cpotrf.c

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/* cpotrf.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"

/* Table of constant values */

static complex c_b1 = {1.f,0.f};
static integer c__1 = 1;
static integer c_n1 = -1;
static real c_b14 = -1.f;
static real c_b15 = 1.f;

/* Subroutine */ int cpotrf_(char *uplo, integer *n, complex *a, integer *lda, 
         integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
    complex q__1;

    /* Local variables */
    integer j, jb, nb;
    extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, 
            integer *, complex *, complex *, integer *, complex *, integer *, 
            complex *, complex *, integer *), cherk_(char *, 
            char *, integer *, integer *, real *, complex *, integer *, real *
, complex *, integer *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 
            integer *, integer *, complex *, complex *, integer *, complex *, 
            integer *);
    logical upper;
    extern /* Subroutine */ int cpotf2_(char *, integer *, complex *, integer 
            *, integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  CPOTRF computes the Cholesky factorization of a complex Hermitian */
/*  positive definite matrix A. */

/*  The factorization has the form */
/*     A = U**H * U,  if UPLO = 'U', or */
/*     A = L  * L**H,  if UPLO = 'L', */
/*  where U is an upper triangular matrix and L is lower triangular. */

/*  This is the block version of the algorithm, calling Level 3 BLAS. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangle of A is stored; */
/*          = 'L':  Lower triangle of A is stored. */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  A       (input/output) COMPLEX array, dimension (LDA,N) */
/*          On entry, the Hermitian 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**H*U or A = L*L**H. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,N). */

/*  INFO    (output) 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. */

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

/*     .. 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_("CPOTRF", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

/*     Determine the block size for this environment. */

    nb = ilaenv_(&c__1, "CPOTRF", uplo, n, &c_n1, &c_n1, &c_n1);
    if (nb <= 1 || nb >= *n) {

/*        Use unblocked code. */

        cpotf2_(uplo, n, &a[a_offset], lda, info);
    } else {

/*        Use blocked code. */

        if (upper) {

/*           Compute the Cholesky factorization A = U'*U. */

            i__1 = *n;
            i__2 = nb;
            for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {

/*              Update and factorize the current diagonal block and test */
/*              for non-positive-definiteness. */

/* Computing MIN */
                i__3 = nb, i__4 = *n - j + 1;
                jb = min(i__3,i__4);
                i__3 = j - 1;
                cherk_("Upper", "Conjugate transpose", &jb, &i__3, &c_b14, &a[
                        j * a_dim1 + 1], lda, &c_b15, &a[j + j * a_dim1], lda);
                cpotf2_("Upper", &jb, &a[j + j * a_dim1], lda, info);
                if (*info != 0) {
                    goto L30;
                }
                if (j + jb <= *n) {

/*                 Compute the current block row. */

                    i__3 = *n - j - jb + 1;
                    i__4 = j - 1;
                    q__1.r = -1.f, q__1.i = -0.f;
                    cgemm_("Conjugate transpose", "No transpose", &jb, &i__3, 
                            &i__4, &q__1, &a[j * a_dim1 + 1], lda, &a[(j + jb)
                             * a_dim1 + 1], lda, &c_b1, &a[j + (j + jb) * 
                            a_dim1], lda);
                    i__3 = *n - j - jb + 1;
                    ctrsm_("Left", "Upper", "Conjugate transpose", "Non-unit", 
                             &jb, &i__3, &c_b1, &a[j + j * a_dim1], lda, &a[j 
                            + (j + jb) * a_dim1], lda);
                }
/* L10: */
            }

        } else {

/*           Compute the Cholesky factorization A = L*L'. */

            i__2 = *n;
            i__1 = nb;
            for (j = 1; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {

/*              Update and factorize the current diagonal block and test */
/*              for non-positive-definiteness. */

/* Computing MIN */
                i__3 = nb, i__4 = *n - j + 1;
                jb = min(i__3,i__4);
                i__3 = j - 1;
                cherk_("Lower", "No transpose", &jb, &i__3, &c_b14, &a[j + 
                        a_dim1], lda, &c_b15, &a[j + j * a_dim1], lda);
                cpotf2_("Lower", &jb, &a[j + j * a_dim1], lda, info);
                if (*info != 0) {
                    goto L30;
                }
                if (j + jb <= *n) {

/*                 Compute the current block column. */

                    i__3 = *n - j - jb + 1;
                    i__4 = j - 1;
                    q__1.r = -1.f, q__1.i = -0.f;
                    cgemm_("No transpose", "Conjugate transpose", &i__3, &jb, 
                            &i__4, &q__1, &a[j + jb + a_dim1], lda, &a[j + 
                            a_dim1], lda, &c_b1, &a[j + jb + j * a_dim1], lda);
                    i__3 = *n - j - jb + 1;
                    ctrsm_("Right", "Lower", "Conjugate transpose", "Non-unit"
, &i__3, &jb, &c_b1, &a[j + j * a_dim1], lda, &a[
                            j + jb + j * a_dim1], lda);
                }
/* L20: */
            }
        }
    }
    goto L40;

L30:
    *info = *info + j - 1;

L40:
    return 0;

/*     End of CPOTRF */

} /* cpotrf_ */