#include "clapack.h"
#include "f2cP.h"

/* Table of constant values */

static integer c__1 = 1;

/* Subroutine */ int dgbsvx_(const char *fact, const char *trans, integer *n, integer *kl, 
	 integer *ku, integer *nrhs, double *ab, integer *ldab, 
	double *afb, integer *ldafb, integer *ipiv, char *equed, 
	double *r__, double *c__, double *b, integer *ldb, 
	double *x, integer *ldx, double *rcond, double *ferr, 
	double *berr, double *work, integer *iwork, integer *info)
{
    /* 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;
    double d__1, d__2, d__3;

    /* Local variables */
    integer i__, j, j1, j2;
    double amax;
    char norm[1];
    double rcmin, rcmax, anorm;
    bool equil;
    double colcnd;
    bool nofact;
    double bignum;
    integer infequ;
    bool colequ;
    double rowcnd;
    bool notran;
    double smlnum;
    bool rowequ;
    double rpvgrw;


/*  -- LAPACK driver routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

/*  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. */

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

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

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    afb_dim1 = *ldafb;
    afb_offset = 1 + afb_dim1;
    afb -= afb_offset;
    --ipiv;
    --r__;
    --c__;
    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 = 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 = std::min(d__1,d__2);
/* Computing MAX */
		d__1 = rcmax, d__2 = r__[j];
		rcmax = std::max(d__1,d__2);
/* L10: */
	    }
	    if (rcmin <= 0.) {
		*info = -13;
	    } else if (*n > 0) {
		rowcnd = std::max(rcmin,smlnum) / std::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 = std::min(d__1,d__2);
/* Computing MAX */
		d__1 = rcmax, d__2 = c__[j];
		rcmax = std::max(d__1,d__2);
/* L20: */
	    }
	    if (rcmin <= 0.) {
		*info = -14;
	    } else if (*n > 0) {
		colcnd = std::max(rcmin,smlnum) / std::min(rcmax,bignum);
	    } else {
		colcnd = 1.;
	    }
	}
	if (*info == 0) {
	    if (*ldb < std::max(1_integer,*n)) {
		*info = -16;
	    } else if (*ldx < std::max(1_integer,*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[i__ + j * b_dim1] = r__[i__] * b[i__ + j * b_dim1];
/* 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[i__ + j * b_dim1] = c__[i__] * b[i__ + j * b_dim1];
/* 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 = std::max(i__2,1_integer);
/* Computing MIN */
	    i__2 = j + *kl;
	    j2 = std::min(i__2,*n);
	    i__2 = j2 - j1 + 1;
	    dcopy_(&i__2, &ab[*ku + 1 - j + j1 + j * ab_dim1], &c__1, &afb[*
		    kl + *ku + 1 - j + j1 + j * afb_dim1], &c__1);
/* L70: */
	}

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

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

	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 = std::min(i__4,i__5);
		for (i__ = std::max(i__2,1_integer); i__ <= i__3; ++i__) {
/* Computing MAX */
		    d__2 = anorm, d__3 = (d__1 = ab[i__ + j * ab_dim1], abs(
			    d__1));
		    anorm = std::max(d__2,d__3);
/* L80: */
		}
/* L90: */
	    }
/* Computing MIN */
	    i__3 = *info - 1, i__2 = *kl + *ku;
	    i__1 = std::min(i__3,i__2);
/* Computing MAX */
	    i__4 = 1, i__5 = *kl + *ku + 2 - *info;
	    rpvgrw = dlantb_("M", "U", "N", info, &i__1, &afb[std::max(i__4, i__5)
		    + afb_dim1], 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);

/*     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[i__ + j * x_dim1] = c__[i__] * x[i__ + j * x_dim1];
/* 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[i__ + j * x_dim1] = r__[i__] * x[i__ + j * x_dim1];
/* L130: */
	    }
/* L140: */
	}
	i__1 = *nrhs;
	for (j = 1; j <= i__1; ++j) {
	    ferr[j] /= rowcnd;
/* L150: */
	}
    }

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

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

    work[1] = rpvgrw;
    return 0;

/*     End of DGBSVX */

} /* dgbsvx_ */
