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

/* Subroutine */ int dgbsvx_(char *fact, char *trans, integer *n, integer *kl,
	 integer *ku, integer *nrhs, doublereal *ab, integer *ldab, 
	doublereal *afb, integer *ldafb, integer *ipiv, char *equed, 
	doublereal *r__, doublereal *c__, doublereal *b, integer *ldb, 
	doublereal *x, integer *ldx, doublereal *rcond, doublereal *ferr, 
	doublereal *berr, doublereal *work, integer *iwork, integer *info)
{
/*  -- LAPACK driver 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   
    =======   

    DGBSVX uses the LU factorization to compute the solution to a real   
    system of linear equations A * X = B, A**T * X = B, or A**H * X = B,   
    where A is a band matrix of order N with KL subdiagonals and KU   
    superdiagonals, 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 by this subroutine:   

    1. If FACT = 'E', real scaling factors are computed to equilibrate   
       the system:   
          TRANS = 'N':  diag(R)*A*diag(C)     *inv(diag(C))*X = diag(R)*B   
          TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B   
          TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B   
       Whether or not the system will be equilibrated depends on the   
       scaling of the matrix A, but if equilibration is used, A is   
       overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')   
       or diag(C)*B (if TRANS = 'T' or 'C').   

    2. If FACT = 'N' or 'E', the LU decomposition is used to factor the   
       matrix A (after equilibration if FACT = 'E') as   
          A = L * U,   
       where L is a product of permutation and unit lower triangular   
       matrices with KL subdiagonals, and U is upper triangular with   
       KL+KU superdiagonals.   

    3. 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.   

    4. The system of equations is solved for X using the factored form   
       of A.   

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

    6. If equilibration was used, the matrix X is premultiplied by   
       diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so   
       that it solves the original system before equilibration.   

    Arguments   
    =========   

    FACT    (input) CHARACTER*1   
            Specifies whether or not the factored form of the matrix A is   
            supplied on entry, and if not, whether the matrix A should be   
            equilibrated before it is factored.   
            = 'F':  On entry, AFB and IPIV contain the factored form of   
                    A.  If EQUED is not 'N', the matrix A has been   
                    equilibrated with scaling factors given by R and C.   
                    AB, AFB, and IPIV are not modified.   
            = 'N':  The matrix A will be copied to AFB and factored.   
            = 'E':  The matrix A will be equilibrated if necessary, then   
                    copied to AFB 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  (Transpose)   

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

    KL      (input) INTEGER   
            The number of subdiagonals within the band of A.  KL >= 0.   

    KU      (input) INTEGER   
            The number of superdiagonals within the band of A.  KU >= 0.   

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

    AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)   
            On entry, the matrix A in band storage, in rows 1 to KL+KU+1.   
            The j-th column of A is stored in the j-th column of the   
            array AB as follows:   
            AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)   

            If FACT = 'F' and EQUED is not 'N', then A must have been   
            equilibrated by the scaling factors in R and/or C.  AB is not   
            modified if FACT = 'F' or 'N', or if FACT = 'E' and   
            EQUED = 'N' on exit.   

            On exit, if EQUED .ne. 'N', A is scaled as follows:   
            EQUED = 'R':  A := diag(R) * A   
            EQUED = 'C':  A := A * diag(C)   
            EQUED = 'B':  A := diag(R) * A * diag(C).   

    LDAB    (input) INTEGER   
            The leading dimension of the array AB.  LDAB >= KL+KU+1.   

    AFB     (input or output) DOUBLE PRECISION array, dimension (LDAFB,N)   
            If FACT = 'F', then AFB is an input argument and on entry   
            contains details of the LU factorization of the band matrix   
            A, as computed by DGBTRF.  U is stored as an upper triangular   
            band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,   
            and the multipliers used during the factorization are stored   
            in rows KL+KU+2 to 2*KL+KU+1.  If EQUED .ne. 'N', then AFB is   
            the factored form of the equilibrated matrix A.   

            If FACT = 'N', then AFB is an output argument and on exit   
            returns details of the LU factorization of A.   

            If FACT = 'E', then AFB is an output argument and on exit   
            returns details of the LU factorization of the equilibrated   
            matrix A (see the description of AB for the form of the   
            equilibrated matrix).   

    LDAFB   (input) INTEGER   
            The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.   

    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 factorization A = L*U   
            as computed by DGBTRF; row i of the matrix was interchanged   
            with row IPIV(i).   

            If FACT = 'N', then IPIV is an output argument and on exit   
            contains the pivot indices from the factorization A = L*U   
            of the original matrix A.   

            If FACT = 'E', then IPIV is an output argument and on exit   
            contains the pivot indices from the factorization A = L*U   
            of the equilibrated matrix A.   

    EQUED   (input or output) CHARACTER*1   
            Specifies the form of equilibration that was done.   
            = 'N':  No equilibration (always true if FACT = 'N').   
            = 'R':  Row equilibration, i.e., A has been premultiplied by   
                    diag(R).   
            = 'C':  Column equilibration, i.e., A has been postmultiplied   
                    by diag(C).   
            = 'B':  Both row and column equilibration, i.e., A has been   
                    replaced by diag(R) * A * diag(C).   
            EQUED is an input argument if FACT = 'F'; otherwise, it is an   
            output argument.   

    R       (input or output) DOUBLE PRECISION array, dimension (N)   
            The row scale factors for A.  If EQUED = 'R' or 'B', A is   
            multiplied on the left by diag(R); if EQUED = 'N' or 'C', R   
            is not accessed.  R is an input argument if FACT = 'F';   
            otherwise, R is an output argument.  If FACT = 'F' and   
            EQUED = 'R' or 'B', each element of R must be positive.   

    C       (input or output) DOUBLE PRECISION array, dimension (N)   
            The column scale factors for A.  If EQUED = 'C' or 'B', A is   
            multiplied on the right by diag(C); if EQUED = 'N' or 'R', C   
            is not accessed.  C is an input argument if FACT = 'F';   
            otherwise, C is an output argument.  If FACT = 'F' and   
            EQUED = 'C' or 'B', each element of C must be positive.   

    B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)   
            On entry, the right hand side matrix B.   
            On exit,   
            if EQUED = 'N', B is not modified;   
            if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by   
            diag(R)*B;   
            if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is   
            overwritten by diag(C)*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   
            to the original system of equations.  Note that A and B are   
            modified on exit if EQUED .ne. 'N', and the solution to the   
            equilibrated system is inv(diag(C))*X if TRANS = 'N' and   
            EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C'   
            and EQUED = 'R' or 'B'.   

    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 after equilibration (if done).  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/output) DOUBLE PRECISION array, dimension (3*N)   
            On exit, WORK(1) contains the reciprocal pivot growth   
            factor norm(A)/norm(U). The "max absolute element" norm is   
            used. If WORK(1) is much less than 1, then the stability   
            of the LU factorization of the (equilibrated) matrix A   
            could be poor. This also means that the solution X, condition   
            estimator RCOND, and forward error bound FERR could be   
            unreliable. If factorization fails with 0<INFO<=N, then   
            WORK(1) contains the reciprocal pivot growth factor for the   
            leading INFO columns of A.   

    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 been completed, 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 ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, 
	    x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
    doublereal d__1, d__2, d__3;
    /* Local variables */
    static doublereal amax;
    static char norm[1];
    static integer i__, j;
    extern logical lsame_(char *, char *);
    static doublereal rcmin, rcmax, anorm;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    static logical equil;
    static integer j1, j2;
    extern doublereal dlamch_(char *), dlangb_(char *, integer *, 
	    integer *, integer *, doublereal *, integer *, doublereal *);
    extern /* Subroutine */ int dlaqgb_(integer *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, char *), 
	    dgbcon_(char *, integer *, integer *, integer *, doublereal *, 
	    integer *, integer *, doublereal *, doublereal *, doublereal *, 
	    integer *, integer *);
    static doublereal colcnd;
    extern doublereal dlantb_(char *, char *, char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *);
    extern /* Subroutine */ int dgbequ_(integer *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, integer *), dgbrfs_(
	    char *, integer *, integer *, integer *, integer *, doublereal *, 
	    integer *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    doublereal *, integer *, integer *), dgbtrf_(integer *, 
	    integer *, integer *, integer *, doublereal *, integer *, integer 
	    *, integer *);
    static logical nofact;
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *), 
	    xerbla_(char *, integer *);
    static doublereal bignum;
    extern /* Subroutine */ int dgbtrs_(char *, integer *, integer *, integer 
	    *, integer *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, integer *);
    static integer infequ;
    static logical colequ;
    static doublereal rowcnd;
    static logical notran;
    static doublereal smlnum;
    static logical rowequ;
    static doublereal rpvgrw;
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define x_ref(a_1,a_2) x[(a_2)*x_dim1 + a_1]
#define ab_ref(a_1,a_2) ab[(a_2)*ab_dim1 + a_1]
#define afb_ref(a_1,a_2) afb[(a_2)*afb_dim1 + a_1]


    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1 * 1;
    ab -= ab_offset;
    afb_dim1 = *ldafb;
    afb_offset = 1 + afb_dim1 * 1;
    afb -= afb_offset;
    --ipiv;
    --r__;
    --c__;
    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");
    equil = lsame_(fact, "E");
    notran = lsame_(trans, "N");
    if (nofact || equil) {
	*(unsigned char *)equed = 'N';
	rowequ = FALSE_;
	colequ = FALSE_;
    } else {
	rowequ = lsame_(equed, "R") || lsame_(equed, 
		"B");
	colequ = lsame_(equed, "C") || lsame_(equed, 
		"B");
	smlnum = dlamch_("Safe minimum");
	bignum = 1. / smlnum;
    }

/*     Test the input parameters. */

    if (! nofact && ! equil && ! lsame_(fact, "F")) {
	*info = -1;
    } else if (! notran && ! lsame_(trans, "T") && ! 
	    lsame_(trans, "C")) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*kl < 0) {
	*info = -4;
    } else if (*ku < 0) {
	*info = -5;
    } else if (*nrhs < 0) {
	*info = -6;
    } else if (*ldab < *kl + *ku + 1) {
	*info = -8;
    } else if (*ldafb < (*kl << 1) + *ku + 1) {
	*info = -10;
    } else if (lsame_(fact, "F") && ! (rowequ || colequ 
	    || lsame_(equed, "N"))) {
	*info = -12;
    } else {
	if (rowequ) {
	    rcmin = bignum;
	    rcmax = 0.;
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
		d__1 = rcmin, d__2 = r__[j];
		rcmin = min(d__1,d__2);
/* Computing MAX */
		d__1 = rcmax, d__2 = r__[j];
		rcmax = max(d__1,d__2);
/* L10: */
	    }
	    if (rcmin <= 0.) {
		*info = -13;
	    } else if (*n > 0) {
		rowcnd = max(rcmin,smlnum) / min(rcmax,bignum);
	    } else {
		rowcnd = 1.;
	    }
	}
	if (colequ && *info == 0) {
	    rcmin = bignum;
	    rcmax = 0.;
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
		d__1 = rcmin, d__2 = c__[j];
		rcmin = min(d__1,d__2);
/* Computing MAX */
		d__1 = rcmax, d__2 = c__[j];
		rcmax = max(d__1,d__2);
/* L20: */
	    }
	    if (rcmin <= 0.) {
		*info = -14;
	    } else if (*n > 0) {
		colcnd = max(rcmin,smlnum) / min(rcmax,bignum);
	    } else {
		colcnd = 1.;
	    }
	}
	if (*info == 0) {
	    if (*ldb < max(1,*n)) {
		*info = -16;
	    } else if (*ldx < max(1,*n)) {
		*info = -18;
	    }
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DGBSVX", &i__1);
	return 0;
    }

    if (equil) {

/*        Compute row and column scalings to equilibrate the matrix A. */

	dgbequ_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], &rowcnd,
		 &colcnd, &amax, &infequ);
	if (infequ == 0) {

/*           Equilibrate the matrix. */

	    dlaqgb_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], &
		    rowcnd, &colcnd, &amax, equed);
	    rowequ = lsame_(equed, "R") || lsame_(equed,
		     "B");
	    colequ = lsame_(equed, "C") || lsame_(equed,
		     "B");
	}
    }

/*     Scale the right hand side. */

    if (notran) {
	if (rowequ) {
	    i__1 = *nrhs;
	    for (j = 1; j <= i__1; ++j) {
		i__2 = *n;
		for (i__ = 1; i__ <= i__2; ++i__) {
		    b_ref(i__, j) = r__[i__] * b_ref(i__, j);
/* L30: */
		}
/* L40: */
	    }
	}
    } else if (colequ) {
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {
	    i__2 = *n;
	    for (i__ = 1; i__ <= i__2; ++i__) {
		b_ref(i__, j) = c__[i__] * b_ref(i__, j);
/* L50: */
	    }
/* L60: */
	}
    }

    if (nofact || equil) {

/*        Compute the LU factorization of the band matrix A. */

	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
	    i__2 = j - *ku;
	    j1 = max(i__2,1);
/* Computing MIN */
	    i__2 = j + *kl;
	    j2 = min(i__2,*n);
	    i__2 = j2 - j1 + 1;
	    dcopy_(&i__2, &ab_ref(*ku + 1 - j + j1, j), &c__1, &afb_ref(*kl + 
		    *ku + 1 - j + j1, j), &c__1);
/* L70: */
	}

	dgbtrf_(n, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], info);

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

	if (*info != 0) {
	    if (*info > 0) {

/*              Compute the reciprocal pivot growth factor of the   
                leading rank-deficient INFO columns of A. */

		anorm = 0.;
		i__1 = *info;
		for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
		    i__2 = *ku + 2 - j;
/* Computing MIN */
		    i__4 = *n + *ku + 1 - j, i__5 = *kl + *ku + 1;
		    i__3 = min(i__4,i__5);
		    for (i__ = max(i__2,1); i__ <= i__3; ++i__) {
/* Computing MAX */
			d__2 = anorm, d__3 = (d__1 = ab_ref(i__, j), abs(d__1)
				);
			anorm = max(d__2,d__3);
/* L80: */
		    }
/* L90: */
		}
/* Computing MAX */
		i__1 = 1, i__3 = *kl + *ku + 2 - *info;
/* Computing MIN */
		i__4 = *info - 1, i__5 = *kl + *ku;
		i__2 = min(i__4,i__5);
		rpvgrw = dlantb_("M", "U", "N", info, &i__2, &afb_ref(max(
			i__1,i__3), 1), ldafb, &work[1]);
		if (rpvgrw == 0.) {
		    rpvgrw = 1.;
		} else {
		    rpvgrw = anorm / rpvgrw;
		}
		work[1] = rpvgrw;
		*rcond = 0.;
	    }
	    return 0;
	}
    }

/*     Compute the norm of the matrix A and the   
       reciprocal pivot growth factor RPVGRW. */

    if (notran) {
	*(unsigned char *)norm = '1';
    } else {
	*(unsigned char *)norm = 'I';
    }
    anorm = dlangb_(norm, n, kl, ku, &ab[ab_offset], ldab, &work[1]);
    i__1 = *kl + *ku;
    rpvgrw = dlantb_("M", "U", "N", n, &i__1, &afb[afb_offset], ldafb, &work[
	    1]);
    if (rpvgrw == 0.) {
	rpvgrw = 1.;
    } else {
	rpvgrw = dlangb_("M", n, kl, ku, &ab[ab_offset], ldab, &work[1]) / rpvgrw;
    }

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

    dgbcon_(norm, n, kl, ku, &afb[afb_offset], ldafb, &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 matrix X. */

    dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    dgbtrs_(trans, n, kl, ku, nrhs, &afb[afb_offset], ldafb, &ipiv[1], &x[
	    x_offset], ldx, info);

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

    dgbrfs_(trans, n, kl, ku, nrhs, &ab[ab_offset], ldab, &afb[afb_offset], 
	    ldafb, &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &
	    berr[1], &work[1], &iwork[1], info);

/*     Transform the solution matrix X to a solution of the original   
       system. */

    if (notran) {
	if (colequ) {
	    i__1 = *nrhs;
	    for (j = 1; j <= i__1; ++j) {
		i__3 = *n;
		for (i__ = 1; i__ <= i__3; ++i__) {
		    x_ref(i__, j) = c__[i__] * x_ref(i__, j);
/* L100: */
		}
/* L110: */
	    }
	    i__1 = *nrhs;
	    for (j = 1; j <= i__1; ++j) {
		ferr[j] /= colcnd;
/* L120: */
	    }
	}
    } else if (rowequ) {
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {
	    i__3 = *n;
	    for (i__ = 1; i__ <= i__3; ++i__) {
		x_ref(i__, j) = r__[i__] * x_ref(i__, j);
/* L130: */
	    }
/* L140: */
	}
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {
	    ferr[j] /= rowcnd;
/* L150: */
	}
    }

    work[1] = rpvgrw;
    return 0;

/*     End of DGBSVX */

} /* dgbsvx_ */

#undef afb_ref
#undef ab_ref
#undef x_ref
#undef b_ref


