zhetrs.c

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/* zhetrs.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 zhetrs_(char *uplo, integer *n, integer *nrhs, 
        doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, 
        integer *ldb, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
    doublecomplex z__1, z__2, z__3;

    /* Builtin functions */
    void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg(
            doublecomplex *, doublecomplex *);

    /* Local variables */
    integer j, k;
    doublereal s;
    doublecomplex ak, bk;
    integer kp;
    doublecomplex akm1, bkm1, akm1k;
    extern logical lsame_(char *, char *);
    doublecomplex denom;
    extern /* Subroutine */ int zgemv_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, doublecomplex *, integer *);
    logical upper;
    extern /* Subroutine */ int zgeru_(integer *, integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *), zswap_(integer *, doublecomplex *, 
            integer *, doublecomplex *, integer *), xerbla_(char *, integer *), zdscal_(integer *, doublereal *, doublecomplex *, 
            integer *), zlacgv_(integer *, doublecomplex *, integer *);


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

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

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

/*  ZHETRS solves a system of linear equations A*X = B with a complex */
/*  Hermitian matrix A using the factorization A = U*D*U**H or */
/*  A = L*D*L**H computed by ZHETRF. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the details of the factorization are stored */
/*          as an upper or lower triangular matrix. */
/*          = 'U':  Upper triangular, form is A = U*D*U**H; */
/*          = 'L':  Lower triangular, form is A = L*D*L**H. */

/*  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. */

/*  A       (input) COMPLEX*16 array, dimension (LDA,N) */
/*          The block diagonal matrix D and the multipliers used to */
/*          obtain the factor U or L as computed by ZHETRF. */

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

/*  IPIV    (input) INTEGER array, dimension (N) */
/*          Details of the interchanges and the block structure of D */
/*          as determined by ZHETRF. */

/*  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 .. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --ipiv;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L")) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*nrhs < 0) {
        *info = -3;
    } else if (*lda < max(1,*n)) {
        *info = -5;
    } else if (*ldb < max(1,*n)) {
        *info = -8;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZHETRS", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

    if (upper) {

/*        Solve A*X = B, where A = U*D*U'. */

/*        First solve U*D*X = B, overwriting B with X. */

/*        K is the main loop index, decreasing from N to 1 in steps of */
/*        1 or 2, depending on the size of the diagonal blocks. */

        k = *n;
L10:

/*        If K < 1, exit from loop. */

        if (k < 1) {
            goto L30;
        }

        if (ipiv[k] > 0) {

/*           1 x 1 diagonal block */

/*           Interchange rows K and IPIV(K). */

            kp = ipiv[k];
            if (kp != k) {
                zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
            }

/*           Multiply by inv(U(K)), where U(K) is the transformation */
/*           stored in column K of A. */

            i__1 = k - 1;
            z__1.r = -1., z__1.i = -0.;
            zgeru_(&i__1, nrhs, &z__1, &a[k * a_dim1 + 1], &c__1, &b[k + 
                    b_dim1], ldb, &b[b_dim1 + 1], ldb);

/*           Multiply by the inverse of the diagonal block. */

            i__1 = k + k * a_dim1;
            s = 1. / a[i__1].r;
            zdscal_(nrhs, &s, &b[k + b_dim1], ldb);
            --k;
        } else {

/*           2 x 2 diagonal block */

/*           Interchange rows K-1 and -IPIV(K). */

            kp = -ipiv[k];
            if (kp != k - 1) {
                zswap_(nrhs, &b[k - 1 + b_dim1], ldb, &b[kp + b_dim1], ldb);
            }

/*           Multiply by inv(U(K)), where U(K) is the transformation */
/*           stored in columns K-1 and K of A. */

            i__1 = k - 2;
            z__1.r = -1., z__1.i = -0.;
            zgeru_(&i__1, nrhs, &z__1, &a[k * a_dim1 + 1], &c__1, &b[k + 
                    b_dim1], ldb, &b[b_dim1 + 1], ldb);
            i__1 = k - 2;
            z__1.r = -1., z__1.i = -0.;
            zgeru_(&i__1, nrhs, &z__1, &a[(k - 1) * a_dim1 + 1], &c__1, &b[k 
                    - 1 + b_dim1], ldb, &b[b_dim1 + 1], ldb);

/*           Multiply by the inverse of the diagonal block. */

            i__1 = k - 1 + k * a_dim1;
            akm1k.r = a[i__1].r, akm1k.i = a[i__1].i;
            z_div(&z__1, &a[k - 1 + (k - 1) * a_dim1], &akm1k);
            akm1.r = z__1.r, akm1.i = z__1.i;
            d_cnjg(&z__2, &akm1k);
            z_div(&z__1, &a[k + k * a_dim1], &z__2);
            ak.r = z__1.r, ak.i = z__1.i;
            z__2.r = akm1.r * ak.r - akm1.i * ak.i, z__2.i = akm1.r * ak.i + 
                    akm1.i * ak.r;
            z__1.r = z__2.r - 1., z__1.i = z__2.i - 0.;
            denom.r = z__1.r, denom.i = z__1.i;
            i__1 = *nrhs;
            for (j = 1; j <= i__1; ++j) {
                z_div(&z__1, &b[k - 1 + j * b_dim1], &akm1k);
                bkm1.r = z__1.r, bkm1.i = z__1.i;
                d_cnjg(&z__2, &akm1k);
                z_div(&z__1, &b[k + j * b_dim1], &z__2);
                bk.r = z__1.r, bk.i = z__1.i;
                i__2 = k - 1 + j * b_dim1;
                z__3.r = ak.r * bkm1.r - ak.i * bkm1.i, z__3.i = ak.r * 
                        bkm1.i + ak.i * bkm1.r;
                z__2.r = z__3.r - bk.r, z__2.i = z__3.i - bk.i;
                z_div(&z__1, &z__2, &denom);
                b[i__2].r = z__1.r, b[i__2].i = z__1.i;
                i__2 = k + j * b_dim1;
                z__3.r = akm1.r * bk.r - akm1.i * bk.i, z__3.i = akm1.r * 
                        bk.i + akm1.i * bk.r;
                z__2.r = z__3.r - bkm1.r, z__2.i = z__3.i - bkm1.i;
                z_div(&z__1, &z__2, &denom);
                b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L20: */
            }
            k += -2;
        }

        goto L10;
L30:

/*        Next solve U'*X = B, overwriting B with X. */

/*        K is the main loop index, increasing from 1 to N in steps of */
/*        1 or 2, depending on the size of the diagonal blocks. */

        k = 1;
L40:

/*        If K > N, exit from loop. */

        if (k > *n) {
            goto L50;
        }

        if (ipiv[k] > 0) {

/*           1 x 1 diagonal block */

/*           Multiply by inv(U'(K)), where U(K) is the transformation */
/*           stored in column K of A. */

            if (k > 1) {
                zlacgv_(nrhs, &b[k + b_dim1], ldb);
                i__1 = k - 1;
                z__1.r = -1., z__1.i = -0.;
                zgemv_("Conjugate transpose", &i__1, nrhs, &z__1, &b[b_offset]
, ldb, &a[k * a_dim1 + 1], &c__1, &c_b1, &b[k + 
                        b_dim1], ldb);
                zlacgv_(nrhs, &b[k + b_dim1], ldb);
            }

/*           Interchange rows K and IPIV(K). */

            kp = ipiv[k];
            if (kp != k) {
                zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
            }
            ++k;
        } else {

/*           2 x 2 diagonal block */

/*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation */
/*           stored in columns K and K+1 of A. */

            if (k > 1) {
                zlacgv_(nrhs, &b[k + b_dim1], ldb);
                i__1 = k - 1;
                z__1.r = -1., z__1.i = -0.;
                zgemv_("Conjugate transpose", &i__1, nrhs, &z__1, &b[b_offset]
, ldb, &a[k * a_dim1 + 1], &c__1, &c_b1, &b[k + 
                        b_dim1], ldb);
                zlacgv_(nrhs, &b[k + b_dim1], ldb);

                zlacgv_(nrhs, &b[k + 1 + b_dim1], ldb);
                i__1 = k - 1;
                z__1.r = -1., z__1.i = -0.;
                zgemv_("Conjugate transpose", &i__1, nrhs, &z__1, &b[b_offset]
, ldb, &a[(k + 1) * a_dim1 + 1], &c__1, &c_b1, &b[k + 
                        1 + b_dim1], ldb);
                zlacgv_(nrhs, &b[k + 1 + b_dim1], ldb);
            }

/*           Interchange rows K and -IPIV(K). */

            kp = -ipiv[k];
            if (kp != k) {
                zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
            }
            k += 2;
        }

        goto L40;
L50:

        ;
    } else {

/*        Solve A*X = B, where A = L*D*L'. */

/*        First solve L*D*X = B, overwriting B with X. */

/*        K is the main loop index, increasing from 1 to N in steps of */
/*        1 or 2, depending on the size of the diagonal blocks. */

        k = 1;
L60:

/*        If K > N, exit from loop. */

        if (k > *n) {
            goto L80;
        }

        if (ipiv[k] > 0) {

/*           1 x 1 diagonal block */

/*           Interchange rows K and IPIV(K). */

            kp = ipiv[k];
            if (kp != k) {
                zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
            }

/*           Multiply by inv(L(K)), where L(K) is the transformation */
/*           stored in column K of A. */

            if (k < *n) {
                i__1 = *n - k;
                z__1.r = -1., z__1.i = -0.;
                zgeru_(&i__1, nrhs, &z__1, &a[k + 1 + k * a_dim1], &c__1, &b[
                        k + b_dim1], ldb, &b[k + 1 + b_dim1], ldb);
            }

/*           Multiply by the inverse of the diagonal block. */

            i__1 = k + k * a_dim1;
            s = 1. / a[i__1].r;
            zdscal_(nrhs, &s, &b[k + b_dim1], ldb);
            ++k;
        } else {

/*           2 x 2 diagonal block */

/*           Interchange rows K+1 and -IPIV(K). */

            kp = -ipiv[k];
            if (kp != k + 1) {
                zswap_(nrhs, &b[k + 1 + b_dim1], ldb, &b[kp + b_dim1], ldb);
            }

/*           Multiply by inv(L(K)), where L(K) is the transformation */
/*           stored in columns K and K+1 of A. */

            if (k < *n - 1) {
                i__1 = *n - k - 1;
                z__1.r = -1., z__1.i = -0.;
                zgeru_(&i__1, nrhs, &z__1, &a[k + 2 + k * a_dim1], &c__1, &b[
                        k + b_dim1], ldb, &b[k + 2 + b_dim1], ldb);
                i__1 = *n - k - 1;
                z__1.r = -1., z__1.i = -0.;
                zgeru_(&i__1, nrhs, &z__1, &a[k + 2 + (k + 1) * a_dim1], &
                        c__1, &b[k + 1 + b_dim1], ldb, &b[k + 2 + b_dim1], 
                        ldb);
            }

/*           Multiply by the inverse of the diagonal block. */

            i__1 = k + 1 + k * a_dim1;
            akm1k.r = a[i__1].r, akm1k.i = a[i__1].i;
            d_cnjg(&z__2, &akm1k);
            z_div(&z__1, &a[k + k * a_dim1], &z__2);
            akm1.r = z__1.r, akm1.i = z__1.i;
            z_div(&z__1, &a[k + 1 + (k + 1) * a_dim1], &akm1k);
            ak.r = z__1.r, ak.i = z__1.i;
            z__2.r = akm1.r * ak.r - akm1.i * ak.i, z__2.i = akm1.r * ak.i + 
                    akm1.i * ak.r;
            z__1.r = z__2.r - 1., z__1.i = z__2.i - 0.;
            denom.r = z__1.r, denom.i = z__1.i;
            i__1 = *nrhs;
            for (j = 1; j <= i__1; ++j) {
                d_cnjg(&z__2, &akm1k);
                z_div(&z__1, &b[k + j * b_dim1], &z__2);
                bkm1.r = z__1.r, bkm1.i = z__1.i;
                z_div(&z__1, &b[k + 1 + j * b_dim1], &akm1k);
                bk.r = z__1.r, bk.i = z__1.i;
                i__2 = k + j * b_dim1;
                z__3.r = ak.r * bkm1.r - ak.i * bkm1.i, z__3.i = ak.r * 
                        bkm1.i + ak.i * bkm1.r;
                z__2.r = z__3.r - bk.r, z__2.i = z__3.i - bk.i;
                z_div(&z__1, &z__2, &denom);
                b[i__2].r = z__1.r, b[i__2].i = z__1.i;
                i__2 = k + 1 + j * b_dim1;
                z__3.r = akm1.r * bk.r - akm1.i * bk.i, z__3.i = akm1.r * 
                        bk.i + akm1.i * bk.r;
                z__2.r = z__3.r - bkm1.r, z__2.i = z__3.i - bkm1.i;
                z_div(&z__1, &z__2, &denom);
                b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L70: */
            }
            k += 2;
        }

        goto L60;
L80:

/*        Next solve L'*X = B, overwriting B with X. */

/*        K is the main loop index, decreasing from N to 1 in steps of */
/*        1 or 2, depending on the size of the diagonal blocks. */

        k = *n;
L90:

/*        If K < 1, exit from loop. */

        if (k < 1) {
            goto L100;
        }

        if (ipiv[k] > 0) {

/*           1 x 1 diagonal block */

/*           Multiply by inv(L'(K)), where L(K) is the transformation */
/*           stored in column K of A. */

            if (k < *n) {
                zlacgv_(nrhs, &b[k + b_dim1], ldb);
                i__1 = *n - k;
                z__1.r = -1., z__1.i = -0.;
                zgemv_("Conjugate transpose", &i__1, nrhs, &z__1, &b[k + 1 + 
                        b_dim1], ldb, &a[k + 1 + k * a_dim1], &c__1, &c_b1, &
                        b[k + b_dim1], ldb);
                zlacgv_(nrhs, &b[k + b_dim1], ldb);
            }

/*           Interchange rows K and IPIV(K). */

            kp = ipiv[k];
            if (kp != k) {
                zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
            }
            --k;
        } else {

/*           2 x 2 diagonal block */

/*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation */
/*           stored in columns K-1 and K of A. */

            if (k < *n) {
                zlacgv_(nrhs, &b[k + b_dim1], ldb);
                i__1 = *n - k;
                z__1.r = -1., z__1.i = -0.;
                zgemv_("Conjugate transpose", &i__1, nrhs, &z__1, &b[k + 1 + 
                        b_dim1], ldb, &a[k + 1 + k * a_dim1], &c__1, &c_b1, &
                        b[k + b_dim1], ldb);
                zlacgv_(nrhs, &b[k + b_dim1], ldb);

                zlacgv_(nrhs, &b[k - 1 + b_dim1], ldb);
                i__1 = *n - k;
                z__1.r = -1., z__1.i = -0.;
                zgemv_("Conjugate transpose", &i__1, nrhs, &z__1, &b[k + 1 + 
                        b_dim1], ldb, &a[k + 1 + (k - 1) * a_dim1], &c__1, &
                        c_b1, &b[k - 1 + b_dim1], ldb);
                zlacgv_(nrhs, &b[k - 1 + b_dim1], ldb);
            }

/*           Interchange rows K and -IPIV(K). */

            kp = -ipiv[k];
            if (kp != k) {
                zswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
            }
            k += -2;
        }

        goto L90;
L100:
        ;
    }

    return 0;

/*     End of ZHETRS */

} /* zhetrs_ */