cpstf2.c

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/* cpstf2.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;

/* Subroutine */ int cpstf2_(char *uplo, integer *n, complex *a, integer *lda, 
         integer *piv, integer *rank, real *tol, real *work, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    real r__1;
    complex q__1, q__2;

    /* Builtin functions */
    void r_cnjg(complex *, complex *);
    double sqrt(doublereal);

    /* Local variables */
    integer i__, j, maxlocval;
    real ajj;
    integer pvt;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *);
    complex ctemp;
    extern /* Subroutine */ int cswap_(integer *, complex *, integer *, 
            complex *, integer *);
    integer itemp;
    real stemp;
    logical upper;
    real sstop;
    extern /* Subroutine */ int clacgv_(integer *, complex *, integer *);
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer 
            *), xerbla_(char *, integer *);
    extern logical sisnan_(real *);
    extern integer smaxloc_(real *, integer *);


/*  -- LAPACK PROTOTYPE routine (version 3.2) -- */
/*     Craig Lucas, University of Manchester / NAG Ltd. */
/*     October, 2008 */

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

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

/*  CPSTF2 computes the Cholesky factorization with complete */
/*  pivoting of a complex Hermitian positive semidefinite matrix A. */

/*  The factorization has the form */
/*     P' * A * P = U' * U ,  if UPLO = 'U', */
/*     P' * A * P = L  * L',  if UPLO = 'L', */
/*  where U is an upper triangular matrix and L is lower triangular, and */
/*  P is stored as vector PIV. */

/*  This algorithm does not attempt to check that A is positive */
/*  semidefinite. This version of the algorithm calls level 2 BLAS. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the upper or lower triangular part of the */
/*          symmetric matrix A is stored. */
/*          = 'U':  Upper triangular */
/*          = 'L':  Lower triangular */

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

/*  A       (input/output) COMPLEX 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 as above. */

/*  PIV     (output) INTEGER array, dimension (N) */
/*          PIV is such that the nonzero entries are P( PIV(K), K ) = 1. */

/*  RANK    (output) INTEGER */
/*          The rank of A given by the number of steps the algorithm */
/*          completed. */

/*  TOL     (input) REAL */
/*          User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) ) */
/*          will be used. The algorithm terminates at the (K-1)st step */
/*          if the pivot <= TOL. */

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

/*  WORK    REAL array, dimension (2*N) */
/*          Work space. */

/*  INFO    (output) INTEGER */
/*          < 0: If INFO = -K, the K-th argument had an illegal value, */
/*          = 0: algorithm completed successfully, and */
/*          > 0: the matrix A is either rank deficient with computed rank */
/*               as returned in RANK, or is indefinite.  See Section 7 of */
/*               LAPACK Working Note #161 for further information. */

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

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

/*     Test the input parameters */

    /* Parameter adjustments */
    --work;
    --piv;
    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_("CPSTF2", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

/*     Initialize PIV */

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        piv[i__] = i__;
/* L100: */
    }

/*     Compute stopping value */

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        i__2 = i__ + i__ * a_dim1;
        work[i__] = a[i__2].r;
/* L110: */
    }
    pvt = smaxloc_(&work[1], n);
    i__1 = pvt + pvt * a_dim1;
    ajj = a[i__1].r;
    if (ajj == 0.f || sisnan_(&ajj)) {
        *rank = 0;
        *info = 1;
        goto L200;
    }

/*     Compute stopping value if not supplied */

    if (*tol < 0.f) {
        sstop = *n * slamch_("Epsilon") * ajj;
    } else {
        sstop = *tol;
    }

/*     Set first half of WORK to zero, holds dot products */

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        work[i__] = 0.f;
/* L120: */
    }

    if (upper) {

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

        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {

/*        Find pivot, test for exit, else swap rows and columns */
/*        Update dot products, compute possible pivots which are */
/*        stored in the second half of WORK */

            i__2 = *n;
            for (i__ = j; i__ <= i__2; ++i__) {

                if (j > 1) {
                    r_cnjg(&q__2, &a[j - 1 + i__ * a_dim1]);
                    i__3 = j - 1 + i__ * a_dim1;
                    q__1.r = q__2.r * a[i__3].r - q__2.i * a[i__3].i, q__1.i =
                             q__2.r * a[i__3].i + q__2.i * a[i__3].r;
                    work[i__] += q__1.r;
                }
                i__3 = i__ + i__ * a_dim1;
                work[*n + i__] = a[i__3].r - work[i__];

/* L130: */
            }

            if (j > 1) {
                maxlocval = (*n << 1) - (*n + j) + 1;
                itemp = smaxloc_(&work[*n + j], &maxlocval);
                pvt = itemp + j - 1;
                ajj = work[*n + pvt];
                if (ajj <= sstop || sisnan_(&ajj)) {
                    i__2 = j + j * a_dim1;
                    a[i__2].r = ajj, a[i__2].i = 0.f;
                    goto L190;
                }
            }

            if (j != pvt) {

/*              Pivot OK, so can now swap pivot rows and columns */

                i__2 = pvt + pvt * a_dim1;
                i__3 = j + j * a_dim1;
                a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i;
                i__2 = j - 1;
                cswap_(&i__2, &a[j * a_dim1 + 1], &c__1, &a[pvt * a_dim1 + 1], 
                         &c__1);
                if (pvt < *n) {
                    i__2 = *n - pvt;
                    cswap_(&i__2, &a[j + (pvt + 1) * a_dim1], lda, &a[pvt + (
                            pvt + 1) * a_dim1], lda);
                }
                i__2 = pvt - 1;
                for (i__ = j + 1; i__ <= i__2; ++i__) {
                    r_cnjg(&q__1, &a[j + i__ * a_dim1]);
                    ctemp.r = q__1.r, ctemp.i = q__1.i;
                    i__3 = j + i__ * a_dim1;
                    r_cnjg(&q__1, &a[i__ + pvt * a_dim1]);
                    a[i__3].r = q__1.r, a[i__3].i = q__1.i;
                    i__3 = i__ + pvt * a_dim1;
                    a[i__3].r = ctemp.r, a[i__3].i = ctemp.i;
/* L140: */
                }
                i__2 = j + pvt * a_dim1;
                r_cnjg(&q__1, &a[j + pvt * a_dim1]);
                a[i__2].r = q__1.r, a[i__2].i = q__1.i;

/*              Swap dot products and PIV */

                stemp = work[j];
                work[j] = work[pvt];
                work[pvt] = stemp;
                itemp = piv[pvt];
                piv[pvt] = piv[j];
                piv[j] = itemp;
            }

            ajj = sqrt(ajj);
            i__2 = j + j * a_dim1;
            a[i__2].r = ajj, a[i__2].i = 0.f;

/*           Compute elements J+1:N of row J */

            if (j < *n) {
                i__2 = j - 1;
                clacgv_(&i__2, &a[j * a_dim1 + 1], &c__1);
                i__2 = j - 1;
                i__3 = *n - j;
                q__1.r = -1.f, q__1.i = -0.f;
                cgemv_("Trans", &i__2, &i__3, &q__1, &a[(j + 1) * a_dim1 + 1], 
                         lda, &a[j * a_dim1 + 1], &c__1, &c_b1, &a[j + (j + 1)
                         * a_dim1], lda);
                i__2 = j - 1;
                clacgv_(&i__2, &a[j * a_dim1 + 1], &c__1);
                i__2 = *n - j;
                r__1 = 1.f / ajj;
                csscal_(&i__2, &r__1, &a[j + (j + 1) * a_dim1], lda);
            }

/* L150: */
        }

    } else {

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

        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {

/*        Find pivot, test for exit, else swap rows and columns */
/*        Update dot products, compute possible pivots which are */
/*        stored in the second half of WORK */

            i__2 = *n;
            for (i__ = j; i__ <= i__2; ++i__) {

                if (j > 1) {
                    r_cnjg(&q__2, &a[i__ + (j - 1) * a_dim1]);
                    i__3 = i__ + (j - 1) * a_dim1;
                    q__1.r = q__2.r * a[i__3].r - q__2.i * a[i__3].i, q__1.i =
                             q__2.r * a[i__3].i + q__2.i * a[i__3].r;
                    work[i__] += q__1.r;
                }
                i__3 = i__ + i__ * a_dim1;
                work[*n + i__] = a[i__3].r - work[i__];

/* L160: */
            }

            if (j > 1) {
                maxlocval = (*n << 1) - (*n + j) + 1;
                itemp = smaxloc_(&work[*n + j], &maxlocval);
                pvt = itemp + j - 1;
                ajj = work[*n + pvt];
                if (ajj <= sstop || sisnan_(&ajj)) {
                    i__2 = j + j * a_dim1;
                    a[i__2].r = ajj, a[i__2].i = 0.f;
                    goto L190;
                }
            }

            if (j != pvt) {

/*              Pivot OK, so can now swap pivot rows and columns */

                i__2 = pvt + pvt * a_dim1;
                i__3 = j + j * a_dim1;
                a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i;
                i__2 = j - 1;
                cswap_(&i__2, &a[j + a_dim1], lda, &a[pvt + a_dim1], lda);
                if (pvt < *n) {
                    i__2 = *n - pvt;
                    cswap_(&i__2, &a[pvt + 1 + j * a_dim1], &c__1, &a[pvt + 1 
                            + pvt * a_dim1], &c__1);
                }
                i__2 = pvt - 1;
                for (i__ = j + 1; i__ <= i__2; ++i__) {
                    r_cnjg(&q__1, &a[i__ + j * a_dim1]);
                    ctemp.r = q__1.r, ctemp.i = q__1.i;
                    i__3 = i__ + j * a_dim1;
                    r_cnjg(&q__1, &a[pvt + i__ * a_dim1]);
                    a[i__3].r = q__1.r, a[i__3].i = q__1.i;
                    i__3 = pvt + i__ * a_dim1;
                    a[i__3].r = ctemp.r, a[i__3].i = ctemp.i;
/* L170: */
                }
                i__2 = pvt + j * a_dim1;
                r_cnjg(&q__1, &a[pvt + j * a_dim1]);
                a[i__2].r = q__1.r, a[i__2].i = q__1.i;

/*              Swap dot products and PIV */

                stemp = work[j];
                work[j] = work[pvt];
                work[pvt] = stemp;
                itemp = piv[pvt];
                piv[pvt] = piv[j];
                piv[j] = itemp;
            }

            ajj = sqrt(ajj);
            i__2 = j + j * a_dim1;
            a[i__2].r = ajj, a[i__2].i = 0.f;

/*           Compute elements J+1:N of column J */

            if (j < *n) {
                i__2 = j - 1;
                clacgv_(&i__2, &a[j + a_dim1], lda);
                i__2 = *n - j;
                i__3 = j - 1;
                q__1.r = -1.f, q__1.i = -0.f;
                cgemv_("No Trans", &i__2, &i__3, &q__1, &a[j + 1 + a_dim1], 
                        lda, &a[j + a_dim1], lda, &c_b1, &a[j + 1 + j * 
                        a_dim1], &c__1);
                i__2 = j - 1;
                clacgv_(&i__2, &a[j + a_dim1], lda);
                i__2 = *n - j;
                r__1 = 1.f / ajj;
                csscal_(&i__2, &r__1, &a[j + 1 + j * a_dim1], &c__1);
            }

/* L180: */
        }

    }

/*     Ran to completion, A has full rank */

    *rank = *n;

    goto L200;
L190:

/*     Rank is number of steps completed.  Set INFO = 1 to signal */
/*     that the factorization cannot be used to solve a system. */

    *rank = j - 1;
    *info = 1;

L200:
    return 0;

/*     End of CPSTF2 */

} /* cpstf2_ */