dspgv.c

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/* dspgv.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;

/* Subroutine */ int dspgv_(integer *itype, char *jobz, char *uplo, integer *
        n, doublereal *ap, doublereal *bp, doublereal *w, doublereal *z__, 
        integer *ldz, doublereal *work, integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1;

    /* Local variables */
    integer j, neig;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dspev_(char *, char *, integer *, doublereal *
, doublereal *, doublereal *, integer *, doublereal *, integer *);
    char trans[1];
    logical upper;
    extern /* Subroutine */ int dtpmv_(char *, char *, char *, integer *, 
            doublereal *, doublereal *, integer *), 
            dtpsv_(char *, char *, char *, integer *, doublereal *, 
            doublereal *, integer *);
    logical wantz;
    extern /* Subroutine */ int xerbla_(char *, integer *), dpptrf_(
            char *, integer *, doublereal *, integer *), dspgst_(
            integer *, char *, integer *, doublereal *, doublereal *, integer 
            *);


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

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

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

/*  DSPGV computes all the eigenvalues and, optionally, the eigenvectors */
/*  of a real generalized symmetric-definite eigenproblem, of the form */
/*  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x. */
/*  Here A and B are assumed to be symmetric, stored in packed format, */
/*  and B is also positive definite. */

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

/*  ITYPE   (input) INTEGER */
/*          Specifies the problem type to be solved: */
/*          = 1:  A*x = (lambda)*B*x */
/*          = 2:  A*B*x = (lambda)*x */
/*          = 3:  B*A*x = (lambda)*x */

/*  JOBZ    (input) CHARACTER*1 */
/*          = 'N':  Compute eigenvalues only; */
/*          = 'V':  Compute eigenvalues and eigenvectors. */

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangles of A and B are stored; */
/*          = 'L':  Lower triangles of A and B are stored. */

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

/*  AP      (input/output) DOUBLE PRECISION array, dimension */
/*                            (N*(N+1)/2) */
/*          On entry, the upper or lower triangle of the symmetric matrix */
/*          A, packed columnwise in a linear array.  The j-th column of A */
/*          is stored in the array AP as follows: */
/*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/*          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */

/*          On exit, the contents of AP are destroyed. */

/*  BP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/*          On entry, the upper or lower triangle of the symmetric matrix */
/*          B, packed columnwise in a linear array.  The j-th column of B */
/*          is stored in the array BP as follows: */
/*          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; */
/*          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. */

/*          On exit, the triangular factor U or L from the Cholesky */
/*          factorization B = U**T*U or B = L*L**T, in the same storage */
/*          format as B. */

/*  W       (output) DOUBLE PRECISION array, dimension (N) */
/*          If INFO = 0, the eigenvalues in ascending order. */

/*  Z       (output) DOUBLE PRECISION array, dimension (LDZ, N) */
/*          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */
/*          eigenvectors.  The eigenvectors are normalized as follows: */
/*          if ITYPE = 1 or 2, Z**T*B*Z = I; */
/*          if ITYPE = 3, Z**T*inv(B)*Z = I. */
/*          If JOBZ = 'N', then Z is not referenced. */

/*  LDZ     (input) INTEGER */
/*          The leading dimension of the array Z.  LDZ >= 1, and if */
/*          JOBZ = 'V', LDZ >= max(1,N). */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (3*N) */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  DPPTRF or DSPEV returned an error code: */
/*             <= N:  if INFO = i, DSPEV failed to converge; */
/*                    i off-diagonal elements of an intermediate */
/*                    tridiagonal form did not converge to zero. */
/*             > N:   if INFO = n + i, for 1 <= i <= n, then the leading */
/*                    minor of order i of B is not positive definite. */
/*                    The factorization of B could not be completed and */
/*                    no eigenvalues or eigenvectors were computed. */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    --ap;
    --bp;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;

    /* Function Body */
    wantz = lsame_(jobz, "V");
    upper = lsame_(uplo, "U");

    *info = 0;
    if (*itype < 1 || *itype > 3) {
        *info = -1;
    } else if (! (wantz || lsame_(jobz, "N"))) {
        *info = -2;
    } else if (! (upper || lsame_(uplo, "L"))) {
        *info = -3;
    } else if (*n < 0) {
        *info = -4;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
        *info = -9;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DSPGV ", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

/*     Form a Cholesky factorization of B. */

    dpptrf_(uplo, n, &bp[1], info);
    if (*info != 0) {
        *info = *n + *info;
        return 0;
    }

/*     Transform problem to standard eigenvalue problem and solve. */

    dspgst_(itype, uplo, n, &ap[1], &bp[1], info);
    dspev_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], info);

    if (wantz) {

/*        Backtransform eigenvectors to the original problem. */

        neig = *n;
        if (*info > 0) {
            neig = *info - 1;
        }
        if (*itype == 1 || *itype == 2) {

/*           For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */
/*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */

            if (upper) {
                *(unsigned char *)trans = 'N';
            } else {
                *(unsigned char *)trans = 'T';
            }

            i__1 = neig;
            for (j = 1; j <= i__1; ++j) {
                dtpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 
                        1], &c__1);
/* L10: */
            }

        } else if (*itype == 3) {

/*           For B*A*x=(lambda)*x; */
/*           backtransform eigenvectors: x = L*y or U'*y */

            if (upper) {
                *(unsigned char *)trans = 'T';
            } else {
                *(unsigned char *)trans = 'N';
            }

            i__1 = neig;
            for (j = 1; j <= i__1; ++j) {
                dtpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 
                        1], &c__1);
/* L20: */
            }
        }
    }
    return 0;

/*     End of DSPGV */

} /* dspgv_ */