spbtrf.c

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/* spbtrf.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 integer c__1 = 1;
static integer c_n1 = -1;
static real c_b18 = 1.f;
static real c_b21 = -1.f;
static integer c__33 = 33;

/* Subroutine */ int spbtrf_(char *uplo, integer *n, integer *kd, real *ab, 
        integer *ldab, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;

    /* Local variables */
    integer i__, j, i2, i3, ib, nb, ii, jj;
    real work[1056]     /* was [33][32] */;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
            integer *, real *, real *, integer *, real *, integer *, real *, 
            real *, integer *), strsm_(char *, char *, char *, 
             char *, integer *, integer *, real *, real *, integer *, real *, 
            integer *), ssyrk_(char *, char *, 
             integer *, integer *, real *, real *, integer *, real *, real *, 
            integer *), spbtf2_(char *, integer *, integer *, 
            real *, integer *, integer *), spotf2_(char *, integer *, 
            real *, 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 */
/*  ======= */

/*  SPBTRF computes the Cholesky factorization of a real symmetric */
/*  positive definite band matrix A. */

/*  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. */

/*  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. */

/*  KD      (input) INTEGER */
/*          The number of superdiagonals of the matrix A if UPLO = 'U', */
/*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0. */

/*  AB      (input/output) REAL array, dimension (LDAB,N) */
/*          On entry, the upper or lower triangle of the symmetric band */
/*          matrix A, stored in the first KD+1 rows of the array.  The */
/*          j-th column of A is stored in the j-th column of the array AB */
/*          as follows: */
/*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd). */

/*          On exit, if INFO = 0, the triangular factor U or L from the */
/*          Cholesky factorization A = U**T*U or A = L*L**T of the band */
/*          matrix A, in the same storage format as A. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= KD+1. */

/*  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. */

/*  Further Details */
/*  =============== */

/*  The band storage scheme is illustrated by the following example, when */
/*  N = 6, KD = 2, and UPLO = 'U': */

/*  On entry:                       On exit: */

/*      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46 */
/*      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56 */
/*     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66 */

/*  Similarly, if UPLO = 'L' the format of A is as follows: */

/*  On entry:                       On exit: */

/*     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66 */
/*     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   * */
/*     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    * */

/*  Array elements marked * are not used by the routine. */

/*  Contributed by */
/*  Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989 */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;

    /* Function Body */
    *info = 0;
    if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*kd < 0) {
        *info = -3;
    } else if (*ldab < *kd + 1) {
        *info = -5;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("SPBTRF", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

/*     Determine the block size for this environment */

    nb = ilaenv_(&c__1, "SPBTRF", uplo, n, kd, &c_n1, &c_n1);

/*     The block size must not exceed the semi-bandwidth KD, and must not */
/*     exceed the limit set by the size of the local array WORK. */

    nb = min(nb,32);

    if (nb <= 1 || nb > *kd) {

/*        Use unblocked code */

        spbtf2_(uplo, n, kd, &ab[ab_offset], ldab, info);
    } else {

/*        Use blocked code */

        if (lsame_(uplo, "U")) {

/*           Compute the Cholesky factorization of a symmetric band */
/*           matrix, given the upper triangle of the matrix in band */
/*           storage. */

/*           Zero the upper triangle of the work array. */

            i__1 = nb;
            for (j = 1; j <= i__1; ++j) {
                i__2 = j - 1;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    work[i__ + j * 33 - 34] = 0.f;
/* L10: */
                }
/* L20: */
            }

/*           Process the band matrix one diagonal block at a time. */

            i__1 = *n;
            i__2 = nb;
            for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
                i__3 = nb, i__4 = *n - i__ + 1;
                ib = min(i__3,i__4);

/*              Factorize the diagonal block */

                i__3 = *ldab - 1;
                spotf2_(uplo, &ib, &ab[*kd + 1 + i__ * ab_dim1], &i__3, &ii);
                if (ii != 0) {
                    *info = i__ + ii - 1;
                    goto L150;
                }
                if (i__ + ib <= *n) {

/*                 Update the relevant part of the trailing submatrix. */
/*                 If A11 denotes the diagonal block which has just been */
/*                 factorized, then we need to update the remaining */
/*                 blocks in the diagram: */

/*                    A11   A12   A13 */
/*                          A22   A23 */
/*                                A33 */

/*                 The numbers of rows and columns in the partitioning */
/*                 are IB, I2, I3 respectively. The blocks A12, A22 and */
/*                 A23 are empty if IB = KD. The upper triangle of A13 */
/*                 lies outside the band. */

/* Computing MIN */
                    i__3 = *kd - ib, i__4 = *n - i__ - ib + 1;
                    i2 = min(i__3,i__4);
/* Computing MIN */
                    i__3 = ib, i__4 = *n - i__ - *kd + 1;
                    i3 = min(i__3,i__4);

                    if (i2 > 0) {

/*                    Update A12 */

                        i__3 = *ldab - 1;
                        i__4 = *ldab - 1;
                        strsm_("Left", "Upper", "Transpose", "Non-unit", &ib, 
                                &i2, &c_b18, &ab[*kd + 1 + i__ * ab_dim1], &
                                i__3, &ab[*kd + 1 - ib + (i__ + ib) * ab_dim1]
, &i__4);

/*                    Update A22 */

                        i__3 = *ldab - 1;
                        i__4 = *ldab - 1;
                        ssyrk_("Upper", "Transpose", &i2, &ib, &c_b21, &ab[*
                                kd + 1 - ib + (i__ + ib) * ab_dim1], &i__3, &
                                c_b18, &ab[*kd + 1 + (i__ + ib) * ab_dim1], &
                                i__4);
                    }

                    if (i3 > 0) {

/*                    Copy the lower triangle of A13 into the work array. */

                        i__3 = i3;
                        for (jj = 1; jj <= i__3; ++jj) {
                            i__4 = ib;
                            for (ii = jj; ii <= i__4; ++ii) {
                                work[ii + jj * 33 - 34] = ab[ii - jj + 1 + (
                                        jj + i__ + *kd - 1) * ab_dim1];
/* L30: */
                            }
/* L40: */
                        }

/*                    Update A13 (in the work array). */

                        i__3 = *ldab - 1;
                        strsm_("Left", "Upper", "Transpose", "Non-unit", &ib, 
                                &i3, &c_b18, &ab[*kd + 1 + i__ * ab_dim1], &
                                i__3, work, &c__33);

/*                    Update A23 */

                        if (i2 > 0) {
                            i__3 = *ldab - 1;
                            i__4 = *ldab - 1;
                            sgemm_("Transpose", "No Transpose", &i2, &i3, &ib, 
                                     &c_b21, &ab[*kd + 1 - ib + (i__ + ib) * 
                                    ab_dim1], &i__3, work, &c__33, &c_b18, &
                                    ab[ib + 1 + (i__ + *kd) * ab_dim1], &i__4);
                        }

/*                    Update A33 */

                        i__3 = *ldab - 1;
                        ssyrk_("Upper", "Transpose", &i3, &ib, &c_b21, work, &
                                c__33, &c_b18, &ab[*kd + 1 + (i__ + *kd) * 
                                ab_dim1], &i__3);

/*                    Copy the lower triangle of A13 back into place. */

                        i__3 = i3;
                        for (jj = 1; jj <= i__3; ++jj) {
                            i__4 = ib;
                            for (ii = jj; ii <= i__4; ++ii) {
                                ab[ii - jj + 1 + (jj + i__ + *kd - 1) * 
                                        ab_dim1] = work[ii + jj * 33 - 34];
/* L50: */
                            }
/* L60: */
                        }
                    }
                }
/* L70: */
            }
        } else {

/*           Compute the Cholesky factorization of a symmetric band */
/*           matrix, given the lower triangle of the matrix in band */
/*           storage. */

/*           Zero the lower triangle of the work array. */

            i__2 = nb;
            for (j = 1; j <= i__2; ++j) {
                i__1 = nb;
                for (i__ = j + 1; i__ <= i__1; ++i__) {
                    work[i__ + j * 33 - 34] = 0.f;
/* L80: */
                }
/* L90: */
            }

/*           Process the band matrix one diagonal block at a time. */

            i__2 = *n;
            i__1 = nb;
            for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
/* Computing MIN */
                i__3 = nb, i__4 = *n - i__ + 1;
                ib = min(i__3,i__4);

/*              Factorize the diagonal block */

                i__3 = *ldab - 1;
                spotf2_(uplo, &ib, &ab[i__ * ab_dim1 + 1], &i__3, &ii);
                if (ii != 0) {
                    *info = i__ + ii - 1;
                    goto L150;
                }
                if (i__ + ib <= *n) {

/*                 Update the relevant part of the trailing submatrix. */
/*                 If A11 denotes the diagonal block which has just been */
/*                 factorized, then we need to update the remaining */
/*                 blocks in the diagram: */

/*                    A11 */
/*                    A21   A22 */
/*                    A31   A32   A33 */

/*                 The numbers of rows and columns in the partitioning */
/*                 are IB, I2, I3 respectively. The blocks A21, A22 and */
/*                 A32 are empty if IB = KD. The lower triangle of A31 */
/*                 lies outside the band. */

/* Computing MIN */
                    i__3 = *kd - ib, i__4 = *n - i__ - ib + 1;
                    i2 = min(i__3,i__4);
/* Computing MIN */
                    i__3 = ib, i__4 = *n - i__ - *kd + 1;
                    i3 = min(i__3,i__4);

                    if (i2 > 0) {

/*                    Update A21 */

                        i__3 = *ldab - 1;
                        i__4 = *ldab - 1;
                        strsm_("Right", "Lower", "Transpose", "Non-unit", &i2, 
                                 &ib, &c_b18, &ab[i__ * ab_dim1 + 1], &i__3, &
                                ab[ib + 1 + i__ * ab_dim1], &i__4);

/*                    Update A22 */

                        i__3 = *ldab - 1;
                        i__4 = *ldab - 1;
                        ssyrk_("Lower", "No Transpose", &i2, &ib, &c_b21, &ab[
                                ib + 1 + i__ * ab_dim1], &i__3, &c_b18, &ab[(
                                i__ + ib) * ab_dim1 + 1], &i__4);
                    }

                    if (i3 > 0) {

/*                    Copy the upper triangle of A31 into the work array. */

                        i__3 = ib;
                        for (jj = 1; jj <= i__3; ++jj) {
                            i__4 = min(jj,i3);
                            for (ii = 1; ii <= i__4; ++ii) {
                                work[ii + jj * 33 - 34] = ab[*kd + 1 - jj + 
                                        ii + (jj + i__ - 1) * ab_dim1];
/* L100: */
                            }
/* L110: */
                        }

/*                    Update A31 (in the work array). */

                        i__3 = *ldab - 1;
                        strsm_("Right", "Lower", "Transpose", "Non-unit", &i3, 
                                 &ib, &c_b18, &ab[i__ * ab_dim1 + 1], &i__3, 
                                work, &c__33);

/*                    Update A32 */

                        if (i2 > 0) {
                            i__3 = *ldab - 1;
                            i__4 = *ldab - 1;
                            sgemm_("No transpose", "Transpose", &i3, &i2, &ib, 
                                     &c_b21, work, &c__33, &ab[ib + 1 + i__ * 
                                    ab_dim1], &i__3, &c_b18, &ab[*kd + 1 - ib 
                                    + (i__ + ib) * ab_dim1], &i__4);
                        }

/*                    Update A33 */

                        i__3 = *ldab - 1;
                        ssyrk_("Lower", "No Transpose", &i3, &ib, &c_b21, 
                                work, &c__33, &c_b18, &ab[(i__ + *kd) * 
                                ab_dim1 + 1], &i__3);

/*                    Copy the upper triangle of A31 back into place. */

                        i__3 = ib;
                        for (jj = 1; jj <= i__3; ++jj) {
                            i__4 = min(jj,i3);
                            for (ii = 1; ii <= i__4; ++ii) {
                                ab[*kd + 1 - jj + ii + (jj + i__ - 1) * 
                                        ab_dim1] = work[ii + jj * 33 - 34];
/* L120: */
                            }
/* L130: */
                        }
                    }
                }
/* L140: */
            }
        }
    }
    return 0;

L150:
    return 0;

/*     End of SPBTRF */

} /* spbtrf_ */