/* ../netlib/v3.9.0/spotrf2.f -- translated by f2c (version 20160102). 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 "FLA_f2c.h" /* Table of constant values */
 static real c_b9 = 1.f;
 static real c_b11 = -1.f;
 /* > \brief \b SPOTRF2 */
 /* =========== DOCUMENTATION =========== */
 /* Online html documentation available at */
 /* http://www.netlib.org/lapack/explore-html/ */
 /* Definition: */
 /* =========== */
 /* SUBROUTINE SPOTRF2( UPLO, N, A, LDA, INFO ) */
 /* .. Scalar Arguments .. */
 /* CHARACTER UPLO */
 /* INTEGER INFO, LDA, N */
 /* .. */
 /* .. Array Arguments .. */
 /* REAL A( LDA, * ) */
 /* .. */
 /* > \par Purpose: */
 /* ============= */
 /* > */
 /* > \verbatim */
 /* > */
 /* > SPOTRF2 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 call 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 REAL 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. */
 /* > \date November 2017 */
 /* > \ingroup realPOcomputational */
 /* ===================================================================== */
 /* Subroutine */
 int spotrf2_(char *uplo, integer *n, real *a, integer *lda, integer *info) {
 AOCL_DTL_TRACE_ENTRY(AOCL_DTL_LEVEL_TRACE_5);
 /* 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 *);
 integer iinfo;
 logical upper;
 extern /* Subroutine */
 int strsm_(char *, char *, char *, char *, integer *, integer *, real *, real *, integer *, real *, integer * ), ssyrk_(char *, char *, integer *, integer *, real *, real *, integer *, real *, real *, integer * ), xerbla_(char *, integer *);
 extern logical sisnan_(real *);
 /* -- LAPACK computational routine (version 3.8.0) -- */
 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
 /* November 2017 */
 /* .. 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, "U");
 if (! upper && ! lsame_(uplo, "L")) {
 *info = -1;
 }
 else if (*n < 0) {
 *info = -2;
 }
 else if (*lda < max(1,*n)) {
 *info = -4;
 }
 if (*info != 0) {
 i__1 = -(*info);
 xerbla_("SPOTRF2", &i__1);
 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.f || sisnan_(&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 */
 spotrf2_(uplo, &n1, &a[a_dim1 + 1], lda, &iinfo);
 if (iinfo != 0) {
 *info = iinfo;
 return 0;
 }
 /* Compute the Cholesky factorization A = U**T*U */
 if (upper) {
 /* Update and scale A12 */
 strsm_("L", "U", "T", "N", &n1, &n2, &c_b9, &a[a_dim1 + 1], lda, & a[(n1 + 1) * a_dim1 + 1], lda);
 /* Update and factor A22 */
 ssyrk_(uplo, "T", &n2, &n1, &c_b11, &a[(n1 + 1) * a_dim1 + 1], lda, &c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda);
 spotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo);
 if (iinfo != 0) {
 *info = iinfo + n1;
 return 0;
 }
 /* Compute the Cholesky factorization A = L*L**T */
 }
 else {
 /* Update and scale A21 */
 strsm_("R", "L", "T", "N", &n2, &n1, &c_b9, &a[a_dim1 + 1], lda, & a[n1 + 1 + a_dim1], lda);
 /* Update and factor A22 */
 ssyrk_(uplo, "N", &n2, &n1, &c_b11, &a[n1 + 1 + a_dim1], lda, & c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda);
 spotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo);
 if (iinfo != 0) {
 *info = iinfo + n1;
 return 0;
 }
 }
 }
 AOCL_DTL_TRACE_EXIT(AOCL_DTL_LEVEL_TRACE_5);
 return 0;
 /* End of SPOTRF2 */
 }
 /* spotrf2_ */
 
