dorgtr.c

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/* dorgtr.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 integer c__1 = 1;
static integer c_n1 = -1;

/* Subroutine */ int dorgtr_(char *uplo, integer *n, doublereal *a, integer *
        lda, doublereal *tau, doublereal *work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;

    /* Local variables */
    integer i__, j, nb;
    extern logical lsame_(char *, char *);
    integer iinfo;
    logical upper;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern /* Subroutine */ int dorgql_(integer *, integer *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *, 
            integer *), dorgqr_(integer *, integer *, integer *, doublereal *, 
             integer *, doublereal *, doublereal *, integer *, integer *);
    integer lwkopt;
    logical lquery;


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

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

/*  DORGTR generates a real orthogonal matrix Q which is defined as the */
/*  product of n-1 elementary reflectors of order N, as returned by */
/*  DSYTRD: */

/*  if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), */

/*  if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). */

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

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U': Upper triangle of A contains elementary reflectors */
/*                 from DSYTRD; */
/*          = 'L': Lower triangle of A contains elementary reflectors */
/*                 from DSYTRD. */

/*  N       (input) INTEGER */
/*          The order of the matrix Q. N >= 0. */

/*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/*          On entry, the vectors which define the elementary reflectors, */
/*          as returned by DSYTRD. */
/*          On exit, the N-by-N orthogonal matrix Q. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A. LDA >= max(1,N). */

/*  TAU     (input) DOUBLE PRECISION array, dimension (N-1) */
/*          TAU(i) must contain the scalar factor of the elementary */
/*          reflector H(i), as returned by DSYTRD. */

/*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

/*  LWORK   (input) INTEGER */
/*          The dimension of the array WORK. LWORK >= max(1,N-1). */
/*          For optimum performance LWORK >= (N-1)*NB, where NB is */
/*          the optimal blocksize. */

/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates the optimal size of the WORK array, returns */
/*          this value as the first entry of the WORK array, and no error */
/*          message related to LWORK is issued by XERBLA. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --tau;
    --work;

    /* Function Body */
    *info = 0;
    lquery = *lwork == -1;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L")) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*lda < max(1,*n)) {
        *info = -4;
    } else /* if(complicated condition) */ {
/* Computing MAX */
        i__1 = 1, i__2 = *n - 1;
        if (*lwork < max(i__1,i__2) && ! lquery) {
            *info = -7;
        }
    }

    if (*info == 0) {
        if (upper) {
            i__1 = *n - 1;
            i__2 = *n - 1;
            i__3 = *n - 1;
            nb = ilaenv_(&c__1, "DORGQL", " ", &i__1, &i__2, &i__3, &c_n1);
        } else {
            i__1 = *n - 1;
            i__2 = *n - 1;
            i__3 = *n - 1;
            nb = ilaenv_(&c__1, "DORGQR", " ", &i__1, &i__2, &i__3, &c_n1);
        }
/* Computing MAX */
        i__1 = 1, i__2 = *n - 1;
        lwkopt = max(i__1,i__2) * nb;
        work[1] = (doublereal) lwkopt;
    }

    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DORGTR", &i__1);
        return 0;
    } else if (lquery) {
        return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
        work[1] = 1.;
        return 0;
    }

    if (upper) {

/*        Q was determined by a call to DSYTRD with UPLO = 'U' */

/*        Shift the vectors which define the elementary reflectors one */
/*        column to the left, and set the last row and column of Q to */
/*        those of the unit matrix */

        i__1 = *n - 1;
        for (j = 1; j <= i__1; ++j) {
            i__2 = j - 1;
            for (i__ = 1; i__ <= i__2; ++i__) {
                a[i__ + j * a_dim1] = a[i__ + (j + 1) * a_dim1];
/* L10: */
            }
            a[*n + j * a_dim1] = 0.;
/* L20: */
        }
        i__1 = *n - 1;
        for (i__ = 1; i__ <= i__1; ++i__) {
            a[i__ + *n * a_dim1] = 0.;
/* L30: */
        }
        a[*n + *n * a_dim1] = 1.;

/*        Generate Q(1:n-1,1:n-1) */

        i__1 = *n - 1;
        i__2 = *n - 1;
        i__3 = *n - 1;
        dorgql_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], 
                lwork, &iinfo);

    } else {

/*        Q was determined by a call to DSYTRD with UPLO = 'L'. */

/*        Shift the vectors which define the elementary reflectors one */
/*        column to the right, and set the first row and column of Q to */
/*        those of the unit matrix */

        for (j = *n; j >= 2; --j) {
            a[j * a_dim1 + 1] = 0.;
            i__1 = *n;
            for (i__ = j + 1; i__ <= i__1; ++i__) {
                a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1];
/* L40: */
            }
/* L50: */
        }
        a[a_dim1 + 1] = 1.;
        i__1 = *n;
        for (i__ = 2; i__ <= i__1; ++i__) {
            a[i__ + a_dim1] = 0.;
/* L60: */
        }
        if (*n > 1) {

/*           Generate Q(2:n,2:n) */

            i__1 = *n - 1;
            i__2 = *n - 1;
            i__3 = *n - 1;
            dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], 
                    &work[1], lwork, &iinfo);
        }
    }
    work[1] = (doublereal) lwkopt;
    return 0;

/*     End of DORGTR */

} /* dorgtr_ */