zhemm.c

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/* zhemm.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"

/* Subroutine */ int zhemm_(char *side, char *uplo, integer *m, integer *n, 
        doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex *
        b, integer *ldb, doublecomplex *beta, doublecomplex *c__, integer *
        ldc)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, 
            i__3, i__4, i__5, i__6;
    doublereal d__1;
    doublecomplex z__1, z__2, z__3, z__4, z__5;

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

    /* Local variables */
    integer i__, j, k, info;
    doublecomplex temp1, temp2;
    extern logical lsame_(char *, char *);
    integer nrowa;
    logical upper;
    extern /* Subroutine */ int xerbla_(char *, integer *);

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

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

/*  ZHEMM  performs one of the matrix-matrix operations */

/*     C := alpha*A*B + beta*C, */

/*  or */

/*     C := alpha*B*A + beta*C, */

/*  where alpha and beta are scalars, A is an hermitian matrix and  B and */
/*  C are m by n matrices. */

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

/*  SIDE   - CHARACTER*1. */
/*           On entry,  SIDE  specifies whether  the  hermitian matrix  A */
/*           appears on the  left or right  in the  operation as follows: */

/*              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C, */

/*              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C, */

/*           Unchanged on exit. */

/*  UPLO   - CHARACTER*1. */
/*           On  entry,   UPLO  specifies  whether  the  upper  or  lower */
/*           triangular  part  of  the  hermitian  matrix   A  is  to  be */
/*           referenced as follows: */

/*              UPLO = 'U' or 'u'   Only the upper triangular part of the */
/*                                  hermitian matrix is to be referenced. */

/*              UPLO = 'L' or 'l'   Only the lower triangular part of the */
/*                                  hermitian matrix is to be referenced. */

/*           Unchanged on exit. */

/*  M      - INTEGER. */
/*           On entry,  M  specifies the number of rows of the matrix  C. */
/*           M  must be at least zero. */
/*           Unchanged on exit. */

/*  N      - INTEGER. */
/*           On entry, N specifies the number of columns of the matrix C. */
/*           N  must be at least zero. */
/*           Unchanged on exit. */

/*  ALPHA  - COMPLEX*16      . */
/*           On entry, ALPHA specifies the scalar alpha. */
/*           Unchanged on exit. */

/*  A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is */
/*           m  when  SIDE = 'L' or 'l'  and is n  otherwise. */
/*           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of */
/*           the array  A  must contain the  hermitian matrix,  such that */
/*           when  UPLO = 'U' or 'u', the leading m by m upper triangular */
/*           part of the array  A  must contain the upper triangular part */
/*           of the  hermitian matrix and the  strictly  lower triangular */
/*           part of  A  is not referenced,  and when  UPLO = 'L' or 'l', */
/*           the leading  m by m  lower triangular part  of the  array  A */
/*           must  contain  the  lower triangular part  of the  hermitian */
/*           matrix and the  strictly upper triangular part of  A  is not */
/*           referenced. */
/*           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of */
/*           the array  A  must contain the  hermitian matrix,  such that */
/*           when  UPLO = 'U' or 'u', the leading n by n upper triangular */
/*           part of the array  A  must contain the upper triangular part */
/*           of the  hermitian matrix and the  strictly  lower triangular */
/*           part of  A  is not referenced,  and when  UPLO = 'L' or 'l', */
/*           the leading  n by n  lower triangular part  of the  array  A */
/*           must  contain  the  lower triangular part  of the  hermitian */
/*           matrix and the  strictly upper triangular part of  A  is not */
/*           referenced. */
/*           Note that the imaginary parts  of the diagonal elements need */
/*           not be set, they are assumed to be zero. */
/*           Unchanged on exit. */

/*  LDA    - INTEGER. */
/*           On entry, LDA specifies the first dimension of A as declared */
/*           in the  calling (sub) program. When  SIDE = 'L' or 'l'  then */
/*           LDA must be at least  max( 1, m ), otherwise  LDA must be at */
/*           least max( 1, n ). */
/*           Unchanged on exit. */

/*  B      - COMPLEX*16       array of DIMENSION ( LDB, n ). */
/*           Before entry, the leading  m by n part of the array  B  must */
/*           contain the matrix B. */
/*           Unchanged on exit. */

/*  LDB    - INTEGER. */
/*           On entry, LDB specifies the first dimension of B as declared */
/*           in  the  calling  (sub)  program.   LDB  must  be  at  least */
/*           max( 1, m ). */
/*           Unchanged on exit. */

/*  BETA   - COMPLEX*16      . */
/*           On entry,  BETA  specifies the scalar  beta.  When  BETA  is */
/*           supplied as zero then C need not be set on input. */
/*           Unchanged on exit. */

/*  C      - COMPLEX*16       array of DIMENSION ( LDC, n ). */
/*           Before entry, the leading  m by n  part of the array  C must */
/*           contain the matrix  C,  except when  beta  is zero, in which */
/*           case C need not be set on entry. */
/*           On exit, the array  C  is overwritten by the  m by n updated */
/*           matrix. */

/*  LDC    - INTEGER. */
/*           On entry, LDC specifies the first dimension of C as declared */
/*           in  the  calling  (sub)  program.   LDC  must  be  at  least */
/*           max( 1, m ). */
/*           Unchanged on exit. */


/*  Level 3 Blas routine. */

/*  -- Written on 8-February-1989. */
/*     Jack Dongarra, Argonne National Laboratory. */
/*     Iain Duff, AERE Harwell. */
/*     Jeremy Du Croz, Numerical Algorithms Group Ltd. */
/*     Sven Hammarling, Numerical Algorithms Group Ltd. */


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

/*     Set NROWA as the number of rows of A. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    c_dim1 = *ldc;
    c_offset = 1 + c_dim1;
    c__ -= c_offset;

    /* Function Body */
    if (lsame_(side, "L")) {
        nrowa = *m;
    } else {
        nrowa = *n;
    }
    upper = lsame_(uplo, "U");

/*     Test the input parameters. */

    info = 0;
    if (! lsame_(side, "L") && ! lsame_(side, "R")) {
        info = 1;
    } else if (! upper && ! lsame_(uplo, "L")) {
        info = 2;
    } else if (*m < 0) {
        info = 3;
    } else if (*n < 0) {
        info = 4;
    } else if (*lda < max(1,nrowa)) {
        info = 7;
    } else if (*ldb < max(1,*m)) {
        info = 9;
    } else if (*ldc < max(1,*m)) {
        info = 12;
    }
    if (info != 0) {
        xerbla_("ZHEMM ", &info);
        return 0;
    }

/*     Quick return if possible. */

    if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 
            1. && beta->i == 0.)) {
        return 0;
    }

/*     And when  alpha.eq.zero. */

    if (alpha->r == 0. && alpha->i == 0.) {
        if (beta->r == 0. && beta->i == 0.) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__2 = *m;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    i__3 = i__ + j * c_dim1;
                    c__[i__3].r = 0., c__[i__3].i = 0.;
/* L10: */
                }
/* L20: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__2 = *m;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    i__3 = i__ + j * c_dim1;
                    i__4 = i__ + j * c_dim1;
                    z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, 
                            z__1.i = beta->r * c__[i__4].i + beta->i * c__[
                            i__4].r;
                    c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L30: */
                }
/* L40: */
            }
        }
        return 0;
    }

/*     Start the operations. */

    if (lsame_(side, "L")) {

/*        Form  C := alpha*A*B + beta*C. */

        if (upper) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__2 = *m;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    i__3 = i__ + j * b_dim1;
                    z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, 
                            z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3]
                            .r;
                    temp1.r = z__1.r, temp1.i = z__1.i;
                    temp2.r = 0., temp2.i = 0.;
                    i__3 = i__ - 1;
                    for (k = 1; k <= i__3; ++k) {
                        i__4 = k + j * c_dim1;
                        i__5 = k + j * c_dim1;
                        i__6 = k + i__ * a_dim1;
                        z__2.r = temp1.r * a[i__6].r - temp1.i * a[i__6].i, 
                                z__2.i = temp1.r * a[i__6].i + temp1.i * a[
                                i__6].r;
                        z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + 
                                z__2.i;
                        c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
                        i__4 = k + j * b_dim1;
                        d_cnjg(&z__3, &a[k + i__ * a_dim1]);
                        z__2.r = b[i__4].r * z__3.r - b[i__4].i * z__3.i, 
                                z__2.i = b[i__4].r * z__3.i + b[i__4].i * 
                                z__3.r;
                        z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
                        temp2.r = z__1.r, temp2.i = z__1.i;
/* L50: */
                    }
                    if (beta->r == 0. && beta->i == 0.) {
                        i__3 = i__ + j * c_dim1;
                        i__4 = i__ + i__ * a_dim1;
                        d__1 = a[i__4].r;
                        z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
                        z__3.r = alpha->r * temp2.r - alpha->i * temp2.i, 
                                z__3.i = alpha->r * temp2.i + alpha->i * 
                                temp2.r;
                        z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
                        c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
                    } else {
                        i__3 = i__ + j * c_dim1;
                        i__4 = i__ + j * c_dim1;
                        z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
                                .i, z__3.i = beta->r * c__[i__4].i + beta->i *
                                 c__[i__4].r;
                        i__5 = i__ + i__ * a_dim1;
                        d__1 = a[i__5].r;
                        z__4.r = d__1 * temp1.r, z__4.i = d__1 * temp1.i;
                        z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + z__4.i;
                        z__5.r = alpha->r * temp2.r - alpha->i * temp2.i, 
                                z__5.i = alpha->r * temp2.i + alpha->i * 
                                temp2.r;
                        z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
                        c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
                    }
/* L60: */
                }
/* L70: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                for (i__ = *m; i__ >= 1; --i__) {
                    i__2 = i__ + j * b_dim1;
                    z__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2].i, 
                            z__1.i = alpha->r * b[i__2].i + alpha->i * b[i__2]
                            .r;
                    temp1.r = z__1.r, temp1.i = z__1.i;
                    temp2.r = 0., temp2.i = 0.;
                    i__2 = *m;
                    for (k = i__ + 1; k <= i__2; ++k) {
                        i__3 = k + j * c_dim1;
                        i__4 = k + j * c_dim1;
                        i__5 = k + i__ * a_dim1;
                        z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, 
                                z__2.i = temp1.r * a[i__5].i + temp1.i * a[
                                i__5].r;
                        z__1.r = c__[i__4].r + z__2.r, z__1.i = c__[i__4].i + 
                                z__2.i;
                        c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
                        i__3 = k + j * b_dim1;
                        d_cnjg(&z__3, &a[k + i__ * a_dim1]);
                        z__2.r = b[i__3].r * z__3.r - b[i__3].i * z__3.i, 
                                z__2.i = b[i__3].r * z__3.i + b[i__3].i * 
                                z__3.r;
                        z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
                        temp2.r = z__1.r, temp2.i = z__1.i;
/* L80: */
                    }
                    if (beta->r == 0. && beta->i == 0.) {
                        i__2 = i__ + j * c_dim1;
                        i__3 = i__ + i__ * a_dim1;
                        d__1 = a[i__3].r;
                        z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
                        z__3.r = alpha->r * temp2.r - alpha->i * temp2.i, 
                                z__3.i = alpha->r * temp2.i + alpha->i * 
                                temp2.r;
                        z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
                        c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
                    } else {
                        i__2 = i__ + j * c_dim1;
                        i__3 = i__ + j * c_dim1;
                        z__3.r = beta->r * c__[i__3].r - beta->i * c__[i__3]
                                .i, z__3.i = beta->r * c__[i__3].i + beta->i *
                                 c__[i__3].r;
                        i__4 = i__ + i__ * a_dim1;
                        d__1 = a[i__4].r;
                        z__4.r = d__1 * temp1.r, z__4.i = d__1 * temp1.i;
                        z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + z__4.i;
                        z__5.r = alpha->r * temp2.r - alpha->i * temp2.i, 
                                z__5.i = alpha->r * temp2.i + alpha->i * 
                                temp2.r;
                        z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i;
                        c__[i__2].r = z__1.r, c__[i__2].i = z__1.i;
                    }
/* L90: */
                }
/* L100: */
            }
        }
    } else {

/*        Form  C := alpha*B*A + beta*C. */

        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            i__2 = j + j * a_dim1;
            d__1 = a[i__2].r;
            z__1.r = d__1 * alpha->r, z__1.i = d__1 * alpha->i;
            temp1.r = z__1.r, temp1.i = z__1.i;
            if (beta->r == 0. && beta->i == 0.) {
                i__2 = *m;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    i__3 = i__ + j * c_dim1;
                    i__4 = i__ + j * b_dim1;
                    z__1.r = temp1.r * b[i__4].r - temp1.i * b[i__4].i, 
                            z__1.i = temp1.r * b[i__4].i + temp1.i * b[i__4]
                            .r;
                    c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L110: */
                }
            } else {
                i__2 = *m;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    i__3 = i__ + j * c_dim1;
                    i__4 = i__ + j * c_dim1;
                    z__2.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, 
                            z__2.i = beta->r * c__[i__4].i + beta->i * c__[
                            i__4].r;
                    i__5 = i__ + j * b_dim1;
                    z__3.r = temp1.r * b[i__5].r - temp1.i * b[i__5].i, 
                            z__3.i = temp1.r * b[i__5].i + temp1.i * b[i__5]
                            .r;
                    z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
                    c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L120: */
                }
            }
            i__2 = j - 1;
            for (k = 1; k <= i__2; ++k) {
                if (upper) {
                    i__3 = k + j * a_dim1;
                    z__1.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, 
                            z__1.i = alpha->r * a[i__3].i + alpha->i * a[i__3]
                            .r;
                    temp1.r = z__1.r, temp1.i = z__1.i;
                } else {
                    d_cnjg(&z__2, &a[j + k * a_dim1]);
                    z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = 
                            alpha->r * z__2.i + alpha->i * z__2.r;
                    temp1.r = z__1.r, temp1.i = z__1.i;
                }
                i__3 = *m;
                for (i__ = 1; i__ <= i__3; ++i__) {
                    i__4 = i__ + j * c_dim1;
                    i__5 = i__ + j * c_dim1;
                    i__6 = i__ + k * b_dim1;
                    z__2.r = temp1.r * b[i__6].r - temp1.i * b[i__6].i, 
                            z__2.i = temp1.r * b[i__6].i + temp1.i * b[i__6]
                            .r;
                    z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + 
                            z__2.i;
                    c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
/* L130: */
                }
/* L140: */
            }
            i__2 = *n;
            for (k = j + 1; k <= i__2; ++k) {
                if (upper) {
                    d_cnjg(&z__2, &a[j + k * a_dim1]);
                    z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = 
                            alpha->r * z__2.i + alpha->i * z__2.r;
                    temp1.r = z__1.r, temp1.i = z__1.i;
                } else {
                    i__3 = k + j * a_dim1;
                    z__1.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, 
                            z__1.i = alpha->r * a[i__3].i + alpha->i * a[i__3]
                            .r;
                    temp1.r = z__1.r, temp1.i = z__1.i;
                }
                i__3 = *m;
                for (i__ = 1; i__ <= i__3; ++i__) {
                    i__4 = i__ + j * c_dim1;
                    i__5 = i__ + j * c_dim1;
                    i__6 = i__ + k * b_dim1;
                    z__2.r = temp1.r * b[i__6].r - temp1.i * b[i__6].i, 
                            z__2.i = temp1.r * b[i__6].i + temp1.i * b[i__6]
                            .r;
                    z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + 
                            z__2.i;
                    c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
/* L150: */
                }
/* L160: */
            }
/* L170: */
        }
    }

    return 0;

/*     End of ZHEMM . */

} /* zhemm_ */