/* static/dpotrf2.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_b9 = 1.;
static doublereal c_b11 = -1.;

/* > \brief \b DPOTRF2 */

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

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

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

/*       RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO ) */

/*       .. Scalar Arguments .. */
/*       CHARACTER          UPLO */
/*       INTEGER            INFO, LDA, N */
/*       .. */
/*       .. Array Arguments .. */
/*       REAL               A( LDA, * ) */
/*       .. */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DPOTRF2 computes the Cholesky factorization of a real symmetric */
/* > positive definite matrix A using the recursive algorithm. */
/* > */
/* > The factorization has the form */
/* >    A = U**T * U,  if UPLO = 'U', or */
/* >    A = L  * L**T,  if UPLO = 'L', */
/* > where U is an upper triangular matrix and L is lower triangular. */
/* > */
/* > This is the recursive version of the algorithm. It divides */
/* > the matrix into four submatrices: */
/* > */
/* >        [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2 */
/* >    A = [ -----|----- ]  with n1 = n/2 */
/* >        [  A21 | A22  ]       n2 = n-n1 */
/* > */
/* > The subroutine calls itself to factor A11. Update and scale A21 */
/* > or A12, update A22 then calls itself to factor A22. */
/* > */
/* > \endverbatim */

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

/* > \param[in] UPLO */
/* > \verbatim */
/* >          UPLO is CHARACTER*1 */
/* >          = 'U':  Upper triangle of A is stored; */
/* >          = 'L':  Lower triangle of A is stored. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix A.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is DOUBLE PRECISION array, dimension (LDA,N) */
/* >          On entry, the symmetric matrix A.  If UPLO = 'U', the leading */
/* >          N-by-N upper triangular part of A contains the upper */
/* >          triangular part of the matrix A, and the strictly lower */
/* >          triangular part of A is not referenced.  If UPLO = 'L', the */
/* >          leading N-by-N lower triangular part of A contains the lower */
/* >          triangular part of the matrix A, and the strictly upper */
/* >          triangular part of A is not referenced. */
/* > */
/* >          On exit, if INFO = 0, the factor U or L from the Cholesky */
/* >          factorization A = U**T*U or A = L*L**T. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= max(1,N). */
/* > \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 leading minor of order i is not */
/* >                positive definite, and the factorization could not be */
/* >                completed. */
/* > \endverbatim */

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

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

/* > \ingroup doublePOcomputational */

/*  ===================================================================== */
/* Subroutine */ int dpotrf2_(char *uplo, integer *n, doublereal *a, integer *
        lda, integer *info, ftnlen uplo_len)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    integer n1, n2;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    integer iinfo;
    extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *,
            integer *, integer *, doublereal *, doublereal *, integer *,
            doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen);
    logical upper;
    extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *,
            doublereal *, doublereal *, integer *, doublereal *, doublereal *,
             integer *, ftnlen, ftnlen);
    extern logical disnan_(doublereal *);
    extern /* Subroutine */ int xerbla_(char *, integer *, 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 */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;

    /* 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;
    } else if (*lda < max(1,*n)) {
        *info = -4;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_((char *)"DPOTRF2", &i__1, (ftnlen)7);
        return 0;
    }

/*     Quick return if possible */

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

/*     N=1 case */

    if (*n == 1) {

/*        Test for non-positive-definiteness */

        if (a[a_dim1 + 1] <= 0. || disnan_(&a[a_dim1 + 1])) {
            *info = 1;
            return 0;
        }

/*        Factor */

        a[a_dim1 + 1] = sqrt(a[a_dim1 + 1]);

/*     Use recursive code */

    } else {
        n1 = *n / 2;
        n2 = *n - n1;

/*        Factor A11 */

        dpotrf2_(uplo, &n1, &a[a_dim1 + 1], lda, &iinfo, (ftnlen)1);
        if (iinfo != 0) {
            *info = iinfo;
            return 0;
        }

/*        Compute the Cholesky factorization A = U**T*U */

        if (upper) {

/*           Update and scale A12 */

            dtrsm_((char *)"L", (char *)"U", (char *)"T", (char *)"N", &n1, &n2, &c_b9, &a[a_dim1 + 1], lda, &
                    a[(n1 + 1) * a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, (
                    ftnlen)1, (ftnlen)1);

/*           Update and factor A22 */

            dsyrk_(uplo, (char *)"T", &n2, &n1, &c_b11, &a[(n1 + 1) * a_dim1 + 1],
                    lda, &c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen)
                    1, (ftnlen)1);
            dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, (
                    ftnlen)1);
            if (iinfo != 0) {
                *info = iinfo + n1;
                return 0;
            }

/*        Compute the Cholesky factorization A = L*L**T */

        } else {

/*           Update and scale A21 */

            dtrsm_((char *)"R", (char *)"L", (char *)"T", (char *)"N", &n2, &n1, &c_b9, &a[a_dim1 + 1], lda, &
                    a[n1 + 1 + a_dim1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1,
                    (ftnlen)1);

/*           Update and factor A22 */

            dsyrk_(uplo, (char *)"N", &n2, &n1, &c_b11, &a[n1 + 1 + a_dim1], lda, &
                    c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen)1, (
                    ftnlen)1);
            dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, (
                    ftnlen)1);
            if (iinfo != 0) {
                *info = iinfo + n1;
                return 0;
            }
        }
    }
    return 0;

/*     End of DPOTRF2 */

} /* dpotrf2_ */

#ifdef __cplusplus
        }
#endif