starpu-max/min-dgels/base/SRC/dspgvd.c

/* dspgvd.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 _starpu_dspgvd_(integer *itype, char *jobz, char *uplo, integer *
	n, doublereal *ap, doublereal *bp, doublereal *w, doublereal *z__, 
	integer *ldz, doublereal *work, integer *lwork, integer *iwork, 
	integer *liwork, integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1;
    doublereal d__1, d__2;

    /* Local variables */
    integer j, neig;
    extern logical _starpu_lsame_(char *, char *);
    integer lwmin;
    char trans[1];
    logical upper;
    extern /* Subroutine */ int _starpu_dtpmv_(char *, char *, char *, integer *, 
	    doublereal *, doublereal *, integer *), 
	    _starpu_dtpsv_(char *, char *, char *, integer *, doublereal *, 
	    doublereal *, integer *);
    logical wantz;
    extern /* Subroutine */ int _starpu_xerbla_(char *, integer *), _starpu_dspevd_(
	    char *, char *, integer *, doublereal *, doublereal *, doublereal 
	    *, integer *, doublereal *, integer *, integer *, integer *, 
	    integer *);
    integer liwmin;
    extern /* Subroutine */ int _starpu_dpptrf_(char *, integer *, doublereal *, 
	    integer *), _starpu_dspgst_(integer *, char *, integer *, 
	    doublereal *, doublereal *, integer *);
    logical lquery;


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

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

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

/*  DSPGVD 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. */
/*  If eigenvectors are desired, it uses a divide and conquer algorithm. */

/*  The divide and conquer algorithm makes very mild assumptions about */
/*  floating point arithmetic. It will work on machines with a guard */
/*  digit in add/subtract, or on those binary machines without guard */
/*  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/*  Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/*  without guard digits, but we know of none. */

/*  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/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/*          On exit, if INFO = 0, WORK(1) returns the required LWORK. */

/*  LWORK   (input) INTEGER */
/*          The dimension of the array WORK. */
/*          If N <= 1,               LWORK >= 1. */
/*          If JOBZ = 'N' and N > 1, LWORK >= 2*N. */
/*          If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. */

/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates the required sizes of the WORK and IWORK */
/*          arrays, returns these values as the first entries of the WORK */
/*          and IWORK arrays, and no error message related to LWORK or */
/*          LIWORK is issued by XERBLA. */

/*  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/*          On exit, if INFO = 0, IWORK(1) returns the required LIWORK. */

/*  LIWORK  (input) INTEGER */
/*          The dimension of the array IWORK. */
/*          If JOBZ  = 'N' or N <= 1, LIWORK >= 1. */
/*          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N. */

/*          If LIWORK = -1, then a workspace query is assumed; the */
/*          routine only calculates the required sizes of the WORK and */
/*          IWORK arrays, returns these values as the first entries of */
/*          the WORK and IWORK arrays, and no error message related to */
/*          LWORK or LIWORK is issued by XERBLA. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  DPPTRF or DSPEVD returned an error code: */
/*             <= N:  if INFO = i, DSPEVD 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. */

/*  Further Details */
/*  =============== */

/*  Based on contributions by */
/*     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */

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

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

/*     Test the input parameters. */

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

    /* Function Body */
    wantz = _starpu_lsame_(jobz, "V");
    upper = _starpu_lsame_(uplo, "U");
    lquery = *lwork == -1 || *liwork == -1;

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

    if (*info == 0) {
	if (*n <= 1) {
	    liwmin = 1;
	    lwmin = 1;
	} else {
	    if (wantz) {
		liwmin = *n * 5 + 3;
/* Computing 2nd power */
		i__1 = *n;
		lwmin = *n * 6 + 1 + (i__1 * i__1 << 1);
	    } else {
		liwmin = 1;
		lwmin = *n << 1;
	    }
	}
	work[1] = (doublereal) lwmin;
	iwork[1] = liwmin;

	if (*lwork < lwmin && ! lquery) {
	    *info = -11;
	} else if (*liwork < liwmin && ! lquery) {
	    *info = -13;
	}
    }

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

/*     Quick return if possible */

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

/*     Form a Cholesky factorization of BP. */

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

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

    _starpu_dspgst_(itype, uplo, n, &ap[1], &bp[1], info);
    _starpu_dspevd_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], 
	    lwork, &iwork[1], liwork, info);
/* Computing MAX */
    d__1 = (doublereal) lwmin;
    lwmin = (integer) max(d__1,work[1]);
/* Computing MAX */
    d__1 = (doublereal) liwmin, d__2 = (doublereal) iwork[1];
    liwmin = (integer) max(d__1,d__2);

    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) {
		_starpu_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) {
		_starpu_dtpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 
			1], &c__1);
/* L20: */
	    }
	}
    }

    work[1] = (doublereal) lwmin;
    iwork[1] = liwmin;

    return 0;

/*     End of DSPGVD */

} /* _starpu_dspgvd_ */