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

/* dspsvx.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_dspsvx_(char *fact, char *uplo, integer *n, integer *
	nrhs, doublereal *ap, doublereal *afp, integer *ipiv, doublereal *b, 
	integer *ldb, doublereal *x, integer *ldx, doublereal *rcond, 
	doublereal *ferr, doublereal *berr, doublereal *work, integer *iwork, 
	integer *info)
{
    /* System generated locals */
    integer b_dim1, b_offset, x_dim1, x_offset, i__1;

    /* Local variables */
    extern logical _starpu_lsame_(char *, char *);
    doublereal anorm;
    extern /* Subroutine */ int _starpu_dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    extern doublereal _starpu_dlamch_(char *);
    logical nofact;
    extern /* Subroutine */ int _starpu_dlacpy_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *), 
	    _starpu_xerbla_(char *, integer *);
    extern doublereal _starpu_dlansp_(char *, char *, integer *, doublereal *, 
	    doublereal *);
    extern /* Subroutine */ int _starpu_dspcon_(char *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, doublereal *, integer *, 
	    integer *), _starpu_dsprfs_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, doublereal *, 
	     integer *, integer *), _starpu_dsptrf_(char *, integer *, 
	    doublereal *, integer *, integer *), _starpu_dsptrs_(char *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    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 */
/*  ======= */

/*  DSPSVX uses the diagonal pivoting factorization A = U*D*U**T or */
/*  A = L*D*L**T to compute the solution to a real system of linear */
/*  equations A * X = B, where A is an N-by-N symmetric matrix stored */
/*  in packed format and X and B are N-by-NRHS matrices. */

/*  Error bounds on the solution and a condition estimate are also */
/*  provided. */

/*  Description */
/*  =========== */

/*  The following steps are performed: */

/*  1. If FACT = 'N', the diagonal pivoting method is used to factor A as */
/*        A = U * D * U**T,  if UPLO = 'U', or */
/*        A = L * D * L**T,  if UPLO = 'L', */
/*     where U (or L) is a product of permutation and unit upper (lower) */
/*     triangular matrices and D is symmetric and block diagonal with */
/*     1-by-1 and 2-by-2 diagonal blocks. */

/*  2. If some D(i,i)=0, so that D is exactly singular, then the routine */
/*     returns with INFO = i. Otherwise, the factored form of A is used */
/*     to estimate the condition number of the matrix A.  If the */
/*     reciprocal of the condition number is less than machine precision, */
/*     INFO = N+1 is returned as a warning, but the routine still goes on */
/*     to solve for X and compute error bounds as described below. */

/*  3. The system of equations is solved for X using the factored form */
/*     of A. */

/*  4. Iterative refinement is applied to improve the computed solution */
/*     matrix and calculate error bounds and backward error estimates */
/*     for it. */

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

/*  FACT    (input) CHARACTER*1 */
/*          Specifies whether or not the factored form of A has been */
/*          supplied on entry. */
/*          = 'F':  On entry, AFP and IPIV contain the factored form of */
/*                  A.  AP, AFP and IPIV will not be modified. */
/*          = 'N':  The matrix A will be copied to AFP and factored. */

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangle of A is stored; */
/*          = 'L':  Lower triangle of A is stored. */

/*  N       (input) INTEGER */
/*          The number of linear equations, i.e., the order of the */
/*          matrix A.  N >= 0. */

/*  NRHS    (input) INTEGER */
/*          The number of right hand sides, i.e., the number of columns */
/*          of the matrices B and X.  NRHS >= 0. */

/*  AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/*          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. */
/*          See below for further details. */

/*  AFP     (input or output) DOUBLE PRECISION array, dimension */
/*                            (N*(N+1)/2) */
/*          If FACT = 'F', then AFP is an input argument and on entry */
/*          contains the block diagonal matrix D and the multipliers used */
/*          to obtain the factor U or L from the factorization */
/*          A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as */
/*          a packed triangular matrix in the same storage format as A. */

/*          If FACT = 'N', then AFP is an output argument and on exit */
/*          contains the block diagonal matrix D and the multipliers used */
/*          to obtain the factor U or L from the factorization */
/*          A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as */
/*          a packed triangular matrix in the same storage format as A. */

/*  IPIV    (input or output) INTEGER array, dimension (N) */
/*          If FACT = 'F', then IPIV is an input argument and on entry */
/*          contains details of the interchanges and the block structure */
/*          of D, as determined by DSPTRF. */
/*          If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
/*          interchanged and D(k,k) is a 1-by-1 diagonal block. */
/*          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */
/*          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */
/*          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) = */
/*          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */
/*          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */

/*          If FACT = 'N', then IPIV is an output argument and on exit */
/*          contains details of the interchanges and the block structure */
/*          of D, as determined by DSPTRF. */

/*  B       (input) DOUBLE PRECISION array, dimension (LDB,NRHS) */
/*          The N-by-NRHS right hand side matrix B. */

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

/*  X       (output) DOUBLE PRECISION array, dimension (LDX,NRHS) */
/*          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X. */

/*  LDX     (input) INTEGER */
/*          The leading dimension of the array X.  LDX >= max(1,N). */

/*  RCOND   (output) DOUBLE PRECISION */
/*          The estimate of the reciprocal condition number of the matrix */
/*          A.  If RCOND is less than the machine precision (in */
/*          particular, if RCOND = 0), the matrix is singular to working */
/*          precision.  This condition is indicated by a return code of */
/*          INFO > 0. */

/*  FERR    (output) DOUBLE PRECISION array, dimension (NRHS) */
/*          The estimated forward error bound for each solution vector */
/*          X(j) (the j-th column of the solution matrix X). */
/*          If XTRUE is the true solution corresponding to X(j), FERR(j) */
/*          is an estimated upper bound for the magnitude of the largest */
/*          element in (X(j) - XTRUE) divided by the magnitude of the */
/*          largest element in X(j).  The estimate is as reliable as */
/*          the estimate for RCOND, and is almost always a slight */
/*          overestimate of the true error. */

/*  BERR    (output) DOUBLE PRECISION array, dimension (NRHS) */
/*          The componentwise relative backward error of each solution */
/*          vector X(j) (i.e., the smallest relative change in */
/*          any element of A or B that makes X(j) an exact solution). */

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

/*  IWORK   (workspace) INTEGER array, dimension (N) */

/*  INFO    (output) INTEGER */
/*          = 0: successful exit */
/*          < 0: if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = i, and i is */
/*                <= N:  D(i,i) is exactly zero.  The factorization */
/*                       has been completed but the factor D is exactly */
/*                       singular, so the solution and error bounds could */
/*                       not be computed. RCOND = 0 is returned. */
/*                = N+1: D is nonsingular, but RCOND is less than machine */
/*                       precision, meaning that the matrix is singular */
/*                       to working precision.  Nevertheless, the */
/*                       solution and error bounds are computed because */
/*                       there are a number of situations where the */
/*                       computed solution can be more accurate than the */
/*                       value of RCOND would suggest. */

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

/*  The packed storage scheme is illustrated by the following example */
/*  when N = 4, UPLO = 'U': */

/*  Two-dimensional storage of the symmetric matrix A: */

/*     a11 a12 a13 a14 */
/*         a22 a23 a24 */
/*             a33 a34     (aij = aji) */
/*                 a44 */

/*  Packed storage of the upper triangle of A: */

/*  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    --ap;
    --afp;
    --ipiv;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1;
    x -= x_offset;
    --ferr;
    --berr;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;
    nofact = _starpu_lsame_(fact, "N");
    if (! nofact && ! _starpu_lsame_(fact, "F")) {
	*info = -1;
    } else if (! _starpu_lsame_(uplo, "U") && ! _starpu_lsame_(uplo, 
	    "L")) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*nrhs < 0) {
	*info = -4;
    } else if (*ldb < max(1,*n)) {
	*info = -9;
    } else if (*ldx < max(1,*n)) {
	*info = -11;
    }
    if (*info != 0) {
	i__1 = -(*info);
	_starpu_xerbla_("DSPSVX", &i__1);
	return 0;
    }

    if (nofact) {

/*        Compute the factorization A = U*D*U' or A = L*D*L'. */

	i__1 = *n * (*n + 1) / 2;
	_starpu_dcopy_(&i__1, &ap[1], &c__1, &afp[1], &c__1);
	_starpu_dsptrf_(uplo, n, &afp[1], &ipiv[1], info);

/*        Return if INFO is non-zero. */

	if (*info > 0) {
	    *rcond = 0.;
	    return 0;
	}
    }

/*     Compute the norm of the matrix A. */

    anorm = _starpu_dlansp_("I", uplo, n, &ap[1], &work[1]);

/*     Compute the reciprocal of the condition number of A. */

    _starpu_dspcon_(uplo, n, &afp[1], &ipiv[1], &anorm, rcond, &work[1], &iwork[1], 
	    info);

/*     Compute the solution vectors X. */

    _starpu_dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    _starpu_dsptrs_(uplo, n, nrhs, &afp[1], &ipiv[1], &x[x_offset], ldx, info);

/*     Use iterative refinement to improve the computed solutions and */
/*     compute error bounds and backward error estimates for them. */

    _starpu_dsprfs_(uplo, n, nrhs, &ap[1], &afp[1], &ipiv[1], &b[b_offset], ldb, &x[
	    x_offset], ldx, &ferr[1], &berr[1], &work[1], &iwork[1], info);

/*     Set INFO = N+1 if the matrix is singular to working precision. */

    if (*rcond < _starpu_dlamch_("Epsilon")) {
	*info = *n + 1;
    }

    return 0;

/*     End of DSPSVX */

} /* _starpu_dspsvx_ */