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

/* Subroutine */ int dgtsvx_(char *fact, char *trans, integer *n, integer *
	nrhs, doublereal *dl, doublereal *d__, doublereal *du, doublereal *
	dlf, doublereal *df, doublereal *duf, doublereal *du2, integer *ipiv, 
	doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
	rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer *
	iwork, 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   
    =======   

    DGTSVX uses the LU factorization to compute the solution to a real   
    system of linear equations A * X = B or A**T * X = B,   
    where A is a tridiagonal matrix of order N 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 LU decomposition is used to factor the matrix A   
       as A = L * U, where L is a product of permutation and unit lower   
       bidiagonal matrices and U is upper triangular with nonzeros in   
       only the main diagonal and first two superdiagonals.   

    2. If some U(i,i)=0, so that U 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':  DLF, DF, DUF, DU2, and IPIV contain the factored   
                    form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV   
                    will not be modified.   
            = 'N':  The matrix will be copied to DLF, DF, and DUF   
                    and factored.   

    TRANS   (input) CHARACTER*1   
            Specifies the form of the system of equations:   
            = 'N':  A * X = B     (No transpose)   
            = 'T':  A**T * X = B  (Transpose)   
            = 'C':  A**H * X = B  (Conjugate transpose = Transpose)   

    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 matrix B.  NRHS >= 0.   

    DL      (input) DOUBLE PRECISION array, dimension (N-1)   
            The (n-1) subdiagonal elements of A.   

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

    DU      (input) DOUBLE PRECISION array, dimension (N-1)   
            The (n-1) superdiagonal elements of A.   

    DLF     (input or output) DOUBLE PRECISION array, dimension (N-1)   
            If FACT = 'F', then DLF is an input argument and on entry   
            contains the (n-1) multipliers that define the matrix L from   
            the LU factorization of A as computed by DGTTRF.   

            If FACT = 'N', then DLF is an output argument and on exit   
            contains the (n-1) multipliers that define the matrix L from   
            the LU factorization of 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 upper triangular   
            matrix U from the LU factorization of A.   

            If FACT = 'N', then DF is an output argument and on exit   
            contains the n diagonal elements of the upper triangular   
            matrix U from the LU factorization of A.   

    DUF     (input or output) DOUBLE PRECISION array, dimension (N-1)   
            If FACT = 'F', then DUF is an input argument and on entry   
            contains the (n-1) elements of the first superdiagonal of U.   

            If FACT = 'N', then DUF is an output argument and on exit   
            contains the (n-1) elements of the first superdiagonal of U.   

    DU2     (input or output) DOUBLE PRECISION array, dimension (N-2)   
            If FACT = 'F', then DU2 is an input argument and on entry   
            contains the (n-2) elements of the second superdiagonal of   
            U.   

            If FACT = 'N', then DU2 is an output argument and on exit   
            contains the (n-2) elements of the second superdiagonal of   
            U.   

    IPIV    (input or output) INTEGER array, dimension (N)   
            If FACT = 'F', then IPIV is an input argument and on entry   
            contains the pivot indices from the LU factorization of A as   
            computed by DGTTRF.   

            If FACT = 'N', then IPIV is an output argument and on exit   
            contains the pivot indices from the LU factorization of A;   
            row i of the matrix was interchanged with row IPIV(i).   
            IPIV(i) will always be either i or i+1; IPIV(i) = i indicates   
            a row interchange was not required.   

    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:  U(i,i) is exactly zero.  The factorization   
                         has not been completed unless i = N, but the   
                         factor U is exactly singular, so the solution   
                         and error bounds could not be 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.   

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


       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 */
    static char norm[1];
    extern logical lsame_(char *, char *);
    static doublereal anorm;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    extern doublereal dlamch_(char *), dlangt_(char *, integer *, 
	    doublereal *, doublereal *, doublereal *);
    static logical nofact;
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *), 
	    xerbla_(char *, integer *), dgtcon_(char *, integer *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, integer *,
	     doublereal *, doublereal *, doublereal *, integer *, integer *), dgtrfs_(char *, integer *, integer *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, doublereal *,
	     integer *, integer *), dgttrf_(integer *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, integer *, integer *);
    static logical notran;
    extern /* Subroutine */ int dgttrs_(char *, integer *, integer *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, integer *,
	     doublereal *, integer *, integer *);


    --dl;
    --d__;
    --du;
    --dlf;
    --df;
    --duf;
    --du2;
    --ipiv;
    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;
    --iwork;

    /* Function Body */
    *info = 0;
    nofact = lsame_(fact, "N");
    notran = lsame_(trans, "N");
    if (! nofact && ! lsame_(fact, "F")) {
	*info = -1;
    } else if (! notran && ! lsame_(trans, "T") && ! 
	    lsame_(trans, "C")) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*nrhs < 0) {
	*info = -4;
    } else if (*ldb < max(1,*n)) {
	*info = -14;
    } else if (*ldx < max(1,*n)) {
	*info = -16;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DGTSVX", &i__1);
	return 0;
    }

    if (nofact) {

/*        Compute the LU factorization of A. */

	dcopy_(n, &d__[1], &c__1, &df[1], &c__1);
	if (*n > 1) {
	    i__1 = *n - 1;
	    dcopy_(&i__1, &dl[1], &c__1, &dlf[1], &c__1);
	    i__1 = *n - 1;
	    dcopy_(&i__1, &du[1], &c__1, &duf[1], &c__1);
	}
	dgttrf_(n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[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. */

    if (notran) {
	*(unsigned char *)norm = '1';
    } else {
	*(unsigned char *)norm = 'I';
    }
    anorm = dlangt_(norm, n, &dl[1], &d__[1], &du[1]);

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

    dgtcon_(norm, n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], &anorm, 
	    rcond, &work[1], &iwork[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. */

    dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    dgttrs_(trans, n, nrhs, &dlf[1], &df[1], &duf[1], &du2[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. */

    dgtrfs_(trans, n, nrhs, &dl[1], &d__[1], &du[1], &dlf[1], &df[1], &duf[1],
	     &du2[1], &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1]
	    , &berr[1], &work[1], &iwork[1], info);

    return 0;

/*     End of DGTSVX */

} /* dgtsvx_ */

