zhpr.c

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/* zhpr.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 zhpr_(char *uplo, integer *n, doublereal *alpha, 
        doublecomplex *x, integer *incx, doublecomplex *ap)
{
    /* System generated locals */
    integer i__1, i__2, i__3, i__4, i__5;
    doublereal d__1;
    doublecomplex z__1, z__2;

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

    /* Local variables */
    integer i__, j, k, kk, ix, jx, kx, info;
    doublecomplex temp;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int xerbla_(char *, integer *);

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

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

/*  ZHPR    performs the hermitian rank 1 operation */

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

/*  where alpha is a real scalar, x is an n element vector and A is an */
/*  n by n hermitian matrix, supplied in packed form. */

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

/*  UPLO   - CHARACTER*1. */
/*           On entry, UPLO specifies whether the upper or lower */
/*           triangular part of the matrix A is supplied in the packed */
/*           array AP as follows: */

/*              UPLO = 'U' or 'u'   The upper triangular part of A is */
/*                                  supplied in AP. */

/*              UPLO = 'L' or 'l'   The lower triangular part of A is */
/*                                  supplied in AP. */

/*           Unchanged on exit. */

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

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

/*  X      - COMPLEX*16       array of dimension at least */
/*           ( 1 + ( n - 1 )*abs( INCX ) ). */
/*           Before entry, the incremented array X must contain the n */
/*           element vector x. */
/*           Unchanged on exit. */

/*  INCX   - INTEGER. */
/*           On entry, INCX specifies the increment for the elements of */
/*           X. INCX must not be zero. */
/*           Unchanged on exit. */

/*  AP     - COMPLEX*16       array of DIMENSION at least */
/*           ( ( n*( n + 1 ) )/2 ). */
/*           Before entry with  UPLO = 'U' or 'u', the array AP must */
/*           contain the upper triangular part of the hermitian matrix */
/*           packed sequentially, column by column, so that AP( 1 ) */
/*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) */
/*           and a( 2, 2 ) respectively, and so on. On exit, the array */
/*           AP is overwritten by the upper triangular part of the */
/*           updated matrix. */
/*           Before entry with UPLO = 'L' or 'l', the array AP must */
/*           contain the lower triangular part of the hermitian matrix */
/*           packed sequentially, column by column, so that AP( 1 ) */
/*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) */
/*           and a( 3, 1 ) respectively, and so on. On exit, the array */
/*           AP 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. */


/*  Level 2 Blas routine. */

/*  -- Written on 22-October-1986. */
/*     Jack Dongarra, Argonne National Lab. */
/*     Jeremy Du Croz, Nag Central Office. */
/*     Sven Hammarling, Nag Central Office. */
/*     Richard Hanson, Sandia National Labs. */


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

/*     Test the input parameters. */

    /* Parameter adjustments */
    --ap;
    --x;

    /* Function Body */
    info = 0;
    if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
        info = 1;
    } else if (*n < 0) {
        info = 2;
    } else if (*incx == 0) {
        info = 5;
    }
    if (info != 0) {
        xerbla_("ZHPR  ", &info);
        return 0;
    }

/*     Quick return if possible. */

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

/*     Set the start point in X if the increment is not unity. */

    if (*incx <= 0) {
        kx = 1 - (*n - 1) * *incx;
    } else if (*incx != 1) {
        kx = 1;
    }

/*     Start the operations. In this version the elements of the array AP */
/*     are accessed sequentially with one pass through AP. */

    kk = 1;
    if (lsame_(uplo, "U")) {

/*        Form  A  when upper triangle is stored in AP. */

        if (*incx == 1) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__2 = j;
                if (x[i__2].r != 0. || x[i__2].i != 0.) {
                    d_cnjg(&z__2, &x[j]);
                    z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i;
                    temp.r = z__1.r, temp.i = z__1.i;
                    k = kk;
                    i__2 = j - 1;
                    for (i__ = 1; i__ <= i__2; ++i__) {
                        i__3 = k;
                        i__4 = k;
                        i__5 = i__;
                        z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, 
                                z__2.i = x[i__5].r * temp.i + x[i__5].i * 
                                temp.r;
                        z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + 
                                z__2.i;
                        ap[i__3].r = z__1.r, ap[i__3].i = z__1.i;
                        ++k;
/* L10: */
                    }
                    i__2 = kk + j - 1;
                    i__3 = kk + j - 1;
                    i__4 = j;
                    z__1.r = x[i__4].r * temp.r - x[i__4].i * temp.i, z__1.i =
                             x[i__4].r * temp.i + x[i__4].i * temp.r;
                    d__1 = ap[i__3].r + z__1.r;
                    ap[i__2].r = d__1, ap[i__2].i = 0.;
                } else {
                    i__2 = kk + j - 1;
                    i__3 = kk + j - 1;
                    d__1 = ap[i__3].r;
                    ap[i__2].r = d__1, ap[i__2].i = 0.;
                }
                kk += j;
/* L20: */
            }
        } else {
            jx = kx;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__2 = jx;
                if (x[i__2].r != 0. || x[i__2].i != 0.) {
                    d_cnjg(&z__2, &x[jx]);
                    z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i;
                    temp.r = z__1.r, temp.i = z__1.i;
                    ix = kx;
                    i__2 = kk + j - 2;
                    for (k = kk; k <= i__2; ++k) {
                        i__3 = k;
                        i__4 = k;
                        i__5 = ix;
                        z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, 
                                z__2.i = x[i__5].r * temp.i + x[i__5].i * 
                                temp.r;
                        z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + 
                                z__2.i;
                        ap[i__3].r = z__1.r, ap[i__3].i = z__1.i;
                        ix += *incx;
/* L30: */
                    }
                    i__2 = kk + j - 1;
                    i__3 = kk + j - 1;
                    i__4 = jx;
                    z__1.r = x[i__4].r * temp.r - x[i__4].i * temp.i, z__1.i =
                             x[i__4].r * temp.i + x[i__4].i * temp.r;
                    d__1 = ap[i__3].r + z__1.r;
                    ap[i__2].r = d__1, ap[i__2].i = 0.;
                } else {
                    i__2 = kk + j - 1;
                    i__3 = kk + j - 1;
                    d__1 = ap[i__3].r;
                    ap[i__2].r = d__1, ap[i__2].i = 0.;
                }
                jx += *incx;
                kk += j;
/* L40: */
            }
        }
    } else {

/*        Form  A  when lower triangle is stored in AP. */

        if (*incx == 1) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__2 = j;
                if (x[i__2].r != 0. || x[i__2].i != 0.) {
                    d_cnjg(&z__2, &x[j]);
                    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__2 = kk;
                    i__3 = kk;
                    i__4 = j;
                    z__1.r = temp.r * x[i__4].r - temp.i * x[i__4].i, z__1.i =
                             temp.r * x[i__4].i + temp.i * x[i__4].r;
                    d__1 = ap[i__3].r + z__1.r;
                    ap[i__2].r = d__1, ap[i__2].i = 0.;
                    k = kk + 1;
                    i__2 = *n;
                    for (i__ = j + 1; i__ <= i__2; ++i__) {
                        i__3 = k;
                        i__4 = k;
                        i__5 = i__;
                        z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, 
                                z__2.i = x[i__5].r * temp.i + x[i__5].i * 
                                temp.r;
                        z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + 
                                z__2.i;
                        ap[i__3].r = z__1.r, ap[i__3].i = z__1.i;
                        ++k;
/* L50: */
                    }
                } else {
                    i__2 = kk;
                    i__3 = kk;
                    d__1 = ap[i__3].r;
                    ap[i__2].r = d__1, ap[i__2].i = 0.;
                }
                kk = kk + *n - j + 1;
/* L60: */
            }
        } else {
            jx = kx;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__2 = jx;
                if (x[i__2].r != 0. || x[i__2].i != 0.) {
                    d_cnjg(&z__2, &x[jx]);
                    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__2 = kk;
                    i__3 = kk;
                    i__4 = jx;
                    z__1.r = temp.r * x[i__4].r - temp.i * x[i__4].i, z__1.i =
                             temp.r * x[i__4].i + temp.i * x[i__4].r;
                    d__1 = ap[i__3].r + z__1.r;
                    ap[i__2].r = d__1, ap[i__2].i = 0.;
                    ix = jx;
                    i__2 = kk + *n - j;
                    for (k = kk + 1; k <= i__2; ++k) {
                        ix += *incx;
                        i__3 = k;
                        i__4 = k;
                        i__5 = ix;
                        z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, 
                                z__2.i = x[i__5].r * temp.i + x[i__5].i * 
                                temp.r;
                        z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + 
                                z__2.i;
                        ap[i__3].r = z__1.r, ap[i__3].i = z__1.i;
/* L70: */
                    }
                } else {
                    i__2 = kk;
                    i__3 = kk;
                    d__1 = ap[i__3].r;
                    ap[i__2].r = d__1, ap[i__2].i = 0.;
                }
                jx += *incx;
                kk = kk + *n - j + 1;
/* L80: */
            }
        }
    }

    return 0;

/*     End of ZHPR  . */

} /* zhpr_ */