#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int zptsvx_(char *fact, integer *n, integer *nrhs, 
	doublereal *d__, doublecomplex *e, doublereal *df, doublecomplex *ef, 
	doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, 
	doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *
	work, doublereal *rwork, integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    ZPTSVX uses the factorization A = L*D*L**H to compute the solution   
    to a complex system of linear equations A*X = B, where A is an   
    N-by-N Hermitian positive definite tridiagonal matrix 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 matrix A is factored as A = L*D*L**H, where L   
       is a unit lower bidiagonal matrix and D is diagonal.  The   
       factorization can also be regarded as having the form   
       A = U**H*D*U.   

    2. If the leading i-by-i principal minor is not positive definite,   
       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 the matrix   
            A is supplied on entry.   
            = 'F':  On entry, DF and EF contain the factored form of A.   
                    D, E, DF, and EF will not be modified.   
            = 'N':  The matrix A will be copied to DF and EF and   
                    factored.   

    N       (input) INTEGER   
            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.   

    D       (input) DOUBLE PRECISION array, dimension (N)   
            The n diagonal elements of the tridiagonal matrix A.   

    E       (input) COMPLEX*16 array, dimension (N-1)   
            The (n-1) subdiagonal elements of the tridiagonal matrix A.   

    DF      (input or output) DOUBLE PRECISION array, dimension (N)   
            If FACT = 'F', then DF is an input argument and on entry   
            contains the n diagonal elements of the diagonal matrix D   
            from the L*D*L**H factorization of A.   
            If FACT = 'N', then DF is an output argument and on exit   
            contains the n diagonal elements of the diagonal matrix D   
            from the L*D*L**H factorization of A.   

    EF      (input or output) COMPLEX*16 array, dimension (N-1)   
            If FACT = 'F', then EF is an input argument and on entry   
            contains the (n-1) subdiagonal elements of the unit   
            bidiagonal factor L from the L*D*L**H factorization of A.   
            If FACT = 'N', then EF is an output argument and on exit   
            contains the (n-1) subdiagonal elements of the unit   
            bidiagonal factor L from the L*D*L**H factorization of A.   

    B       (input) COMPLEX*16 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) COMPLEX*16 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 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 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).   

    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) COMPLEX*16 array, dimension (N)   

    RWORK   (workspace) DOUBLE PRECISION 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:  the leading minor of order i of A is   
                         not positive definite, so the factorization   
                         could not be completed, and the solution has not   
                         been computed. RCOND = 0 is returned.   
                  = N+1: U 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.   

    =====================================================================   


       Test the input parameters.   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    
    /* System generated locals */
    integer b_dim1, b_offset, x_dim1, x_offset, i__1;
    /* Local variables */
    extern logical lsame_(char *, char *);
    static doublereal anorm;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *), zcopy_(integer *, doublecomplex *, 
	    integer *, doublecomplex *, integer *);
    extern doublereal dlamch_(char *);
    static logical nofact;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern doublereal zlanht_(char *, integer *, doublereal *, doublecomplex *
	    );
    extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *), 
	    zptcon_(integer *, doublereal *, doublecomplex *, doublereal *, 
	    doublereal *, doublereal *, integer *), zptrfs_(char *, integer *,
	     integer *, doublereal *, doublecomplex *, doublereal *, 
	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
	    integer *, doublereal *, doublereal *, doublecomplex *, 
	    doublereal *, integer *), zpttrf_(integer *, doublereal *,
	     doublecomplex *, integer *), zpttrs_(char *, integer *, integer *
	    , doublereal *, doublecomplex *, doublecomplex *, integer *, 
	    integer *);


    --d__;
    --e;
    --df;
    --ef;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1 * 1;
    x -= x_offset;
    --ferr;
    --berr;
    --work;
    --rwork;

    /* Function Body */
    *info = 0;
    nofact = lsame_(fact, "N");
    if (! nofact && ! lsame_(fact, "F")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*nrhs < 0) {
	*info = -3;
    } else if (*ldb < max(1,*n)) {
	*info = -9;
    } else if (*ldx < max(1,*n)) {
	*info = -11;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZPTSVX", &i__1);
	return 0;
    }

    if (nofact) {

/*        Compute the L*D*L' (or U'*D*U) factorization of A. */

	dcopy_(n, &d__[1], &c__1, &df[1], &c__1);
	if (*n > 1) {
	    i__1 = *n - 1;
	    zcopy_(&i__1, &e[1], &c__1, &ef[1], &c__1);
	}
	zpttrf_(n, &df[1], &ef[1], info);

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

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

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

    anorm = zlanht_("1", n, &d__[1], &e[1]);

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

    zptcon_(n, &df[1], &ef[1], &anorm, rcond, &rwork[1], info);

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

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

/*     Compute the solution vectors X. */

    zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    zpttrs_("Lower", n, nrhs, &df[1], &ef[1], &x[x_offset], ldx, info);

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

    zptrfs_("Lower", n, nrhs, &d__[1], &e[1], &df[1], &ef[1], &b[b_offset], 
	    ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1], &rwork[1], 
	    info);

    return 0;

/*     End of ZPTSVX */

} /* zptsvx_ */

