zherk.c

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/* zherk.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 zherk_(char *uplo, char *trans, integer *n, integer *k, 
        doublereal *alpha, doublecomplex *a, integer *lda, doublereal *beta, 
        doublecomplex *c__, integer *ldc)
{
    /* System generated locals */
    integer a_dim1, a_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;

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

    /* Local variables */
    integer i__, j, l, info;
    doublecomplex temp;
    extern logical lsame_(char *, char *);
    integer nrowa;
    doublereal rtemp;
    logical upper;
    extern /* Subroutine */ int xerbla_(char *, integer *);

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

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

/*  ZHERK  performs one of the hermitian rank k operations */

/*     C := alpha*A*conjg( A' ) + beta*C, */

/*  or */

/*     C := alpha*conjg( A' )*A + beta*C, */

/*  where  alpha and beta  are  real scalars,  C is an  n by n  hermitian */
/*  matrix and  A  is an  n by k  matrix in the  first case and a  k by n */
/*  matrix in the second case. */

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

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

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

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

/*           Unchanged on exit. */

/*  TRANS  - CHARACTER*1. */
/*           On entry,  TRANS  specifies the operation to be performed as */
/*           follows: */

/*              TRANS = 'N' or 'n'   C := alpha*A*conjg( A' ) + beta*C. */

/*              TRANS = 'C' or 'c'   C := alpha*conjg( A' )*A + beta*C. */

/*           Unchanged on exit. */

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

/*  K      - INTEGER. */
/*           On entry with  TRANS = 'N' or 'n',  K  specifies  the number */
/*           of  columns   of  the   matrix   A,   and  on   entry   with */
/*           TRANS = 'C' or 'c',  K  specifies  the number of rows of the */
/*           matrix A.  K must be at least zero. */
/*           Unchanged on exit. */

/*  ALPHA  - DOUBLE PRECISION            . */
/*           On entry, ALPHA specifies the scalar alpha. */
/*           Unchanged on exit. */

/*  A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is */
/*           k  when  TRANS = 'N' or 'n',  and is  n  otherwise. */
/*           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k */
/*           part of the array  A  must contain the matrix  A,  otherwise */
/*           the leading  k by n  part of the array  A  must contain  the */
/*           matrix A. */
/*           Unchanged on exit. */

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

/*  BETA   - DOUBLE PRECISION. */
/*           On entry, BETA specifies the scalar beta. */
/*           Unchanged on exit. */

/*  C      - COMPLEX*16          array of DIMENSION ( LDC, n ). */
/*           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n */
/*           upper triangular part of the array C must contain the upper */
/*           triangular part  of the  hermitian matrix  and the strictly */
/*           lower triangular part of C is not referenced.  On exit, the */
/*           upper triangular part of the array  C is overwritten by the */
/*           upper triangular part of the updated matrix. */
/*           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n */
/*           lower triangular part of the array C must contain the lower */
/*           triangular part  of the  hermitian matrix  and the strictly */
/*           upper triangular part of C is not referenced.  On exit, the */
/*           lower triangular part of the array  C is overwritten by the */
/*           lower triangular part of the updated matrix. */
/*           Note that the imaginary parts of the diagonal elements need */
/*           not be set,  they are assumed to be zero,  and on exit they */
/*           are set to zero. */

/*  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, n ). */
/*           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. */

/*  -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. */
/*     Ed Anderson, Cray Research Inc. */


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

/*     Test the input parameters. */

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

    /* Function Body */
    if (lsame_(trans, "N")) {
        nrowa = *n;
    } else {
        nrowa = *k;
    }
    upper = lsame_(uplo, "U");

    info = 0;
    if (! upper && ! lsame_(uplo, "L")) {
        info = 1;
    } else if (! lsame_(trans, "N") && ! lsame_(trans, 
            "C")) {
        info = 2;
    } else if (*n < 0) {
        info = 3;
    } else if (*k < 0) {
        info = 4;
    } else if (*lda < max(1,nrowa)) {
        info = 7;
    } else if (*ldc < max(1,*n)) {
        info = 10;
    }
    if (info != 0) {
        xerbla_("ZHERK ", &info);
        return 0;
    }

/*     Quick return if possible. */

    if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
        return 0;
    }

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

    if (*alpha == 0.) {
        if (upper) {
            if (*beta == 0.) {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    i__2 = j;
                    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 = j - 1;
                    for (i__ = 1; i__ <= i__2; ++i__) {
                        i__3 = i__ + j * c_dim1;
                        i__4 = i__ + j * c_dim1;
                        z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[
                                i__4].i;
                        c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L30: */
                    }
                    i__2 = j + j * c_dim1;
                    i__3 = j + j * c_dim1;
                    d__1 = *beta * c__[i__3].r;
                    c__[i__2].r = d__1, c__[i__2].i = 0.;
/* L40: */
                }
            }
        } else {
            if (*beta == 0.) {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    i__2 = *n;
                    for (i__ = j; i__ <= i__2; ++i__) {
                        i__3 = i__ + j * c_dim1;
                        c__[i__3].r = 0., c__[i__3].i = 0.;
/* L50: */
                    }
/* L60: */
                }
            } else {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    i__2 = j + j * c_dim1;
                    i__3 = j + j * c_dim1;
                    d__1 = *beta * c__[i__3].r;
                    c__[i__2].r = d__1, c__[i__2].i = 0.;
                    i__2 = *n;
                    for (i__ = j + 1; i__ <= i__2; ++i__) {
                        i__3 = i__ + j * c_dim1;
                        i__4 = i__ + j * c_dim1;
                        z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[
                                i__4].i;
                        c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L70: */
                    }
/* L80: */
                }
            }
        }
        return 0;
    }

/*     Start the operations. */

    if (lsame_(trans, "N")) {

/*        Form  C := alpha*A*conjg( A' ) + beta*C. */

        if (upper) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                if (*beta == 0.) {
                    i__2 = j;
                    for (i__ = 1; i__ <= i__2; ++i__) {
                        i__3 = i__ + j * c_dim1;
                        c__[i__3].r = 0., c__[i__3].i = 0.;
/* L90: */
                    }
                } else if (*beta != 1.) {
                    i__2 = j - 1;
                    for (i__ = 1; i__ <= i__2; ++i__) {
                        i__3 = i__ + j * c_dim1;
                        i__4 = i__ + j * c_dim1;
                        z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[
                                i__4].i;
                        c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L100: */
                    }
                    i__2 = j + j * c_dim1;
                    i__3 = j + j * c_dim1;
                    d__1 = *beta * c__[i__3].r;
                    c__[i__2].r = d__1, c__[i__2].i = 0.;
                } else {
                    i__2 = j + j * c_dim1;
                    i__3 = j + j * c_dim1;
                    d__1 = c__[i__3].r;
                    c__[i__2].r = d__1, c__[i__2].i = 0.;
                }
                i__2 = *k;
                for (l = 1; l <= i__2; ++l) {
                    i__3 = j + l * a_dim1;
                    if (a[i__3].r != 0. || a[i__3].i != 0.) {
                        d_cnjg(&z__2, &a[j + l * a_dim1]);
                        z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i;
                        temp.r = z__1.r, temp.i = z__1.i;
                        i__3 = j - 1;
                        for (i__ = 1; i__ <= i__3; ++i__) {
                            i__4 = i__ + j * c_dim1;
                            i__5 = i__ + j * c_dim1;
                            i__6 = i__ + l * a_dim1;
                            z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, 
                                    z__2.i = temp.r * a[i__6].i + temp.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;
/* L110: */
                        }
                        i__3 = j + j * c_dim1;
                        i__4 = j + j * c_dim1;
                        i__5 = i__ + l * a_dim1;
                        z__1.r = temp.r * a[i__5].r - temp.i * a[i__5].i, 
                                z__1.i = temp.r * a[i__5].i + temp.i * a[i__5]
                                .r;
                        d__1 = c__[i__4].r + z__1.r;
                        c__[i__3].r = d__1, c__[i__3].i = 0.;
                    }
/* L120: */
                }
/* L130: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                if (*beta == 0.) {
                    i__2 = *n;
                    for (i__ = j; i__ <= i__2; ++i__) {
                        i__3 = i__ + j * c_dim1;
                        c__[i__3].r = 0., c__[i__3].i = 0.;
/* L140: */
                    }
                } else if (*beta != 1.) {
                    i__2 = j + j * c_dim1;
                    i__3 = j + j * c_dim1;
                    d__1 = *beta * c__[i__3].r;
                    c__[i__2].r = d__1, c__[i__2].i = 0.;
                    i__2 = *n;
                    for (i__ = j + 1; i__ <= i__2; ++i__) {
                        i__3 = i__ + j * c_dim1;
                        i__4 = i__ + j * c_dim1;
                        z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[
                                i__4].i;
                        c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L150: */
                    }
                } else {
                    i__2 = j + j * c_dim1;
                    i__3 = j + j * c_dim1;
                    d__1 = c__[i__3].r;
                    c__[i__2].r = d__1, c__[i__2].i = 0.;
                }
                i__2 = *k;
                for (l = 1; l <= i__2; ++l) {
                    i__3 = j + l * a_dim1;
                    if (a[i__3].r != 0. || a[i__3].i != 0.) {
                        d_cnjg(&z__2, &a[j + l * a_dim1]);
                        z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i;
                        temp.r = z__1.r, temp.i = z__1.i;
                        i__3 = j + j * c_dim1;
                        i__4 = j + j * c_dim1;
                        i__5 = j + l * a_dim1;
                        z__1.r = temp.r * a[i__5].r - temp.i * a[i__5].i, 
                                z__1.i = temp.r * a[i__5].i + temp.i * a[i__5]
                                .r;
                        d__1 = c__[i__4].r + z__1.r;
                        c__[i__3].r = d__1, c__[i__3].i = 0.;
                        i__3 = *n;
                        for (i__ = j + 1; i__ <= i__3; ++i__) {
                            i__4 = i__ + j * c_dim1;
                            i__5 = i__ + j * c_dim1;
                            i__6 = i__ + l * a_dim1;
                            z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, 
                                    z__2.i = temp.r * a[i__6].i + temp.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;
/* L160: */
                        }
                    }
/* L170: */
                }
/* L180: */
            }
        }
    } else {

/*        Form  C := alpha*conjg( A' )*A + beta*C. */

        if (upper) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__2 = j - 1;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    temp.r = 0., temp.i = 0.;
                    i__3 = *k;
                    for (l = 1; l <= i__3; ++l) {
                        d_cnjg(&z__3, &a[l + i__ * a_dim1]);
                        i__4 = l + j * a_dim1;
                        z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, 
                                z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4]
                                .r;
                        z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
                        temp.r = z__1.r, temp.i = z__1.i;
/* L190: */
                    }
                    if (*beta == 0.) {
                        i__3 = i__ + j * c_dim1;
                        z__1.r = *alpha * temp.r, z__1.i = *alpha * temp.i;
                        c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
                    } else {
                        i__3 = i__ + j * c_dim1;
                        z__2.r = *alpha * temp.r, z__2.i = *alpha * temp.i;
                        i__4 = i__ + j * c_dim1;
                        z__3.r = *beta * c__[i__4].r, z__3.i = *beta * c__[
                                i__4].i;
                        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;
                    }
/* L200: */
                }
                rtemp = 0.;
                i__2 = *k;
                for (l = 1; l <= i__2; ++l) {
                    d_cnjg(&z__3, &a[l + j * a_dim1]);
                    i__3 = l + j * a_dim1;
                    z__2.r = z__3.r * a[i__3].r - z__3.i * a[i__3].i, z__2.i =
                             z__3.r * a[i__3].i + z__3.i * a[i__3].r;
                    z__1.r = rtemp + z__2.r, z__1.i = z__2.i;
                    rtemp = z__1.r;
/* L210: */
                }
                if (*beta == 0.) {
                    i__2 = j + j * c_dim1;
                    d__1 = *alpha * rtemp;
                    c__[i__2].r = d__1, c__[i__2].i = 0.;
                } else {
                    i__2 = j + j * c_dim1;
                    i__3 = j + j * c_dim1;
                    d__1 = *alpha * rtemp + *beta * c__[i__3].r;
                    c__[i__2].r = d__1, c__[i__2].i = 0.;
                }
/* L220: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                rtemp = 0.;
                i__2 = *k;
                for (l = 1; l <= i__2; ++l) {
                    d_cnjg(&z__3, &a[l + j * a_dim1]);
                    i__3 = l + j * a_dim1;
                    z__2.r = z__3.r * a[i__3].r - z__3.i * a[i__3].i, z__2.i =
                             z__3.r * a[i__3].i + z__3.i * a[i__3].r;
                    z__1.r = rtemp + z__2.r, z__1.i = z__2.i;
                    rtemp = z__1.r;
/* L230: */
                }
                if (*beta == 0.) {
                    i__2 = j + j * c_dim1;
                    d__1 = *alpha * rtemp;
                    c__[i__2].r = d__1, c__[i__2].i = 0.;
                } else {
                    i__2 = j + j * c_dim1;
                    i__3 = j + j * c_dim1;
                    d__1 = *alpha * rtemp + *beta * c__[i__3].r;
                    c__[i__2].r = d__1, c__[i__2].i = 0.;
                }
                i__2 = *n;
                for (i__ = j + 1; i__ <= i__2; ++i__) {
                    temp.r = 0., temp.i = 0.;
                    i__3 = *k;
                    for (l = 1; l <= i__3; ++l) {
                        d_cnjg(&z__3, &a[l + i__ * a_dim1]);
                        i__4 = l + j * a_dim1;
                        z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, 
                                z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4]
                                .r;
                        z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
                        temp.r = z__1.r, temp.i = z__1.i;
/* L240: */
                    }
                    if (*beta == 0.) {
                        i__3 = i__ + j * c_dim1;
                        z__1.r = *alpha * temp.r, z__1.i = *alpha * temp.i;
                        c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
                    } else {
                        i__3 = i__ + j * c_dim1;
                        z__2.r = *alpha * temp.r, z__2.i = *alpha * temp.i;
                        i__4 = i__ + j * c_dim1;
                        z__3.r = *beta * c__[i__4].r, z__3.i = *beta * c__[
                                i__4].i;
                        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;
                    }
/* L250: */
                }
/* L260: */
            }
        }
    }

    return 0;

/*     End of ZHERK . */

} /* zherk_ */