zlatme.c

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/* zlatme.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 doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;
static integer c__0 = 0;
static integer c__5 = 5;

/* Subroutine */ int zlatme_(integer *n, char *dist, integer *iseed, 
        doublecomplex *d__, integer *mode, doublereal *cond, doublecomplex *
        dmax__, char *ei, char *rsign, char *upper, char *sim, doublereal *ds, 
         integer *modes, doublereal *conds, integer *kl, integer *ku, 
        doublereal *anorm, doublecomplex *a, integer *lda, doublecomplex *
        work, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;
    doublereal d__1, d__2;
    doublecomplex z__1, z__2;

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

    /* Local variables */
    integer i__, j, ic, jc, ir, jcr;
    doublecomplex tau;
    logical bads;
    integer isim;
    doublereal temp;
    doublecomplex alpha;
    extern logical lsame_(char *, char *);
    integer iinfo;
    doublereal tempa[1];
    integer icols;
    extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *);
    integer idist;
    extern /* Subroutine */ int zscal_(integer *, doublecomplex *, 
            doublecomplex *, integer *), zgemv_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, doublecomplex *, integer *);
    integer irows;
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *), dlatm1_(integer *, doublereal *, 
            integer *, integer *, integer *, doublereal *, integer *, integer 
            *), zlatm1_(integer *, doublereal *, integer *, integer *, 
            integer *, doublecomplex *, integer *, integer *);
    doublereal ralpha;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, 
            integer *, doublereal *);
    extern /* Subroutine */ int zdscal_(integer *, doublereal *, 
            doublecomplex *, integer *), zlarge_(integer *, doublecomplex *, 
            integer *, integer *, doublecomplex *, integer *), zlarfg_(
            integer *, doublecomplex *, doublecomplex *, integer *, 
            doublecomplex *), zlacgv_(integer *, doublecomplex *, integer *);
    extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *, 
            integer *);
    integer irsign;
    extern /* Subroutine */ int zlaset_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, doublecomplex *, integer *);
    integer iupper;
    extern /* Subroutine */ int zlarnv_(integer *, integer *, integer *, 
            doublecomplex *);
    doublecomplex xnorms;


/*  -- LAPACK test routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*     ZLATME generates random non-symmetric square matrices with */
/*     specified eigenvalues for testing LAPACK programs. */

/*     ZLATME operates by applying the following sequence of */
/*     operations: */

/*     1. Set the diagonal to D, where D may be input or */
/*          computed according to MODE, COND, DMAX, and RSIGN */
/*          as described below. */

/*     2. If UPPER='T', the upper triangle of A is set to random values */
/*          out of distribution DIST. */

/*     3. If SIM='T', A is multiplied on the left by a random matrix */
/*          X, whose singular values are specified by DS, MODES, and */
/*          CONDS, and on the right by X inverse. */

/*     4. If KL < N-1, the lower bandwidth is reduced to KL using */
/*          Householder transformations.  If KU < N-1, the upper */
/*          bandwidth is reduced to KU. */

/*     5. If ANORM is not negative, the matrix is scaled to have */
/*          maximum-element-norm ANORM. */

/*     (Note: since the matrix cannot be reduced beyond Hessenberg form, */
/*      no packing options are available.) */

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

/*  N      - INTEGER */
/*           The number of columns (or rows) of A. Not modified. */

/*  DIST   - CHARACTER*1 */
/*           On entry, DIST specifies the type of distribution to be used */
/*           to generate the random eigen-/singular values, and on the */
/*           upper triangle (see UPPER). */
/*           'U' => UNIFORM( 0, 1 )  ( 'U' for uniform ) */
/*           'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) */
/*           'N' => NORMAL( 0, 1 )   ( 'N' for normal ) */
/*           'D' => uniform on the complex disc |z| < 1. */
/*           Not modified. */

/*  ISEED  - INTEGER array, dimension ( 4 ) */
/*           On entry ISEED specifies the seed of the random number */
/*           generator. They should lie between 0 and 4095 inclusive, */
/*           and ISEED(4) should be odd. The random number generator */
/*           uses a linear congruential sequence limited to small */
/*           integers, and so should produce machine independent */
/*           random numbers. The values of ISEED are changed on */
/*           exit, and can be used in the next call to ZLATME */
/*           to continue the same random number sequence. */
/*           Changed on exit. */

/*  D      - COMPLEX*16 array, dimension ( N ) */
/*           This array is used to specify the eigenvalues of A.  If */
/*           MODE=0, then D is assumed to contain the eigenvalues */
/*           otherwise they will be computed according to MODE, COND, */
/*           DMAX, and RSIGN and placed in D. */
/*           Modified if MODE is nonzero. */

/*  MODE   - INTEGER */
/*           On entry this describes how the eigenvalues are to */
/*           be specified: */
/*           MODE = 0 means use D as input */
/*           MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND */
/*           MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND */
/*           MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) */
/*           MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) */
/*           MODE = 5 sets D to random numbers in the range */
/*                    ( 1/COND , 1 ) such that their logarithms */
/*                    are uniformly distributed. */
/*           MODE = 6 set D to random numbers from same distribution */
/*                    as the rest of the matrix. */
/*           MODE < 0 has the same meaning as ABS(MODE), except that */
/*              the order of the elements of D is reversed. */
/*           Thus if MODE is between 1 and 4, D has entries ranging */
/*              from 1 to 1/COND, if between -1 and -4, D has entries */
/*              ranging from 1/COND to 1, */
/*           Not modified. */

/*  COND   - DOUBLE PRECISION */
/*           On entry, this is used as described under MODE above. */
/*           If used, it must be >= 1. Not modified. */

/*  DMAX   - COMPLEX*16 */
/*           If MODE is neither -6, 0 nor 6, the contents of D, as */
/*           computed according to MODE and COND, will be scaled by */
/*           DMAX / max(abs(D(i))).  Note that DMAX need not be */
/*           positive or real: if DMAX is negative or complex (or zero), */
/*           D will be scaled by a negative or complex number (or zero). */
/*           If RSIGN='F' then the largest (absolute) eigenvalue will be */
/*           equal to DMAX. */
/*           Not modified. */

/*  EI     - CHARACTER*1 (ignored) */
/*           Not modified. */

/*  RSIGN  - CHARACTER*1 */
/*           If MODE is not 0, 6, or -6, and RSIGN='T', then the */
/*           elements of D, as computed according to MODE and COND, will */
/*           be multiplied by a random complex number from the unit */
/*           circle |z| = 1.  If RSIGN='F', they will not be.  RSIGN may */
/*           only have the values 'T' or 'F'. */
/*           Not modified. */

/*  UPPER  - CHARACTER*1 */
/*           If UPPER='T', then the elements of A above the diagonal */
/*           will be set to random numbers out of DIST.  If UPPER='F', */
/*           they will not.  UPPER may only have the values 'T' or 'F'. */
/*           Not modified. */

/*  SIM    - CHARACTER*1 */
/*           If SIM='T', then A will be operated on by a "similarity */
/*           transform", i.e., multiplied on the left by a matrix X and */
/*           on the right by X inverse.  X = U S V, where U and V are */
/*           random unitary matrices and S is a (diagonal) matrix of */
/*           singular values specified by DS, MODES, and CONDS.  If */
/*           SIM='F', then A will not be transformed. */
/*           Not modified. */

/*  DS     - DOUBLE PRECISION array, dimension ( N ) */
/*           This array is used to specify the singular values of X, */
/*           in the same way that D specifies the eigenvalues of A. */
/*           If MODE=0, the DS contains the singular values, which */
/*           may not be zero. */
/*           Modified if MODE is nonzero. */

/*  MODES  - INTEGER */
/*  CONDS  - DOUBLE PRECISION */
/*           Similar to MODE and COND, but for specifying the diagonal */
/*           of S.  MODES=-6 and +6 are not allowed (since they would */
/*           result in randomly ill-conditioned eigenvalues.) */

/*  KL     - INTEGER */
/*           This specifies the lower bandwidth of the  matrix.  KL=1 */
/*           specifies upper Hessenberg form.  If KL is at least N-1, */
/*           then A will have full lower bandwidth. */
/*           Not modified. */

/*  KU     - INTEGER */
/*           This specifies the upper bandwidth of the  matrix.  KU=1 */
/*           specifies lower Hessenberg form.  If KU is at least N-1, */
/*           then A will have full upper bandwidth; if KU and KL */
/*           are both at least N-1, then A will be dense.  Only one of */
/*           KU and KL may be less than N-1. */
/*           Not modified. */

/*  ANORM  - DOUBLE PRECISION */
/*           If ANORM is not negative, then A will be scaled by a non- */
/*           negative real number to make the maximum-element-norm of A */
/*           to be ANORM. */
/*           Not modified. */

/*  A      - COMPLEX*16 array, dimension ( LDA, N ) */
/*           On exit A is the desired test matrix. */
/*           Modified. */

/*  LDA    - INTEGER */
/*           LDA specifies the first dimension of A as declared in the */
/*           calling program.  LDA must be at least M. */
/*           Not modified. */

/*  WORK   - COMPLEX*16 array, dimension ( 3*N ) */
/*           Workspace. */
/*           Modified. */

/*  INFO   - INTEGER */
/*           Error code.  On exit, INFO will be set to one of the */
/*           following values: */
/*             0 => normal return */
/*            -1 => N negative */
/*            -2 => DIST illegal string */
/*            -5 => MODE not in range -6 to 6 */
/*            -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 */
/*            -9 => RSIGN is not 'T' or 'F' */
/*           -10 => UPPER is not 'T' or 'F' */
/*           -11 => SIM   is not 'T' or 'F' */
/*           -12 => MODES=0 and DS has a zero singular value. */
/*           -13 => MODES is not in the range -5 to 5. */
/*           -14 => MODES is nonzero and CONDS is less than 1. */
/*           -15 => KL is less than 1. */
/*           -16 => KU is less than 1, or KL and KU are both less than */
/*                  N-1. */
/*           -19 => LDA is less than M. */
/*            1  => Error return from ZLATM1 (computing D) */
/*            2  => Cannot scale to DMAX (max. eigenvalue is 0) */
/*            3  => Error return from DLATM1 (computing DS) */
/*            4  => Error return from ZLARGE */
/*            5  => Zero singular value from DLATM1. */

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

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

/*     1)      Decode and Test the input parameters. */
/*             Initialize flags & seed. */

    /* Parameter adjustments */
    --iseed;
    --d__;
    --ds;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --work;

    /* Function Body */
    *info = 0;

/*     Quick return if possible */

    if (*n == 0) {
        return 0;
    }

/*     Decode DIST */

    if (lsame_(dist, "U")) {
        idist = 1;
    } else if (lsame_(dist, "S")) {
        idist = 2;
    } else if (lsame_(dist, "N")) {
        idist = 3;
    } else if (lsame_(dist, "D")) {
        idist = 4;
    } else {
        idist = -1;
    }

/*     Decode RSIGN */

    if (lsame_(rsign, "T")) {
        irsign = 1;
    } else if (lsame_(rsign, "F")) {
        irsign = 0;
    } else {
        irsign = -1;
    }

/*     Decode UPPER */

    if (lsame_(upper, "T")) {
        iupper = 1;
    } else if (lsame_(upper, "F")) {
        iupper = 0;
    } else {
        iupper = -1;
    }

/*     Decode SIM */

    if (lsame_(sim, "T")) {
        isim = 1;
    } else if (lsame_(sim, "F")) {
        isim = 0;
    } else {
        isim = -1;
    }

/*     Check DS, if MODES=0 and ISIM=1 */

    bads = FALSE_;
    if (*modes == 0 && isim == 1) {
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            if (ds[j] == 0.) {
                bads = TRUE_;
            }
/* L10: */
        }
    }

/*     Set INFO if an error */

    if (*n < 0) {
        *info = -1;
    } else if (idist == -1) {
        *info = -2;
    } else if (abs(*mode) > 6) {
        *info = -5;
    } else if (*mode != 0 && abs(*mode) != 6 && *cond < 1.) {
        *info = -6;
    } else if (irsign == -1) {
        *info = -9;
    } else if (iupper == -1) {
        *info = -10;
    } else if (isim == -1) {
        *info = -11;
    } else if (bads) {
        *info = -12;
    } else if (isim == 1 && abs(*modes) > 5) {
        *info = -13;
    } else if (isim == 1 && *modes != 0 && *conds < 1.) {
        *info = -14;
    } else if (*kl < 1) {
        *info = -15;
    } else if (*ku < 1 || *ku < *n - 1 && *kl < *n - 1) {
        *info = -16;
    } else if (*lda < max(1,*n)) {
        *info = -19;
    }

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

/*     Initialize random number generator */

    for (i__ = 1; i__ <= 4; ++i__) {
        iseed[i__] = (i__1 = iseed[i__], abs(i__1)) % 4096;
/* L20: */
    }

    if (iseed[4] % 2 != 1) {
        ++iseed[4];
    }

/*     2)      Set up diagonal of A */

/*             Compute D according to COND and MODE */

    zlatm1_(mode, cond, &irsign, &idist, &iseed[1], &d__[1], n, &iinfo);
    if (iinfo != 0) {
        *info = 1;
        return 0;
    }
    if (*mode != 0 && abs(*mode) != 6) {

/*        Scale by DMAX */

        temp = z_abs(&d__[1]);
        i__1 = *n;
        for (i__ = 2; i__ <= i__1; ++i__) {
/* Computing MAX */
            d__1 = temp, d__2 = z_abs(&d__[i__]);
            temp = max(d__1,d__2);
/* L30: */
        }

        if (temp > 0.) {
            z__1.r = dmax__->r / temp, z__1.i = dmax__->i / temp;
            alpha.r = z__1.r, alpha.i = z__1.i;
        } else {
            *info = 2;
            return 0;
        }

        zscal_(n, &alpha, &d__[1], &c__1);

    }

    zlaset_("Full", n, n, &c_b1, &c_b1, &a[a_offset], lda);
    i__1 = *lda + 1;
    zcopy_(n, &d__[1], &c__1, &a[a_offset], &i__1);

/*     3)      If UPPER='T', set upper triangle of A to random numbers. */

    if (iupper != 0) {
        i__1 = *n;
        for (jc = 2; jc <= i__1; ++jc) {
            i__2 = jc - 1;
            zlarnv_(&idist, &iseed[1], &i__2, &a[jc * a_dim1 + 1]);
/* L40: */
        }
    }

/*     4)      If SIM='T', apply similarity transformation. */

/*                                -1 */
/*             Transform is  X A X  , where X = U S V, thus */

/*             it is  U S V A V' (1/S) U' */

    if (isim != 0) {

/*        Compute S (singular values of the eigenvector matrix) */
/*        according to CONDS and MODES */

        dlatm1_(modes, conds, &c__0, &c__0, &iseed[1], &ds[1], n, &iinfo);
        if (iinfo != 0) {
            *info = 3;
            return 0;
        }

/*        Multiply by V and V' */

        zlarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo);
        if (iinfo != 0) {
            *info = 4;
            return 0;
        }

/*        Multiply by S and (1/S) */

        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            zdscal_(n, &ds[j], &a[j + a_dim1], lda);
            if (ds[j] != 0.) {
                d__1 = 1. / ds[j];
                zdscal_(n, &d__1, &a[j * a_dim1 + 1], &c__1);
            } else {
                *info = 5;
                return 0;
            }
/* L50: */
        }

/*        Multiply by U and U' */

        zlarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo);
        if (iinfo != 0) {
            *info = 4;
            return 0;
        }
    }

/*     5)      Reduce the bandwidth. */

    if (*kl < *n - 1) {

/*        Reduce bandwidth -- kill column */

        i__1 = *n - 1;
        for (jcr = *kl + 1; jcr <= i__1; ++jcr) {
            ic = jcr - *kl;
            irows = *n + 1 - jcr;
            icols = *n + *kl - jcr;

            zcopy_(&irows, &a[jcr + ic * a_dim1], &c__1, &work[1], &c__1);
            xnorms.r = work[1].r, xnorms.i = work[1].i;
            zlarfg_(&irows, &xnorms, &work[2], &c__1, &tau);
            d_cnjg(&z__1, &tau);
            tau.r = z__1.r, tau.i = z__1.i;
            work[1].r = 1., work[1].i = 0.;
            zlarnd_(&z__1, &c__5, &iseed[1]);
            alpha.r = z__1.r, alpha.i = z__1.i;

            zgemv_("C", &irows, &icols, &c_b2, &a[jcr + (ic + 1) * a_dim1], 
                    lda, &work[1], &c__1, &c_b1, &work[irows + 1], &c__1);
            z__1.r = -tau.r, z__1.i = -tau.i;
            zgerc_(&irows, &icols, &z__1, &work[1], &c__1, &work[irows + 1], &
                    c__1, &a[jcr + (ic + 1) * a_dim1], lda);

            zgemv_("N", n, &irows, &c_b2, &a[jcr * a_dim1 + 1], lda, &work[1], 
                     &c__1, &c_b1, &work[irows + 1], &c__1);
            d_cnjg(&z__2, &tau);
            z__1.r = -z__2.r, z__1.i = -z__2.i;
            zgerc_(n, &irows, &z__1, &work[irows + 1], &c__1, &work[1], &c__1, 
                     &a[jcr * a_dim1 + 1], lda);

            i__2 = jcr + ic * a_dim1;
            a[i__2].r = xnorms.r, a[i__2].i = xnorms.i;
            i__2 = irows - 1;
            zlaset_("Full", &i__2, &c__1, &c_b1, &c_b1, &a[jcr + 1 + ic * 
                    a_dim1], lda);

            i__2 = icols + 1;
            zscal_(&i__2, &alpha, &a[jcr + ic * a_dim1], lda);
            d_cnjg(&z__1, &alpha);
            zscal_(n, &z__1, &a[jcr * a_dim1 + 1], &c__1);
/* L60: */
        }
    } else if (*ku < *n - 1) {

/*        Reduce upper bandwidth -- kill a row at a time. */

        i__1 = *n - 1;
        for (jcr = *ku + 1; jcr <= i__1; ++jcr) {
            ir = jcr - *ku;
            irows = *n + *ku - jcr;
            icols = *n + 1 - jcr;

            zcopy_(&icols, &a[ir + jcr * a_dim1], lda, &work[1], &c__1);
            xnorms.r = work[1].r, xnorms.i = work[1].i;
            zlarfg_(&icols, &xnorms, &work[2], &c__1, &tau);
            d_cnjg(&z__1, &tau);
            tau.r = z__1.r, tau.i = z__1.i;
            work[1].r = 1., work[1].i = 0.;
            i__2 = icols - 1;
            zlacgv_(&i__2, &work[2], &c__1);
            zlarnd_(&z__1, &c__5, &iseed[1]);
            alpha.r = z__1.r, alpha.i = z__1.i;

            zgemv_("N", &irows, &icols, &c_b2, &a[ir + 1 + jcr * a_dim1], lda, 
                     &work[1], &c__1, &c_b1, &work[icols + 1], &c__1);
            z__1.r = -tau.r, z__1.i = -tau.i;
            zgerc_(&irows, &icols, &z__1, &work[icols + 1], &c__1, &work[1], &
                    c__1, &a[ir + 1 + jcr * a_dim1], lda);

            zgemv_("C", &icols, n, &c_b2, &a[jcr + a_dim1], lda, &work[1], &
                    c__1, &c_b1, &work[icols + 1], &c__1);
            d_cnjg(&z__2, &tau);
            z__1.r = -z__2.r, z__1.i = -z__2.i;
            zgerc_(&icols, n, &z__1, &work[1], &c__1, &work[icols + 1], &c__1, 
                     &a[jcr + a_dim1], lda);

            i__2 = ir + jcr * a_dim1;
            a[i__2].r = xnorms.r, a[i__2].i = xnorms.i;
            i__2 = icols - 1;
            zlaset_("Full", &c__1, &i__2, &c_b1, &c_b1, &a[ir + (jcr + 1) * 
                    a_dim1], lda);

            i__2 = irows + 1;
            zscal_(&i__2, &alpha, &a[ir + jcr * a_dim1], &c__1);
            d_cnjg(&z__1, &alpha);
            zscal_(n, &z__1, &a[jcr + a_dim1], lda);
/* L70: */
        }
    }

/*     Scale the matrix to have norm ANORM */

    if (*anorm >= 0.) {
        temp = zlange_("M", n, n, &a[a_offset], lda, tempa);
        if (temp > 0.) {
            ralpha = *anorm / temp;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                zdscal_(n, &ralpha, &a[j * a_dim1 + 1], &c__1);
/* L80: */
            }
        }
    }

    return 0;

/*     End of ZLATME */

} /* zlatme_ */