lammps/lib/linalg/zpptri.cpp

/* fortran/zpptri.f -- translated by f2c (version 20200916).
   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
*/

#ifdef __cplusplus
extern "C" {
#endif
#include "lmp_f2c.h"

/* Table of constant values */

static doublereal c_b8 = 1.;
static integer c__1 = 1;

/* > \brief \b ZPPTRI */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download ZPPTRI + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpptri.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpptri.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpptri.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE ZPPTRI( UPLO, N, AP, INFO ) */

/*       .. Scalar Arguments .. */
/*       CHARACTER          UPLO */
/*       INTEGER            INFO, N */
/*       .. */
/*       .. Array Arguments .. */
/*       COMPLEX*16         AP( * ) */
/*       .. */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > ZPPTRI computes the inverse of a complex Hermitian positive definite */
/* > matrix A using the Cholesky factorization A = U**H*U or A = L*L**H */
/* > computed by ZPPTRF. */
/* > \endverbatim */

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

/* > \param[in] UPLO */
/* > \verbatim */
/* >          UPLO is CHARACTER*1 */
/* >          = 'U':  Upper triangular factor is stored in AP; */
/* >          = 'L':  Lower triangular factor is stored in AP. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix A.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] AP */
/* > \verbatim */
/* >          AP is COMPLEX*16 array, dimension (N*(N+1)/2) */
/* >          On entry, the triangular factor U or L from the Cholesky */
/* >          factorization A = U**H*U or A = L*L**H, packed columnwise as */
/* >          a linear array.  The j-th column of U or L is stored in the */
/* >          array AP as follows: */
/* >          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; */
/* >          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. */
/* > */
/* >          On exit, the upper or lower triangle of the (Hermitian) */
/* >          inverse of A, overwriting the input factor U or L. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit */
/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
/* >          > 0:  if INFO = i, the (i,i) element of the factor U or L is */
/* >                zero, and the inverse could not be computed. */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \ingroup complex16OTHERcomputational */

/*  ===================================================================== */
/* Subroutine */ int zpptri_(char *uplo, integer *n, doublecomplex *ap,
        integer *info, ftnlen uplo_len)
{
    /* System generated locals */
    integer i__1, i__2, i__3;
    doublereal d__1;
    doublecomplex z__1;

    /* Local variables */
    integer j, jc, jj;
    doublereal ajj;
    integer jjn;
    extern /* Subroutine */ int zhpr_(char *, integer *, doublereal *,
            doublecomplex *, integer *, doublecomplex *, ftnlen);
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
            doublecomplex *, integer *, doublecomplex *, integer *);
    logical upper;
    extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *,
            doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen,
            ftnlen), xerbla_(char *, integer *, ftnlen), zdscal_(integer *,
            doublereal *, doublecomplex *, integer *), ztptri_(char *, char *,
             integer *, doublecomplex *, integer *, ftnlen, ftnlen);


/*  -- LAPACK computational routine -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

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

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    --ap;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1);
    if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_((char *)"ZPPTRI", &i__1, (ftnlen)6);
        return 0;
    }

/*     Quick return if possible */

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

/*     Invert the triangular Cholesky factor U or L. */

    ztptri_(uplo, (char *)"Non-unit", n, &ap[1], info, (ftnlen)1, (ftnlen)8);
    if (*info > 0) {
        return 0;
    }
    if (upper) {

/*        Compute the product inv(U) * inv(U)**H. */

        jj = 0;
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            jc = jj + 1;
            jj += j;
            if (j > 1) {
                i__2 = j - 1;
                zhpr_((char *)"Upper", &i__2, &c_b8, &ap[jc], &c__1, &ap[1], (ftnlen)
                        5);
            }
            i__2 = jj;
            ajj = ap[i__2].r;
            zdscal_(&j, &ajj, &ap[jc], &c__1);
/* L10: */
        }

    } else {

/*        Compute the product inv(L)**H * inv(L). */

        jj = 1;
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            jjn = jj + *n - j + 1;
            i__2 = jj;
            i__3 = *n - j + 1;
            zdotc_(&z__1, &i__3, &ap[jj], &c__1, &ap[jj], &c__1);
            d__1 = z__1.r;
            ap[i__2].r = d__1, ap[i__2].i = 0.;
            if (j < *n) {
                i__2 = *n - j;
                ztpmv_((char *)"Lower", (char *)"Conjugate transpose", (char *)"Non-unit", &i__2, &ap[
                        jjn], &ap[jj + 1], &c__1, (ftnlen)5, (ftnlen)19, (
                        ftnlen)8);
            }
            jj = jjn;
/* L20: */
        }
    }

    return 0;

/*     End of ZPPTRI */

} /* zpptri_ */

#ifdef __cplusplus
        }
#endif