f2c/c/shseqr.c

/* ../netlib/shseqr.f -- translated by f2c (version 20100827). 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 "FLA_f2c.h" /* Table of constant values */
static real c_b11 = 0.f;
static real c_b12 = 1.f;
static integer c__12 = 12;
static integer c__49 = 49;
/* > \brief \b SHSEQR */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SHSEQR + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/shseqr. f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/shseqr. f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/shseqr. f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, WR, WI, Z, */
/* LDZ, WORK, LWORK, INFO ) */
/* .. Scalar Arguments .. */
/* INTEGER IHI, ILO, INFO, LDH, LDZ, LWORK, N */
/* CHARACTER COMPZ, JOB */
/* .. */
/* .. Array Arguments .. */
/* REAL H( LDH, * ), WI( * ), WORK( * ), WR( * ), */
/* $ Z( LDZ, * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SHSEQR computes the eigenvalues of a Hessenberg matrix H */
/* > and, optionally, the matrices T and Z from the Schur decomposition */
/* > H = Z T Z**T, where T is an upper quasi-triangular matrix (the */
/* > Schur form), and Z is the orthogonal matrix of Schur vectors. */
/* > */
/* > Optionally Z may be postmultiplied into an input orthogonal */
/* > matrix Q so that this routine can give the Schur factorization */
/* > of a matrix A which has been reduced to the Hessenberg form H */
/* > by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOB */
/* > \verbatim */
/* > JOB is CHARACTER*1 */
/* > = 'E': compute eigenvalues only;
*/
/* > = 'S': compute eigenvalues and the Schur form T. */
/* > \endverbatim */
/* > */
/* > \param[in] COMPZ */
/* > \verbatim */
/* > COMPZ is CHARACTER*1 */
/* > = 'N': no Schur vectors are computed;
*/
/* > = 'I': Z is initialized to the unit matrix and the matrix Z */
/* > of Schur vectors of H is returned;
*/
/* > = 'V': Z must contain an orthogonal matrix Q on entry, and */
/* > the product Q*Z is returned. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix H. N .GE. 0. */
/* > \endverbatim */
/* > */
/* > \param[in] ILO */
/* > \verbatim */
/* > ILO is INTEGER */
/* > \endverbatim */
/* > */
/* > \param[in] IHI */
/* > \verbatim */
/* > IHI is INTEGER */
/* > */
/* > It is assumed that H is already upper triangular in rows */
/* > and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
/* > set by a previous call to SGEBAL, and then passed to ZGEHRD */
/* > when the matrix output by SGEBAL is reduced to Hessenberg */
/* > form. Otherwise ILO and IHI should be set to 1 and N */
/* > respectively. If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N. */
/* > If N = 0, then ILO = 1 and IHI = 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] H */
/* > \verbatim */
/* > H is REAL array, dimension (LDH,N) */
/* > On entry, the upper Hessenberg matrix H. */
/* > On exit, if INFO = 0 and JOB = 'S', then H contains the */
/* > upper quasi-triangular matrix T from the Schur decomposition */
/* > (the Schur form);
2-by-2 diagonal blocks (corresponding to */
/* > complex conjugate pairs of eigenvalues) are returned in */
/* > standard form, with H(i,i) = H(i+1,i+1) and */
/* > H(i+1,i)*H(i,i+1).LT.0. If INFO = 0 and JOB = 'E', the */
/* > contents of H are unspecified on exit. (The output value of */
/* > H when INFO.GT.0 is given under the description of INFO */
/* > below.) */
/* > */
/* > Unlike earlier versions of SHSEQR, this subroutine may */
/* > explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1 */
/* > or j = IHI+1, IHI+2, ... N. */
/* > \endverbatim */
/* > */
/* > \param[in] LDH */
/* > \verbatim */
/* > LDH is INTEGER */
/* > The leading dimension of the array H. LDH .GE. max(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] WR */
/* > \verbatim */
/* > WR is REAL array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] WI */
/* > \verbatim */
/* > WI is REAL array, dimension (N) */
/* > */
/* > The real and imaginary parts, respectively, of the computed */
/* > eigenvalues. If two eigenvalues are computed as a complex */
/* > conjugate pair, they are stored in consecutive elements of */
/* > WR and WI, say the i-th and (i+1)th, with WI(i) .GT. 0 and */
/* > WI(i+1) .LT. 0. If JOB = 'S', the eigenvalues are stored in */
/* > the same order as on the diagonal of the Schur form returned */
/* > in H, with WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2 */
/* > diagonal block, WI(i) = sqrt(-H(i+1,i)*H(i,i+1)) and */
/* > WI(i+1) = -WI(i). */
/* > \endverbatim */
/* > */
/* > \param[in,out] Z */
/* > \verbatim */
/* > Z is REAL array, dimension (LDZ,N) */
/* > If COMPZ = 'N', Z is not referenced. */
/* > If COMPZ = 'I', on entry Z need not be set and on exit, */
/* > if INFO = 0, Z contains the orthogonal matrix Z of the Schur */
/* > vectors of H. If COMPZ = 'V', on entry Z must contain an */
/* > N-by-N matrix Q, which is assumed to be equal to the unit */
/* > matrix except for the submatrix Z(ILO:IHI,ILO:IHI). On exit, */
/* > if INFO = 0, Z contains Q*Z. */
/* > Normally Q is the orthogonal matrix generated by SORGHR */
/* > after the call to SGEHRD which formed the Hessenberg matrix */
/* > H. (The output value of Z when INFO.GT.0 is given under */
/* > the description of INFO below.) */
/* > \endverbatim */
/* > */
/* > \param[in] LDZ */
/* > \verbatim */
/* > LDZ is INTEGER */
/* > The leading dimension of the array Z. if COMPZ = 'I' or */
/* > COMPZ = 'V', then LDZ.GE.MAX(1,N). Otherwize, LDZ.GE.1. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (LWORK) */
/* > On exit, if INFO = 0, WORK(1) returns an estimate of */
/* > the optimal value for LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK. LWORK .GE. max(1,N) */
/* > is sufficient and delivers very good and sometimes */
/* > optimal performance. However, LWORK as large as 11*N */
/* > may be required for optimal performance. A workspace */
/* > query is recommended to determine the optimal workspace */
/* > size. */
/* > */
/* > If LWORK = -1, then SHSEQR does a workspace query. */
/* > In this case, SHSEQR checks the input parameters and */
/* > estimates the optimal workspace size for the given */
/* > values of N, ILO and IHI. The estimate is returned */
/* > in WORK(1). No error message related to LWORK is */
/* > issued by XERBLA. Neither H nor Z are accessed. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > .LT. 0: if INFO = -i, the i-th argument had an illegal */
/* > value */
/* > .GT. 0: if INFO = i, SHSEQR failed to compute all of */
/* > the eigenvalues. Elements 1:ilo-1 and i+1:n of WR */
/* > and WI contain those eigenvalues which have been */
/* > successfully computed. (Failures are rare.) */
/* > */
/* > If INFO .GT. 0 and JOB = 'E', then on exit, the */
/* > remaining unconverged eigenvalues are the eigen- */
/* > values of the upper Hessenberg matrix rows and */
/* > columns ILO through INFO of the final, output */
/* > value of H. */
/* > */
/* > If INFO .GT. 0 and JOB = 'S', then on exit */
/* > */
/* > (*) (initial value of H)*U = U*(final value of H) */
/* > */
/* > where U is an orthogonal matrix. The final */
/* > value of H is upper Hessenberg and quasi-triangular */
/* > in rows and columns INFO+1 through IHI. */
/* > */
/* > If INFO .GT. 0 and COMPZ = 'V', then on exit */
/* > */
/* > (final value of Z) = (initial value of Z)*U */
/* > */
/* > where U is the orthogonal matrix in (*) (regard- */
/* > less of the value of JOB.) */
/* > */
/* > If INFO .GT. 0 and COMPZ = 'I', then on exit */
/* > (final value of Z) = U */
/* > where U is the orthogonal matrix in (*) (regard- */
/* > less of the value of JOB.) */
/* > */
/* > If INFO .GT. 0 and COMPZ = 'N', then Z is not */
/* > accessed. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date November 2011 */
/* > \ingroup realOTHERcomputational */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Karen Braman and Ralph Byers, Department of Mathematics, */
/* > University of Kansas, USA */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > Default values supplied by */
/* > ILAENV(ISPEC,'SHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK). */
/* > It is suggested that these defaults be adjusted in order */
/* > to attain best performance in each particular */
/* > computational environment. */
/* > */
/* > ISPEC=12: The SLAHQR vs SLAQR0 crossover point. */
/* > Default: 75. (Must be at least 11.) */
/* > */
/* > ISPEC=13: Recommended deflation window size. */
/* > This depends on ILO, IHI and NS. NS is the */
/* > number of simultaneous shifts returned */
/* > by ILAENV(ISPEC=15). (See ISPEC=15 below.) */
/* > The default for (IHI-ILO+1).LE.500 is NS. */
/* > The default for (IHI-ILO+1).GT.500 is 3*NS/2. */
/* > */
/* > ISPEC=14: Nibble crossover point. (See IPARMQ for */
/* > details.) Default: 14% of deflation window */
/* > size. */
/* > */
/* > ISPEC=15: Number of simultaneous shifts in a multishift */
/* > QR iteration. */
/* > */
/* > If IHI-ILO+1 is ... */
/* > */
/* > greater than ...but less ... the */
/* > or equal to ... than default is */
/* > */
/* > 1 30 NS = 2(+) */
/* > 30 60 NS = 4(+) */
/* > 60 150 NS = 10(+) */
/* > 150 590 NS = ** */
/* > 590 3000 NS = 64 */
/* > 3000 6000 NS = 128 */
/* > 6000 infinity NS = 256 */
/* > */
/* > (+) By default some or all matrices of this order */
/* > are passed to the implicit double shift routine */
/* > SLAHQR and this parameter is ignored. See */
/* > ISPEC=12 above and comments in IPARMQ for */
/* > details. */
/* > */
/* > (**) The asterisks (**) indicate an ad-hoc */
/* > function of N increasing from 10 to 64. */
/* > */
/* > ISPEC=16: Select structured matrix multiply. */
/* > If the number of simultaneous shifts (specified */
/* > by ISPEC=15) is less than 14, then the default */
/* > for ISPEC=16 is 0. Otherwise the default for */
/* > ISPEC=16 is 2. */
/* > \endverbatim */
/* > \par References: */
/* ================ */
/* > */
/* > K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
/* > Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 */
/* > Performance, SIAM Journal of Matrix Analysis, volume 23, pages */
/* > 929--947, 2002. */
/* > \n */
/* > K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
/* > Algorithm Part II: Aggressive Early Deflation, SIAM Journal */
/* > of Matrix Analysis, volume 23, pages 948--973, 2002. */
/* ===================================================================== */
/* Subroutine */
int shseqr_(char *job, char *compz, integer *n, integer *ilo, integer *ihi, real *h__, integer *ldh, real *wr, real *wi, real *z__, integer *ldz, real *work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__3;
    real r__1;
    char ch__1[2];
    /* Builtin functions */
    /* Subroutine */

    /* Local variables */
    integer i__;
    real hl[2401] /* was [49][49] */
    ;
    integer kbot, nmin;
    extern logical lsame_(char *, char *);
    logical initz;
    real workl[49];
    logical wantt, wantz;
    extern /* Subroutine */
    int slaqr0_(logical *, logical *, integer *, integer *, integer *, real *, integer *, real *, real *, integer * , integer *, real *, integer *, real *, integer *, integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
    extern /* Subroutine */
    int slahqr_(logical *, logical *, integer *, integer *, integer *, real *, integer *, real *, real *, integer * , integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *);
    logical lquery;
    /* -- LAPACK computational routine (version 3.4.0) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* November 2011 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. Parameters .. */
    /* ==== Matrices of order NTINY or smaller must be processed by */
    /* . SLAHQR because of insufficient subdiagonal scratch space. */
    /* . (This is a hard limit.) ==== */
    /* ==== NL allocates some local workspace to help small matrices */
    /* . through a rare SLAHQR failure. NL .GT. NTINY = 11 is */
    /* . required and NL .LE. NMIN = ILAENV(ISPEC=12,...) is recom- */
    /* . mended. (The default value of NMIN is 75.) Using NL = 49 */
    /* . allows up to six simultaneous shifts and a 16-by-16 */
    /* . deflation window. ==== */
    /* .. */
    /* .. Local Arrays .. */
    /* .. */
    /* .. Local Scalars .. */
    /* .. */
    /* .. External Functions .. */
    /* .. */
    /* .. External Subroutines .. */
    /* .. */
    /* .. Intrinsic Functions .. */
    /* .. */
    /* .. Executable Statements .. */
    /* ==== Decode and check the input parameters. ==== */
    /* Parameter adjustments */
    h_dim1 = *ldh;
    h_offset = 1 + h_dim1;
    h__ -= h_offset;
    --wr;
    --wi;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;
    /* Function Body */
    wantt = lsame_(job, "S");
    initz = lsame_(compz, "I");
    wantz = initz || lsame_(compz, "V");
    work[1] = (real) max(1,*n);
    lquery = *lwork == -1;
    *info = 0;
    if (! lsame_(job, "E") && ! wantt)
    {
        *info = -1;
    }
    else if (! lsame_(compz, "N") && ! wantz)
    {
        *info = -2;
    }
    else if (*n < 0)
    {
        *info = -3;
    }
    else if (*ilo < 1 || *ilo > max(1,*n))
    {
        *info = -4;
    }
    else if (*ihi < min(*ilo,*n) || *ihi > *n)
    {
        *info = -5;
    }
    else if (*ldh < max(1,*n))
    {
        *info = -7;
    }
    else if (*ldz < 1 || wantz && *ldz < max(1,*n))
    {
        *info = -11;
    }
    else if (*lwork < max(1,*n) && ! lquery)
    {
        *info = -13;
    }
    if (*info != 0)
    {
        /* ==== Quick return in case of invalid argument. ==== */
        i__1 = -(*info);
        xerbla_("SHSEQR", &i__1);
        return 0;
    }
    else if (*n == 0)
    {
        /* ==== Quick return in case N = 0;
        nothing to do. ==== */
        return 0;
    }
    else if (lquery)
    {
        /* ==== Quick return in case of a workspace query ==== */
        slaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[ 1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info);
        /* ==== Ensure reported workspace size is backward-compatible with */
        /* . previous LAPACK versions. ==== */
        /* Computing MAX */
        r__1 = (real) max(1,*n);
        work[1] = max(r__1,work[1]);
        return 0;
    }
    else
    {
        /* ==== copy eigenvalues isolated by SGEBAL ==== */
        i__1 = *ilo - 1;
        for (i__ = 1;
                i__ <= i__1;
                ++i__)
        {
            wr[i__] = h__[i__ + i__ * h_dim1];
            wi[i__] = 0.f;
            /* L10: */
        }
        i__1 = *n;
        for (i__ = *ihi + 1;
                i__ <= i__1;
                ++i__)
        {
            wr[i__] = h__[i__ + i__ * h_dim1];
            wi[i__] = 0.f;
            /* L20: */
        }
        /* ==== Initialize Z, if requested ==== */
        if (initz)
        {
            slaset_("A", n, n, &c_b11, &c_b12, &z__[z_offset], ldz) ;
        }
        /* ==== Quick return if possible ==== */
        if (*ilo == *ihi)
        {
            wr[*ilo] = h__[*ilo + *ilo * h_dim1];
            wi[*ilo] = 0.f;
            return 0;
        }
        /* ==== SLAHQR/SLAQR0 crossover point ==== */
        nmin = ilaenv_(&c__12, "SHSEQR", ch__1, n, ilo, ihi, lwork);
        nmin = max(11,nmin);
        /* ==== SLAQR0 for big matrices;
        SLAHQR for small ones ==== */
        if (*n > nmin)
        {
            slaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info);
        }
        else
        {
            /* ==== Small matrix ==== */
            slahqr_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, info);
            if (*info > 0)
            {
                /* ==== A rare SLAHQR failure! SLAQR0 sometimes succeeds */
                /* . when SLAHQR fails. ==== */
                kbot = *info;
                if (*n >= 49)
                {
                    /* ==== Larger matrices have enough subdiagonal scratch */
                    /* . space to call SLAQR0 directly. ==== */
                    slaqr0_(&wantt, &wantz, n, ilo, &kbot, &h__[h_offset], ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info);
                }
                else
                {
                    /* ==== Tiny matrices don't have enough subdiagonal */
                    /* . scratch space to benefit from SLAQR0. Hence, */
                    /* . tiny matrices must be copied into a larger */
                    /* . array before calling SLAQR0. ==== */
                    slacpy_("A", n, n, &h__[h_offset], ldh, hl, &c__49);
                    hl[*n + 1 + *n * 49 - 50] = 0.f;
                    i__1 = 49 - *n;
                    slaset_("A", &c__49, &i__1, &c_b11, &c_b11, &hl[(*n + 1) * 49 - 49], &c__49);
                    slaqr0_(&wantt, &wantz, &c__49, ilo, &kbot, hl, &c__49, & wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, workl, &c__49, info);
                    if (wantt || *info != 0)
                    {
                        slacpy_("A", n, n, hl, &c__49, &h__[h_offset], ldh);
                    }
                }
            }
        }
        /* ==== Clear out the trash, if necessary. ==== */
        if ((wantt || *info != 0) && *n > 2)
        {
            i__1 = *n - 2;
            i__3 = *n - 2;
            slaset_("L", &i__1, &i__3, &c_b11, &c_b11, &h__[h_dim1 + 3], ldh);
        }
        /* ==== Ensure reported workspace size is backward-compatible with */
        /* . previous LAPACK versions. ==== */
        /* Computing MAX */
        r__1 = (real) max(1,*n);
        work[1] = max(r__1,work[1]);
    }
    /* ==== End of SHSEQR ==== */
    return 0;
}
/* shseqr_ */