sggev.c

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/* sggev.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__0 = 0;
static integer c_n1 = -1;
static real c_b36 = 0.f;
static real c_b37 = 1.f;

/* Subroutine */ int sggev_(char *jobvl, char *jobvr, integer *n, real *a, 
        integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real 
        *beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work, 
        integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, 
            vr_offset, i__1, i__2;
    real r__1, r__2, r__3, r__4;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    integer jc, in, jr, ihi, ilo;
    real eps;
    logical ilv;
    real anrm, bnrm;
    integer ierr, itau;
    real temp;
    logical ilvl, ilvr;
    integer iwrk;
    extern logical lsame_(char *, char *);
    integer ileft, icols, irows;
    extern /* Subroutine */ int slabad_(real *, real *), sggbak_(char *, char 
            *, integer *, integer *, integer *, real *, real *, integer *, 
            real *, integer *, integer *), sggbal_(char *, 
            integer *, real *, integer *, real *, integer *, integer *, 
            integer *, real *, real *, real *, integer *);
    logical ilascl, ilbscl;
    extern doublereal slamch_(char *), slange_(char *, integer *, 
            integer *, real *, integer *, real *);
    extern /* Subroutine */ int xerbla_(char *, integer *), sgghrd_(
            char *, char *, integer *, integer *, integer *, real *, integer *
, real *, integer *, real *, integer *, real *, integer *, 
            integer *);
    logical ldumma[1];
    char chtemp[1];
    real bignum;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
            real *, integer *, integer *, real *, integer *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    integer ijobvl, iright;
    extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer 
            *, real *, real *, integer *, integer *);
    integer ijobvr;
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
            integer *, real *, integer *), slaset_(char *, integer *, 
            integer *, real *, real *, real *, integer *), stgevc_(
            char *, char *, logical *, integer *, real *, integer *, real *, 
            integer *, real *, integer *, real *, integer *, integer *, 
            integer *, real *, integer *);
    real anrmto, bnrmto;
    extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *, 
            integer *, integer *, real *, integer *, real *, integer *, real *
, real *, real *, real *, integer *, real *, integer *, real *, 
            integer *, integer *);
    integer minwrk, maxwrk;
    real smlnum;
    extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real 
            *, integer *, real *, real *, integer *, integer *);
    logical lquery;
    extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, 
            integer *, real *, integer *, real *, real *, integer *, real *, 
            integer *, integer *);


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

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

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

/*  SGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B) */
/*  the generalized eigenvalues, and optionally, the left and/or right */
/*  generalized eigenvectors. */

/*  A generalized eigenvalue for a pair of matrices (A,B) is a scalar */
/*  lambda or a ratio alpha/beta = lambda, such that A - lambda*B is */
/*  singular. It is usually represented as the pair (alpha,beta), as */
/*  there is a reasonable interpretation for beta=0, and even for both */
/*  being zero. */

/*  The right eigenvector v(j) corresponding to the eigenvalue lambda(j) */
/*  of (A,B) satisfies */

/*                   A * v(j) = lambda(j) * B * v(j). */

/*  The left eigenvector u(j) corresponding to the eigenvalue lambda(j) */
/*  of (A,B) satisfies */

/*                   u(j)**H * A  = lambda(j) * u(j)**H * B . */

/*  where u(j)**H is the conjugate-transpose of u(j). */


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

/*  JOBVL   (input) CHARACTER*1 */
/*          = 'N':  do not compute the left generalized eigenvectors; */
/*          = 'V':  compute the left generalized eigenvectors. */

/*  JOBVR   (input) CHARACTER*1 */
/*          = 'N':  do not compute the right generalized eigenvectors; */
/*          = 'V':  compute the right generalized eigenvectors. */

/*  N       (input) INTEGER */
/*          The order of the matrices A, B, VL, and VR.  N >= 0. */

/*  A       (input/output) REAL array, dimension (LDA, N) */
/*          On entry, the matrix A in the pair (A,B). */
/*          On exit, A has been overwritten. */

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

/*  B       (input/output) REAL array, dimension (LDB, N) */
/*          On entry, the matrix B in the pair (A,B). */
/*          On exit, B has been overwritten. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of B.  LDB >= max(1,N). */

/*  ALPHAR  (output) REAL array, dimension (N) */
/*  ALPHAI  (output) REAL array, dimension (N) */
/*  BETA    (output) REAL array, dimension (N) */
/*          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will */
/*          be the generalized eigenvalues.  If ALPHAI(j) is zero, then */
/*          the j-th eigenvalue is real; if positive, then the j-th and */
/*          (j+1)-st eigenvalues are a complex conjugate pair, with */
/*          ALPHAI(j+1) negative. */

/*          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) */
/*          may easily over- or underflow, and BETA(j) may even be zero. */
/*          Thus, the user should avoid naively computing the ratio */
/*          alpha/beta.  However, ALPHAR and ALPHAI will be always less */
/*          than and usually comparable with norm(A) in magnitude, and */
/*          BETA always less than and usually comparable with norm(B). */

/*  VL      (output) REAL array, dimension (LDVL,N) */
/*          If JOBVL = 'V', the left eigenvectors u(j) are stored one */
/*          after another in the columns of VL, in the same order as */
/*          their eigenvalues. If the j-th eigenvalue is real, then */
/*          u(j) = VL(:,j), the j-th column of VL. If the j-th and */
/*          (j+1)-th eigenvalues form a complex conjugate pair, then */
/*          u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1). */
/*          Each eigenvector is scaled so the largest component has */
/*          abs(real part)+abs(imag. part)=1. */
/*          Not referenced if JOBVL = 'N'. */

/*  LDVL    (input) INTEGER */
/*          The leading dimension of the matrix VL. LDVL >= 1, and */
/*          if JOBVL = 'V', LDVL >= N. */

/*  VR      (output) REAL array, dimension (LDVR,N) */
/*          If JOBVR = 'V', the right eigenvectors v(j) are stored one */
/*          after another in the columns of VR, in the same order as */
/*          their eigenvalues. If the j-th eigenvalue is real, then */
/*          v(j) = VR(:,j), the j-th column of VR. If the j-th and */
/*          (j+1)-th eigenvalues form a complex conjugate pair, then */
/*          v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1). */
/*          Each eigenvector is scaled so the largest component has */
/*          abs(real part)+abs(imag. part)=1. */
/*          Not referenced if JOBVR = 'N'. */

/*  LDVR    (input) INTEGER */
/*          The leading dimension of the matrix VR. LDVR >= 1, and */
/*          if JOBVR = 'V', LDVR >= N. */

/*  WORK    (workspace/output) REAL 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(1,8*N). */
/*          For good performance, LWORK must generally be larger. */

/*          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. */
/*          = 1,...,N: */
/*                The QZ iteration failed.  No eigenvectors have been */
/*                calculated, but ALPHAR(j), ALPHAI(j), and BETA(j) */
/*                should be correct for j=INFO+1,...,N. */
/*          > N:  =N+1: other than QZ iteration failed in SHGEQZ. */
/*                =N+2: error return from STGEVC. */

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

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

/*     Decode the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --alphar;
    --alphai;
    --beta;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1;
    vr -= vr_offset;
    --work;

    /* Function Body */
    if (lsame_(jobvl, "N")) {
        ijobvl = 1;
        ilvl = FALSE_;
    } else if (lsame_(jobvl, "V")) {
        ijobvl = 2;
        ilvl = TRUE_;
    } else {
        ijobvl = -1;
        ilvl = FALSE_;
    }

    if (lsame_(jobvr, "N")) {
        ijobvr = 1;
        ilvr = FALSE_;
    } else if (lsame_(jobvr, "V")) {
        ijobvr = 2;
        ilvr = TRUE_;
    } else {
        ijobvr = -1;
        ilvr = FALSE_;
    }
    ilv = ilvl || ilvr;

/*     Test the input arguments */

    *info = 0;
    lquery = *lwork == -1;
    if (ijobvl <= 0) {
        *info = -1;
    } else if (ijobvr <= 0) {
        *info = -2;
    } else if (*n < 0) {
        *info = -3;
    } else if (*lda < max(1,*n)) {
        *info = -5;
    } else if (*ldb < max(1,*n)) {
        *info = -7;
    } else if (*ldvl < 1 || ilvl && *ldvl < *n) {
        *info = -12;
    } else if (*ldvr < 1 || ilvr && *ldvr < *n) {
        *info = -14;
    }

/*     Compute workspace */
/*      (Note: Comments in the code beginning "Workspace:" describe the */
/*       minimal amount of workspace needed at that point in the code, */
/*       as well as the preferred amount for good performance. */
/*       NB refers to the optimal block size for the immediately */
/*       following subroutine, as returned by ILAENV. The workspace is */
/*       computed assuming ILO = 1 and IHI = N, the worst case.) */

    if (*info == 0) {
/* Computing MAX */
        i__1 = 1, i__2 = *n << 3;
        minwrk = max(i__1,i__2);
/* Computing MAX */
        i__1 = 1, i__2 = *n * (ilaenv_(&c__1, "SGEQRF", " ", n, &c__1, n, &
                c__0) + 7);
        maxwrk = max(i__1,i__2);
/* Computing MAX */
        i__1 = maxwrk, i__2 = *n * (ilaenv_(&c__1, "SORMQR", " ", n, &c__1, n, 
                 &c__0) + 7);
        maxwrk = max(i__1,i__2);
        if (ilvl) {
/* Computing MAX */
            i__1 = maxwrk, i__2 = *n * (ilaenv_(&c__1, "SORGQR", " ", n, &
                    c__1, n, &c_n1) + 7);
            maxwrk = max(i__1,i__2);
        }
        work[1] = (real) maxwrk;

        if (*lwork < minwrk && ! lquery) {
            *info = -16;
        }
    }

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

/*     Quick return if possible */

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

/*     Get machine constants */

    eps = slamch_("P");
    smlnum = slamch_("S");
    bignum = 1.f / smlnum;
    slabad_(&smlnum, &bignum);
    smlnum = sqrt(smlnum) / eps;
    bignum = 1.f / smlnum;

/*     Scale A if max element outside range [SMLNUM,BIGNUM] */

    anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
    ilascl = FALSE_;
    if (anrm > 0.f && anrm < smlnum) {
        anrmto = smlnum;
        ilascl = TRUE_;
    } else if (anrm > bignum) {
        anrmto = bignum;
        ilascl = TRUE_;
    }
    if (ilascl) {
        slascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
                ierr);
    }

/*     Scale B if max element outside range [SMLNUM,BIGNUM] */

    bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
    ilbscl = FALSE_;
    if (bnrm > 0.f && bnrm < smlnum) {
        bnrmto = smlnum;
        ilbscl = TRUE_;
    } else if (bnrm > bignum) {
        bnrmto = bignum;
        ilbscl = TRUE_;
    }
    if (ilbscl) {
        slascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
                ierr);
    }

/*     Permute the matrices A, B to isolate eigenvalues if possible */
/*     (Workspace: need 6*N) */

    ileft = 1;
    iright = *n + 1;
    iwrk = iright + *n;
    sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
            ileft], &work[iright], &work[iwrk], &ierr);

/*     Reduce B to triangular form (QR decomposition of B) */
/*     (Workspace: need N, prefer N*NB) */

    irows = ihi + 1 - ilo;
    if (ilv) {
        icols = *n + 1 - ilo;
    } else {
        icols = irows;
    }
    itau = iwrk;
    iwrk = itau + irows;
    i__1 = *lwork + 1 - iwrk;
    sgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
            iwrk], &i__1, &ierr);

/*     Apply the orthogonal transformation to matrix A */
/*     (Workspace: need N, prefer N*NB) */

    i__1 = *lwork + 1 - iwrk;
    sormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
            work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
            ierr);

/*     Initialize VL */
/*     (Workspace: need N, prefer N*NB) */

    if (ilvl) {
        slaset_("Full", n, n, &c_b36, &c_b37, &vl[vl_offset], ldvl)
                ;
        if (irows > 1) {
            i__1 = irows - 1;
            i__2 = irows - 1;
            slacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[
                    ilo + 1 + ilo * vl_dim1], ldvl);
        }
        i__1 = *lwork + 1 - iwrk;
        sorgqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[
                itau], &work[iwrk], &i__1, &ierr);
    }

/*     Initialize VR */

    if (ilvr) {
        slaset_("Full", n, n, &c_b36, &c_b37, &vr[vr_offset], ldvr)
                ;
    }

/*     Reduce to generalized Hessenberg form */
/*     (Workspace: none needed) */

    if (ilv) {

/*        Eigenvectors requested -- work on whole matrix. */

        sgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], 
                ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ierr);
    } else {
        sgghrd_("N", "N", &irows, &c__1, &irows, &a[ilo + ilo * a_dim1], lda, 
                &b[ilo + ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[
                vr_offset], ldvr, &ierr);
    }

/*     Perform QZ algorithm (Compute eigenvalues, and optionally, the */
/*     Schur forms and Schur vectors) */
/*     (Workspace: need N) */

    iwrk = itau;
    if (ilv) {
        *(unsigned char *)chtemp = 'S';
    } else {
        *(unsigned char *)chtemp = 'E';
    }
    i__1 = *lwork + 1 - iwrk;
    shgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[
            b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset], 
            ldvl, &vr[vr_offset], ldvr, &work[iwrk], &i__1, &ierr);
    if (ierr != 0) {
        if (ierr > 0 && ierr <= *n) {
            *info = ierr;
        } else if (ierr > *n && ierr <= *n << 1) {
            *info = ierr - *n;
        } else {
            *info = *n + 1;
        }
        goto L110;
    }

/*     Compute Eigenvectors */
/*     (Workspace: need 6*N) */

    if (ilv) {
        if (ilvl) {
            if (ilvr) {
                *(unsigned char *)chtemp = 'B';
            } else {
                *(unsigned char *)chtemp = 'L';
            }
        } else {
            *(unsigned char *)chtemp = 'R';
        }
        stgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb, 
                &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
                iwrk], &ierr);
        if (ierr != 0) {
            *info = *n + 2;
            goto L110;
        }

/*        Undo balancing on VL and VR and normalization */
/*        (Workspace: none needed) */

        if (ilvl) {
            sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
                    vl[vl_offset], ldvl, &ierr);
            i__1 = *n;
            for (jc = 1; jc <= i__1; ++jc) {
                if (alphai[jc] < 0.f) {
                    goto L50;
                }
                temp = 0.f;
                if (alphai[jc] == 0.f) {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
                        r__2 = temp, r__3 = (r__1 = vl[jr + jc * vl_dim1], 
                                dabs(r__1));
                        temp = dmax(r__2,r__3);
/* L10: */
                    }
                } else {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
                        r__3 = temp, r__4 = (r__1 = vl[jr + jc * vl_dim1], 
                                dabs(r__1)) + (r__2 = vl[jr + (jc + 1) * 
                                vl_dim1], dabs(r__2));
                        temp = dmax(r__3,r__4);
/* L20: */
                    }
                }
                if (temp < smlnum) {
                    goto L50;
                }
                temp = 1.f / temp;
                if (alphai[jc] == 0.f) {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
                        vl[jr + jc * vl_dim1] *= temp;
/* L30: */
                    }
                } else {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
                        vl[jr + jc * vl_dim1] *= temp;
                        vl[jr + (jc + 1) * vl_dim1] *= temp;
/* L40: */
                    }
                }
L50:
                ;
            }
        }
        if (ilvr) {
            sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
                    vr[vr_offset], ldvr, &ierr);
            i__1 = *n;
            for (jc = 1; jc <= i__1; ++jc) {
                if (alphai[jc] < 0.f) {
                    goto L100;
                }
                temp = 0.f;
                if (alphai[jc] == 0.f) {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
                        r__2 = temp, r__3 = (r__1 = vr[jr + jc * vr_dim1], 
                                dabs(r__1));
                        temp = dmax(r__2,r__3);
/* L60: */
                    }
                } else {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
                        r__3 = temp, r__4 = (r__1 = vr[jr + jc * vr_dim1], 
                                dabs(r__1)) + (r__2 = vr[jr + (jc + 1) * 
                                vr_dim1], dabs(r__2));
                        temp = dmax(r__3,r__4);
/* L70: */
                    }
                }
                if (temp < smlnum) {
                    goto L100;
                }
                temp = 1.f / temp;
                if (alphai[jc] == 0.f) {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
                        vr[jr + jc * vr_dim1] *= temp;
/* L80: */
                    }
                } else {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
                        vr[jr + jc * vr_dim1] *= temp;
                        vr[jr + (jc + 1) * vr_dim1] *= temp;
/* L90: */
                    }
                }
L100:
                ;
            }
        }

/*        End of eigenvector calculation */

    }

/*     Undo scaling if necessary */

    if (ilascl) {
        slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
                ierr);
        slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
                ierr);
    }

    if (ilbscl) {
        slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
                ierr);
    }

L110:

    work[1] = (real) maxwrk;

    return 0;

/*     End of SGGEV */

} /* sggev_ */