zgbtrs.c

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/* zgbtrs.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 doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;

/* Subroutine */ int zgbtrs_(char *trans, integer *n, integer *kl, integer *
        ku, integer *nrhs, doublecomplex *ab, integer *ldab, integer *ipiv, 
        doublecomplex *b, integer *ldb, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, b_dim1, b_offset, i__1, i__2, i__3;
    doublecomplex z__1;

    /* Local variables */
    integer i__, j, l, kd, lm;
    extern logical lsame_(char *, char *);
    logical lnoti;
    extern /* Subroutine */ int zgemv_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, doublecomplex *, integer *), 
            zgeru_(integer *, integer *, doublecomplex *, doublecomplex *, 
            integer *, doublecomplex *, integer *, doublecomplex *, integer *)
            , zswap_(integer *, doublecomplex *, integer *, doublecomplex *, 
            integer *), ztbsv_(char *, char *, char *, integer *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(char *, integer *), zlacgv_(
            integer *, doublecomplex *, integer *);
    logical notran;


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

/*  Purpose */
/*  ======= */

/*  ZGBTRS solves a system of linear equations */
/*     A * X = B,  A**T * X = B,  or  A**H * X = B */
/*  with a general band matrix A using the LU factorization computed */
/*  by ZGBTRF. */

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

/*  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) */

/*  N       (input) INTEGER */
/*          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 matrix B.  NRHS >= 0. */

/*  AB      (input) COMPLEX*16 array, dimension (LDAB,N) */
/*          Details of the LU factorization of the band matrix A, as */
/*          computed by ZGBTRF.  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. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1. */

/*  IPIV    (input) INTEGER array, dimension (N) */
/*          The pivot indices; for 1 <= i <= N, row i of the matrix was */
/*          interchanged with row IPIV(i). */

/*  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS) */
/*          On entry, the right hand side matrix B. */
/*          On exit, the solution matrix X. */

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

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    --ipiv;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;

    /* Function Body */
    *info = 0;
    notran = lsame_(trans, "N");
    if (! notran && ! lsame_(trans, "T") && ! lsame_(
            trans, "C")) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*kl < 0) {
        *info = -3;
    } else if (*ku < 0) {
        *info = -4;
    } else if (*nrhs < 0) {
        *info = -5;
    } else if (*ldab < (*kl << 1) + *ku + 1) {
        *info = -7;
    } else if (*ldb < max(1,*n)) {
        *info = -10;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZGBTRS", &i__1);
        return 0;
    }

/*     Quick return if possible */

    if (*n == 0 || *nrhs == 0) {
        return 0;
    }

    kd = *ku + *kl + 1;
    lnoti = *kl > 0;

    if (notran) {

/*        Solve  A*X = B. */

/*        Solve L*X = B, overwriting B with X. */

/*        L is represented as a product of permutations and unit lower */
/*        triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1), */
/*        where each transformation L(i) is a rank-one modification of */
/*        the identity matrix. */

        if (lnoti) {
            i__1 = *n - 1;
            for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
                i__2 = *kl, i__3 = *n - j;
                lm = min(i__2,i__3);
                l = ipiv[j];
                if (l != j) {
                    zswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb);
                }
                z__1.r = -1., z__1.i = -0.;
                zgeru_(&lm, nrhs, &z__1, &ab[kd + 1 + j * ab_dim1], &c__1, &b[
                        j + b_dim1], ldb, &b[j + 1 + b_dim1], ldb);
/* L10: */
            }
        }

        i__1 = *nrhs;
        for (i__ = 1; i__ <= i__1; ++i__) {

/*           Solve U*X = B, overwriting B with X. */

            i__2 = *kl + *ku;
            ztbsv_("Upper", "No transpose", "Non-unit", n, &i__2, &ab[
                    ab_offset], ldab, &b[i__ * b_dim1 + 1], &c__1);
/* L20: */
        }

    } else if (lsame_(trans, "T")) {

/*        Solve A**T * X = B. */

        i__1 = *nrhs;
        for (i__ = 1; i__ <= i__1; ++i__) {

/*           Solve U**T * X = B, overwriting B with X. */

            i__2 = *kl + *ku;
            ztbsv_("Upper", "Transpose", "Non-unit", n, &i__2, &ab[ab_offset], 
                     ldab, &b[i__ * b_dim1 + 1], &c__1);
/* L30: */
        }

/*        Solve L**T * X = B, overwriting B with X. */

        if (lnoti) {
            for (j = *n - 1; j >= 1; --j) {
/* Computing MIN */
                i__1 = *kl, i__2 = *n - j;
                lm = min(i__1,i__2);
                z__1.r = -1., z__1.i = -0.;
                zgemv_("Transpose", &lm, nrhs, &z__1, &b[j + 1 + b_dim1], ldb, 
                         &ab[kd + 1 + j * ab_dim1], &c__1, &c_b1, &b[j + 
                        b_dim1], ldb);
                l = ipiv[j];
                if (l != j) {
                    zswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb);
                }
/* L40: */
            }
        }

    } else {

/*        Solve A**H * X = B. */

        i__1 = *nrhs;
        for (i__ = 1; i__ <= i__1; ++i__) {

/*           Solve U**H * X = B, overwriting B with X. */

            i__2 = *kl + *ku;
            ztbsv_("Upper", "Conjugate transpose", "Non-unit", n, &i__2, &ab[
                    ab_offset], ldab, &b[i__ * b_dim1 + 1], &c__1);
/* L50: */
        }

/*        Solve L**H * X = B, overwriting B with X. */

        if (lnoti) {
            for (j = *n - 1; j >= 1; --j) {
/* Computing MIN */
                i__1 = *kl, i__2 = *n - j;
                lm = min(i__1,i__2);
                zlacgv_(nrhs, &b[j + b_dim1], ldb);
                z__1.r = -1., z__1.i = -0.;
                zgemv_("Conjugate transpose", &lm, nrhs, &z__1, &b[j + 1 + 
                        b_dim1], ldb, &ab[kd + 1 + j * ab_dim1], &c__1, &c_b1, 
                         &b[j + b_dim1], ldb);
                zlacgv_(nrhs, &b[j + b_dim1], ldb);
                l = ipiv[j];
                if (l != j) {
                    zswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb);
                }
/* L60: */
            }
        }
    }
    return 0;

/*     End of ZGBTRS */

} /* zgbtrs_ */