          Indicates how the vectors which define the elementary */
/*          reflectors are stored: */
/*          = 'C': Columnwise */
/*          = 'R': Rowwise */

/*  M       (input) INTEGER */
/*          The number of rows of the matrix C. */

/*  N       (input) INTEGER */
/*          The number of columns of the matrix C. */

/*  K       (input) INTEGER */
/*          The order of the matrix T (= the number of elementary */
/*          reflectors whose product defines the block reflector). */

/*  V       (input) COMPLEX*16 array, dimension */
/*                                (LDV,K) if STOREV = 'C' */
/*                                (LDV,M) if STOREV = 'R' and SIDE = 'L' */
/*                                (LDV,N) if STOREV = 'R' and SIDE = 'R' */
/*          The matrix V. See further details. */

/*  LDV     (input) INTEGER */
/*          The leading dimension of the array V. */
/*          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); */
/*          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); */
/*          if STOREV = 'R', LDV >= K. */

/*  T       (input) COMPLEX*16 array, dimension (LDT,K) */
/*          The triangular K-by-K matrix T in the representation of the */
/*          block reflector. */

/*  LDT     (input) INTEGER */
/*          The leading dimension of the array T. LDT >= K. */

/*  C       (input/output) COMPLEX*16 array, dimension (LDC,N) */
/*          On entry, the M-by-N matrix C. */
/*          On exit, C is overwritten by H*C or H'*C or C*H or C*H'. */

/*  LDC     (input) INTEGER */
/*          The leading dimension of the array C. LDC >= max(1,M). */

/*  WORK    (workspace) COMPLEX*16 array, dimension (LDWORK,K) */

/*  LDWORK  (input) INTEGER */
/*          The leading dimension of the array WORK. */
/*          If SIDE = 'L', LDWORK >= max(1,N); */
/*          if SIDE = 'R', LDWORK >= max(1,M). */

/*  ===================================================================== */

/*     .. Parameters .. */
/*<       COMPLEX*16         ONE >*/
/*<       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) ) >*/
/*     .. */
/*     .. Local Scalars .. */
/*<       CHARACTER          TRANST >*/
/*<       INTEGER            I, J >*/
/*     .. */
/*     .. External Functions .. */
/*<       LOGICAL            LSAME >*/
/*<       EXTERNAL           LSAME >*/
/*     .. */
/*     .. External Subroutines .. */
/*<       EXTERNAL           ZCOPY, ZGEMM, ZLACGV, ZTRMM >*/
/*     .. */
/*     .. Intrinsic Functions .. */
/*<       INTRINSIC          DCONJG >*/
/*     .. */
/*     .. Executable Statements .. */

/*     Quick return if possible */

/*<    >*/
    /* Parameter adjustments */
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    t_dim1 = *ldt;
    t_offset = 1 + t_dim1;
    t -= t_offset;
    c_dim1 = *ldc;
    c_offset = 1 + c_dim1;
    c__ -= c_offset;
    work_dim1 = *ldwork;
    work_offset = 1 + work_dim1;
    work -= work_offset;

    /* Function Body */
    if (*m <= 0 || *n <= 0) {
        return 0;
    }

/*<       IF( LSAME( TRANS, 'N' ) ) THEN >*/
    if (lsame_(trans, "N", (ftnlen)1, (ftnlen)1)) {
/*<          TRANST = 'C' >*/
        *(unsigned char *)transt = 'C';
/*<       ELSE >*/
    } else {
/*<          TRANST = 'N' >*/
        *(unsigned char *)transt = 'N';
/*<       END IF >*/
    }

/*<       IF( LSAME( STOREV, 'C' ) ) THEN >*/
    if (lsame_(storev, "C", (ftnlen)1, (ftnlen)1)) {

/*<          IF( LSAME( DIRECT, 'F' ) ) THEN >*/
        if (lsame_(direct, "F", (ftnlen)1, (ftnlen)1)) {

/*           Let  V =  ( V1 )    (first K rows) */
/*                     ( V2 ) */
/*           where  V1  is unit lower triangular. */

/*<             IF( LSAME( SIDE, 'L' ) ) THEN >*/
            if (lsame_(side, "L", (ftnlen)1, (ftnlen)1)) {

/*              Form  H * C  or  H' * C  where  C = ( C1 ) */
/*                                                  ( C2 ) */

/*              W := C' * V  =  (C1'*V1 + C2'*V2)  (stored in WORK) */

/*              W := C1' */

/*<                DO 10 J = 1, K >*/
                i__1 = *k;
                for (j = 1; j <= i__1; ++j) {
/*<                   CALL ZCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) >*/
                    zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1],
                             &c__1);
/*<                   CALL ZLACGV( N, WORK( 1, J ), 1 ) >*/
                    zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
/*<    10          CONTINUE >*/
/* L10: */
                }

/*              W := W * V1 */

/*<    >*/
                ztrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b1, 
                        &v[v_offset], ldv, &work[work_offset], ldwork, (
                        ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4);
/*<                IF( M.GT.K ) THEN >*/
                if (*m > *k) {

/*                 W := W + C2'*V2 */

/*<    >*/
                    i__1 = *m - *k;
                    zgemm_("Conjugate transpose", "No transpose", n, k, &i__1,
                             &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + 
                            v_dim1], ldv, &c_b1, &work[work_offset], ldwork, (
                            ftnlen)19, (ftnlen)12);
/*<                END IF >*/
                }

/*              W := W * T'  or  W * T */

/*<    >*/
                ztrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b1, &t[
                        t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5,
                         (ftnlen)5, (ftnlen)1, (ftnlen)8);

/*              C := C - V * W' */

/*<                IF( M.GT.K ) THEN >*/
                if (*m > *k) {

/*                 C2 := C2 - V2 * W' */

/*<    >*/
                    i__1 = *m - *k;
                    z__1.r = -1., z__1.i = -0.;
                    zgemm_("No transpose", "Conjugate transpose", &i__1, n, k,
                             &z__1, &v[*k + 1 + v_dim1], ldv, &work[
                            work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1]
                            , ldc, (ftnlen)12, (ftnlen)19);
/*<                END IF >*/
                }

/*              W := W * V1' */

/*<    >*/
                ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", n, k, 
                        &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, 
                        (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4);

/*              C1 := C1 - W' */

/*<                DO 30 J = 1, K >*/
                i__1 = *k;
                for (j = 1; j <= i__1; ++j) {
/*<                   DO 20 I = 1, N >*/
                    i__2 = *n;
                    for (i__ = 1; i__ <= i__2; ++i__) {
/*<                      C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) ) >*/
                        i__3 = j + i__ * c_dim1;
                        i__4 = j + i__ * c_dim1;
                        d_cnjg(&z__2, &work[i__ + j * work_dim1]);
                        z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - 
                                z__2.i;
                        c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/*<    20             CONTINUE >*/
/* L20: */
                    }
/*<    30          CONTINUE >*/
/* L30: */
                }

/*<             ELSE IF( LSAME( SIDE, 'R' ) ) THEN >*/
            } else if (lsame_(side, "R", (ftnlen)1, (ftnlen)1)) {

/*              Form  C * H  or  C * H'  where  C = ( C1  C2 ) */

/*              W := C * V  =  (C1*V1 + C2*V2)  (stored in WORK) */

/*              W := C1 */

/*<                DO 40 J = 1, K >*/
                i__1 = *k;
                for (j = 1; j <= i__1; ++j) {
/*<                   CALL ZCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) >*/
                    zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * 
                            work_dim1 + 1], &c__1);
/*<    40          CONTINUE >*/
/* L40: */
                }

/*              W := W * V1 */

/*<    >*/
                ztrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b1, 
                        &v[v_offset], ldv, &work[work_offset], ldwork, (
                        ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4);
/*<                IF( N.GT.K ) THEN >*/
                if (*n > *k) {

/*                 W := W + C2 * V2 */

/*<    >*/
                    i__1 = *n - *k;
                    zgemm_("No transpose", "No transpose", m, k, &i__1, &c_b1,
                             &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 + 
                            v_dim1], ldv, &c_b1, &work[work_offset], ldwork, (
                            ftnlen)12, (ftnlen)12);
/*<                END IF >*/