slatme.c

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/* slatme.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 real c_b23 = 0.f;
static integer c__0 = 0;
static real c_b39 = 1.f;

/* Subroutine */ int slatme_(integer *n, char *dist, integer *iseed, real *
        d__, integer *mode, real *cond, real *dmax__, char *ei, char *rsign, 
        char *upper, char *sim, real *ds, integer *modes, real *conds, 
        integer *kl, integer *ku, real *anorm, real *a, integer *lda, real *
        work, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;
    real r__1, r__2, r__3;

    /* Local variables */
    integer i__, j, ic, jc, ir, jr, jcr;
    real tau;
    logical bads;
    extern /* Subroutine */ int sger_(integer *, integer *, real *, real *, 
            integer *, real *, integer *, real *, integer *);
    integer isim;
    real temp;
    logical badei;
    real alpha;
    extern logical lsame_(char *, char *);
    integer iinfo;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    real tempa[1];
    integer icols;
    logical useei;
    integer idist;
    extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, 
            real *, integer *, real *, integer *, real *, real *, integer *), scopy_(integer *, real *, integer *, real *, integer *);
    integer irows;
    extern /* Subroutine */ int slatm1_(integer *, real *, integer *, integer 
            *, integer *, real *, integer *, integer *);
    extern doublereal slange_(char *, integer *, integer *, real *, integer *, 
             real *);
    extern /* Subroutine */ int slarge_(integer *, real *, integer *, integer 
            *, real *, integer *), slarfg_(integer *, real *, real *, integer 
            *, real *), xerbla_(char *, integer *);
    extern doublereal slaran_(integer *);
    integer irsign;
    extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *, 
            real *, real *, integer *);
    integer iupper;
    extern /* Subroutine */ int slarnv_(integer *, integer *, integer *, real 
            *);
    real xnorms;


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

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

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

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

/*     SLATME 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 complex conjugate pairs are desired (MODE=0 and EI(1)='R', */
/*          or MODE=5), certain pairs of adjacent elements of D are */
/*          interpreted as the real and complex parts of a complex */
/*          conjugate pair; A thus becomes block diagonal, with 1x1 */
/*          and 2x2 blocks. */

/*     3. If UPPER='T', the upper triangle of A is set to random values */
/*          out of distribution DIST. */

/*     4. 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. */

/*     5. 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. */

/*     6. 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 for 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 ) */
/*           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 SLATME */
/*           to continue the same random number sequence. */
/*           Changed on exit. */

/*  D      - REAL array, dimension ( N ) */
/*           This array is used to specify the eigenvalues of A.  If */
/*           MODE=0, then D is assumed to contain the eigenvalues (but */
/*           see the description of EI), 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 (with EI) 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.  Each odd-even pair */
/*                    of elements will be either used as two real */
/*                    eigenvalues or as the real and imaginary part */
/*                    of a complex conjugate pair of eigenvalues; */
/*                    the choice of which is done is random, with */
/*                    50-50 probability, for each pair. */
/*           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   - REAL */
/*           On entry, this is used as described under MODE above. */
/*           If used, it must be >= 1. Not modified. */

/*  DMAX   - REAL */
/*           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: if DMAX is negative (or zero), D will be */
/*           scaled by a negative number (or zero). */
/*           Not modified. */

/*  EI     - CHARACTER*1 array, dimension ( N ) */
/*           If MODE is 0, and EI(1) is not ' ' (space character), */
/*           this array specifies which elements of D (on input) are */
/*           real eigenvalues and which are the real and imaginary parts */
/*           of a complex conjugate pair of eigenvalues.  The elements */
/*           of EI may then only have the values 'R' and 'I'.  If */
/*           EI(j)='R' and EI(j+1)='I', then the j-th eigenvalue is */
/*           CMPLX( D(j) , D(j+1) ), and the (j+1)-th is the complex */
/*           conjugate thereof.  If EI(j)=EI(j+1)='R', then the j-th */
/*           eigenvalue is D(j) (i.e., real).  EI(1) may not be 'I', */
/*           nor may two adjacent elements of EI both have the value 'I'. */
/*           If MODE is not 0, then EI is ignored.  If MODE is 0 and */
/*           EI(1)=' ', then the eigenvalues will all be real. */
/*           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 sign (+1 or -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 */
/*           (and above the 2x2 diagonal blocks, if A has complex */
/*           eigenvalues) 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     - REAL 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  - REAL */
/*           Same as 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.  KL must be at */
/*           least 1. */
/*           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.  KU must be at least 1. */
/*           Not modified. */

/*  ANORM  - REAL */
/*           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      - REAL 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 N. */
/*           Not modified. */

/*  WORK   - REAL 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 */
/*            -8 => EI(1) is not ' ' or 'R', EI(j) is not 'R' or 'I', or */
/*                  two adjacent elements of EI are 'I'. */
/*            -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 N. */
/*            1  => Error return from SLATM1 (computing D) */
/*            2  => Cannot scale to DMAX (max. eigenvalue is 0) */
/*            3  => Error return from SLATM1 (computing DS) */
/*            4  => Error return from SLARGE */
/*            5  => Zero singular value from SLATM1. */

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

/*     .. 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__;
    --ei;
    --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 {
        idist = -1;
    }

/*     Check EI */

    useei = TRUE_;
    badei = FALSE_;
    if (lsame_(ei + 1, " ") || *mode != 0) {
        useei = FALSE_;
    } else {
        if (lsame_(ei + 1, "R")) {
            i__1 = *n;
            for (j = 2; j <= i__1; ++j) {
                if (lsame_(ei + j, "I")) {
                    if (lsame_(ei + (j - 1), "I")) {
                        badei = TRUE_;
                    }
                } else {
                    if (! lsame_(ei + j, "R")) {
                        badei = TRUE_;
                    }
                }
/* L10: */
            }
        } else {
            badei = TRUE_;
        }
    }

/*     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.f) {
                bads = TRUE_;
            }
/* L20: */
        }
    }

/*     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.f) {
        *info = -6;
    } else if (badei) {
        *info = -8;
    } 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.f) {
        *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_("SLATME", &i__1);
        return 0;
    }

/*     Initialize random number generator */

    for (i__ = 1; i__ <= 4; ++i__) {
        iseed[i__] = (i__1 = iseed[i__], abs(i__1)) % 4096;
/* L30: */
    }

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

/*     2)      Set up diagonal of A */

/*             Compute D according to COND and MODE */

    slatm1_(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 = dabs(d__[1]);
        i__1 = *n;
        for (i__ = 2; i__ <= i__1; ++i__) {
/* Computing MAX */
            r__2 = temp, r__3 = (r__1 = d__[i__], dabs(r__1));
            temp = dmax(r__2,r__3);
/* L40: */
        }

        if (temp > 0.f) {
            alpha = *dmax__ / temp;
        } else if (*dmax__ != 0.f) {
            *info = 2;
            return 0;
        } else {
            alpha = 0.f;
        }

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

    }

    slaset_("Full", n, n, &c_b23, &c_b23, &a[a_offset], lda);
    i__1 = *lda + 1;
    scopy_(n, &d__[1], &c__1, &a[a_offset], &i__1);

/*     Set up complex conjugate pairs */

    if (*mode == 0) {
        if (useei) {
            i__1 = *n;
            for (j = 2; j <= i__1; ++j) {
                if (lsame_(ei + j, "I")) {
                    a[j - 1 + j * a_dim1] = a[j + j * a_dim1];
                    a[j + (j - 1) * a_dim1] = -a[j + j * a_dim1];
                    a[j + j * a_dim1] = a[j - 1 + (j - 1) * a_dim1];
                }
/* L50: */
            }
        }

    } else if (abs(*mode) == 5) {

        i__1 = *n;
        for (j = 2; j <= i__1; j += 2) {
            if (slaran_(&iseed[1]) > .5f) {
                a[j - 1 + j * a_dim1] = a[j + j * a_dim1];
                a[j + (j - 1) * a_dim1] = -a[j + j * a_dim1];
                a[j + j * a_dim1] = a[j - 1 + (j - 1) * a_dim1];
            }
/* L60: */
        }
    }

/*     3)      If UPPER='T', set upper triangle of A to random numbers. */
/*             (but don't modify the corners of 2x2 blocks.) */

    if (iupper != 0) {
        i__1 = *n;
        for (jc = 2; jc <= i__1; ++jc) {
            if (a[jc - 1 + jc * a_dim1] != 0.f) {
                jr = jc - 2;
            } else {
                jr = jc - 1;
            }
            slarnv_(&idist, &iseed[1], &jr, &a[jc * a_dim1 + 1]);
/* L70: */
        }
    }

/*     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 */

        slatm1_(modes, conds, &c__0, &c__0, &iseed[1], &ds[1], n, &iinfo);
        if (iinfo != 0) {
            *info = 3;
            return 0;
        }

/*        Multiply by V and V' */

        slarge_(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) {
            sscal_(n, &ds[j], &a[j + a_dim1], lda);
            if (ds[j] != 0.f) {
                r__1 = 1.f / ds[j];
                sscal_(n, &r__1, &a[j * a_dim1 + 1], &c__1);
            } else {
                *info = 5;
                return 0;
            }
/* L80: */
        }

/*        Multiply by U and U' */

        slarge_(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;

            scopy_(&irows, &a[jcr + ic * a_dim1], &c__1, &work[1], &c__1);
            xnorms = work[1];
            slarfg_(&irows, &xnorms, &work[2], &c__1, &tau);
            work[1] = 1.f;

            sgemv_("T", &irows, &icols, &c_b39, &a[jcr + (ic + 1) * a_dim1], 
                    lda, &work[1], &c__1, &c_b23, &work[irows + 1], &c__1);
            r__1 = -tau;
            sger_(&irows, &icols, &r__1, &work[1], &c__1, &work[irows + 1], &
                    c__1, &a[jcr + (ic + 1) * a_dim1], lda);

            sgemv_("N", n, &irows, &c_b39, &a[jcr * a_dim1 + 1], lda, &work[1]
, &c__1, &c_b23, &work[irows + 1], &c__1);
            r__1 = -tau;
            sger_(n, &irows, &r__1, &work[irows + 1], &c__1, &work[1], &c__1, 
                    &a[jcr * a_dim1 + 1], lda);

            a[jcr + ic * a_dim1] = xnorms;
            i__2 = irows - 1;
            slaset_("Full", &i__2, &c__1, &c_b23, &c_b23, &a[jcr + 1 + ic * 
                    a_dim1], lda);
/* L90: */
        }
    } 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;

            scopy_(&icols, &a[ir + jcr * a_dim1], lda, &work[1], &c__1);
            xnorms = work[1];
            slarfg_(&icols, &xnorms, &work[2], &c__1, &tau);
            work[1] = 1.f;

            sgemv_("N", &irows, &icols, &c_b39, &a[ir + 1 + jcr * a_dim1], 
                    lda, &work[1], &c__1, &c_b23, &work[icols + 1], &c__1);
            r__1 = -tau;
            sger_(&irows, &icols, &r__1, &work[icols + 1], &c__1, &work[1], &
                    c__1, &a[ir + 1 + jcr * a_dim1], lda);

            sgemv_("C", &icols, n, &c_b39, &a[jcr + a_dim1], lda, &work[1], &
                    c__1, &c_b23, &work[icols + 1], &c__1);
            r__1 = -tau;
            sger_(&icols, n, &r__1, &work[1], &c__1, &work[icols + 1], &c__1, 
                    &a[jcr + a_dim1], lda);

            a[ir + jcr * a_dim1] = xnorms;
            i__2 = icols - 1;
            slaset_("Full", &c__1, &i__2, &c_b23, &c_b23, &a[ir + (jcr + 1) * 
                    a_dim1], lda);
/* L100: */
        }
    }

/*     Scale the matrix to have norm ANORM */

    if (*anorm >= 0.f) {
        temp = slange_("M", n, n, &a[a_offset], lda, tempa);
        if (temp > 0.f) {
            alpha = *anorm / temp;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                sscal_(n, &alpha, &a[j * a_dim1 + 1], &c__1);
/* L110: */
            }
        }
    }

    return 0;

/*     End of SLATME */

} /* slatme_ */