sgbtrf.c

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/* sgbtrf.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__65 = 65;
static real c_b18 = -1.f;
static real c_b31 = 1.f;

/* Subroutine */ int sgbtrf_(integer *m, integer *n, integer *kl, integer *ku, 
         real *ab, integer *ldab, integer *ipiv, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5, i__6;
    real r__1;

    /* Local variables */
    integer i__, j, i2, i3, j2, j3, k2, jb, nb, ii, jj, jm, ip, jp, km, ju, 
            kv, nw;
    extern /* Subroutine */ int sger_(integer *, integer *, real *, real *, 
            integer *, real *, integer *, real *, integer *);
    real temp;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *), 
            sgemm_(char *, char *, integer *, integer *, integer *, real *, 
            real *, integer *, real *, integer *, real *, real *, integer *);
    real work13[4160]   /* was [65][64] */, work31[4160]        /* was [65][
            64] */;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
            integer *), sswap_(integer *, real *, integer *, real *, integer *
), strsm_(char *, char *, char *, char *, integer *, integer *, 
            real *, real *, integer *, real *, integer *), sgbtf2_(integer *, integer *, integer *, integer 
            *, real *, integer *, integer *, integer *), xerbla_(char *, 
            integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *), isamax_(integer *, real *, 
            integer *);
    extern /* Subroutine */ int slaswp_(integer *, real *, integer *, 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 */
/*  ======= */

/*  SGBTRF computes an LU factorization of a real m-by-n band matrix A */
/*  using partial pivoting with row interchanges. */

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

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

/*  M       (input) INTEGER */
/*          The number of rows of the matrix A.  M >= 0. */

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

/*  KL      (input) INTEGER */
/*          The number of subdiagonals within the band of A.  KL >= 0. */

/*  KU      (input) INTEGER */
/*          The number of superdiagonals within the band of A.  KU >= 0. */

/*  AB      (input/output) REAL array, dimension (LDAB,N) */
/*          On entry, the matrix A in band storage, in rows KL+1 to */
/*          2*KL+KU+1; rows 1 to KL of the array need not be set. */
/*          The j-th column of A is stored in the j-th column of the */
/*          array AB as follows: */
/*          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) */

/*          On exit, details of the factorization: U is stored as an */
/*          upper triangular band matrix with KL+KU superdiagonals in */
/*          rows 1 to KL+KU+1, and the multipliers used during the */
/*          factorization are stored in rows KL+KU+2 to 2*KL+KU+1. */
/*          See below for further details. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1. */

/*  IPIV    (output) INTEGER array, dimension (min(M,N)) */
/*          The pivot indices; for 1 <= i <= min(M,N), row i of the */
/*          matrix was interchanged with row IPIV(i). */

/*  INFO    (output) INTEGER */
/*          = 0: successful exit */
/*          < 0: if INFO = -i, the i-th argument had an illegal value */
/*          > 0: if INFO = +i, U(i,i) is exactly zero. The factorization */
/*               has been completed, but the factor U is exactly */
/*               singular, and division by zero will occur if it is used */
/*               to solve a system of equations. */

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

/*  The band storage scheme is illustrated by the following example, when */
/*  M = N = 6, KL = 2, KU = 1: */

/*  On entry:                       On exit: */

/*      *    *    *    +    +    +       *    *    *   u14  u25  u36 */
/*      *    *    +    +    +    +       *    *   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 */
/*     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   * */
/*     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    * */

/*  Array elements marked * are not used by the routine; elements marked */
/*  + need not be set on entry, but are required by the routine to store */
/*  elements of U because of fill-in resulting from the row interchanges. */

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

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

/*     KV is the number of superdiagonals in the factor U, allowing for */
/*     fill-in */

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

    /* Function Body */
    kv = *ku + *kl;

/*     Test the input parameters. */

    *info = 0;
    if (*m < 0) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*kl < 0) {
        *info = -3;
    } else if (*ku < 0) {
        *info = -4;
    } else if (*ldab < *kl + kv + 1) {
        *info = -6;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("SGBTRF", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

/*     Determine the block size for this environment */

    nb = ilaenv_(&c__1, "SGBTRF", " ", m, n, kl, ku);

/*     The block size must not exceed the limit set by the size of the */
/*     local arrays WORK13 and WORK31. */

    nb = min(nb,64);

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

/*        Use unblocked code */

        sgbtf2_(m, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info);
    } else {

/*        Use blocked code */

/*        Zero the superdiagonal elements of the work array WORK13 */

        i__1 = nb;
        for (j = 1; j <= i__1; ++j) {
            i__2 = j - 1;
            for (i__ = 1; i__ <= i__2; ++i__) {
                work13[i__ + j * 65 - 66] = 0.f;
/* L10: */
            }
/* L20: */
        }

/*        Zero the subdiagonal elements of the work array WORK31 */

        i__1 = nb;
        for (j = 1; j <= i__1; ++j) {
            i__2 = nb;
            for (i__ = j + 1; i__ <= i__2; ++i__) {
                work31[i__ + j * 65 - 66] = 0.f;
/* L30: */
            }
/* L40: */
        }

/*        Gaussian elimination with partial pivoting */

/*        Set fill-in elements in columns KU+2 to KV to zero */

        i__1 = min(kv,*n);
        for (j = *ku + 2; j <= i__1; ++j) {
            i__2 = *kl;
            for (i__ = kv - j + 2; i__ <= i__2; ++i__) {
                ab[i__ + j * ab_dim1] = 0.f;
/* L50: */
            }
/* L60: */
        }

/*        JU is the index of the last column affected by the current */
/*        stage of the factorization */

        ju = 1;

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

/*           The active part of the matrix is partitioned */

/*              A11   A12   A13 */
/*              A21   A22   A23 */
/*              A31   A32   A33 */

/*           Here A11, A21 and A31 denote the current block of JB columns */
/*           which is about to be factorized. The number of rows in the */
/*           partitioning are JB, I2, I3 respectively, and the numbers */
/*           of columns are JB, J2, J3. The superdiagonal elements of A13 */
/*           and the subdiagonal elements of A31 lie outside the band. */

/* Computing MIN */
            i__3 = *kl - jb, i__4 = *m - j - jb + 1;
            i2 = min(i__3,i__4);
/* Computing MIN */
            i__3 = jb, i__4 = *m - j - *kl + 1;
            i3 = min(i__3,i__4);

/*           J2 and J3 are computed after JU has been updated. */

/*           Factorize the current block of JB columns */

            i__3 = j + jb - 1;
            for (jj = j; jj <= i__3; ++jj) {

/*              Set fill-in elements in column JJ+KV to zero */

                if (jj + kv <= *n) {
                    i__4 = *kl;
                    for (i__ = 1; i__ <= i__4; ++i__) {
                        ab[i__ + (jj + kv) * ab_dim1] = 0.f;
/* L70: */
                    }
                }

/*              Find pivot and test for singularity. KM is the number of */
/*              subdiagonal elements in the current column. */

/* Computing MIN */
                i__4 = *kl, i__5 = *m - jj;
                km = min(i__4,i__5);
                i__4 = km + 1;
                jp = isamax_(&i__4, &ab[kv + 1 + jj * ab_dim1], &c__1);
                ipiv[jj] = jp + jj - j;
                if (ab[kv + jp + jj * ab_dim1] != 0.f) {
/* Computing MAX */
/* Computing MIN */
                    i__6 = jj + *ku + jp - 1;
                    i__4 = ju, i__5 = min(i__6,*n);
                    ju = max(i__4,i__5);
                    if (jp != 1) {

/*                    Apply interchange to columns J to J+JB-1 */

                        if (jp + jj - 1 < j + *kl) {

                            i__4 = *ldab - 1;
                            i__5 = *ldab - 1;
                            sswap_(&jb, &ab[kv + 1 + jj - j + j * ab_dim1], &
                                    i__4, &ab[kv + jp + jj - j + j * ab_dim1], 
                                     &i__5);
                        } else {

/*                       The interchange affects columns J to JJ-1 of A31 */
/*                       which are stored in the work array WORK31 */

                            i__4 = jj - j;
                            i__5 = *ldab - 1;
                            sswap_(&i__4, &ab[kv + 1 + jj - j + j * ab_dim1], 
                                    &i__5, &work31[jp + jj - j - *kl - 1], &
                                    c__65);
                            i__4 = j + jb - jj;
                            i__5 = *ldab - 1;
                            i__6 = *ldab - 1;
                            sswap_(&i__4, &ab[kv + 1 + jj * ab_dim1], &i__5, &
                                    ab[kv + jp + jj * ab_dim1], &i__6);
                        }
                    }

/*                 Compute multipliers */

                    r__1 = 1.f / ab[kv + 1 + jj * ab_dim1];
                    sscal_(&km, &r__1, &ab[kv + 2 + jj * ab_dim1], &c__1);

/*                 Update trailing submatrix within the band and within */
/*                 the current block. JM is the index of the last column */
/*                 which needs to be updated. */

/* Computing MIN */
                    i__4 = ju, i__5 = j + jb - 1;
                    jm = min(i__4,i__5);
                    if (jm > jj) {
                        i__4 = jm - jj;
                        i__5 = *ldab - 1;
                        i__6 = *ldab - 1;
                        sger_(&km, &i__4, &c_b18, &ab[kv + 2 + jj * ab_dim1], 
                                &c__1, &ab[kv + (jj + 1) * ab_dim1], &i__5, &
                                ab[kv + 1 + (jj + 1) * ab_dim1], &i__6);
                    }
                } else {

/*                 If pivot is zero, set INFO to the index of the pivot */
/*                 unless a zero pivot has already been found. */

                    if (*info == 0) {
                        *info = jj;
                    }
                }

/*              Copy current column of A31 into the work array WORK31 */

/* Computing MIN */
                i__4 = jj - j + 1;
                nw = min(i__4,i3);
                if (nw > 0) {
                    scopy_(&nw, &ab[kv + *kl + 1 - jj + j + jj * ab_dim1], &
                            c__1, &work31[(jj - j + 1) * 65 - 65], &c__1);
                }
/* L80: */
            }
            if (j + jb <= *n) {

/*              Apply the row interchanges to the other blocks. */

/* Computing MIN */
                i__3 = ju - j + 1;
                j2 = min(i__3,kv) - jb;
/* Computing MAX */
                i__3 = 0, i__4 = ju - j - kv + 1;
                j3 = max(i__3,i__4);

/*              Use SLASWP to apply the row interchanges to A12, A22, and */
/*              A32. */

                i__3 = *ldab - 1;
                slaswp_(&j2, &ab[kv + 1 - jb + (j + jb) * ab_dim1], &i__3, &
                        c__1, &jb, &ipiv[j], &c__1);

/*              Adjust the pivot indices. */

                i__3 = j + jb - 1;
                for (i__ = j; i__ <= i__3; ++i__) {
                    ipiv[i__] = ipiv[i__] + j - 1;
/* L90: */
                }

/*              Apply the row interchanges to A13, A23, and A33 */
/*              columnwise. */

                k2 = j - 1 + jb + j2;
                i__3 = j3;
                for (i__ = 1; i__ <= i__3; ++i__) {
                    jj = k2 + i__;
                    i__4 = j + jb - 1;
                    for (ii = j + i__ - 1; ii <= i__4; ++ii) {
                        ip = ipiv[ii];
                        if (ip != ii) {
                            temp = ab[kv + 1 + ii - jj + jj * ab_dim1];
                            ab[kv + 1 + ii - jj + jj * ab_dim1] = ab[kv + 1 + 
                                    ip - jj + jj * ab_dim1];
                            ab[kv + 1 + ip - jj + jj * ab_dim1] = temp;
                        }
/* L100: */
                    }
/* L110: */
                }

/*              Update the relevant part of the trailing submatrix */

                if (j2 > 0) {

/*                 Update A12 */

                    i__3 = *ldab - 1;
                    i__4 = *ldab - 1;
                    strsm_("Left", "Lower", "No transpose", "Unit", &jb, &j2, 
                            &c_b31, &ab[kv + 1 + j * ab_dim1], &i__3, &ab[kv 
                            + 1 - jb + (j + jb) * ab_dim1], &i__4);

                    if (i2 > 0) {

/*                    Update A22 */

                        i__3 = *ldab - 1;
                        i__4 = *ldab - 1;
                        i__5 = *ldab - 1;
                        sgemm_("No transpose", "No transpose", &i2, &j2, &jb, 
                                &c_b18, &ab[kv + 1 + jb + j * ab_dim1], &i__3, 
                                 &ab[kv + 1 - jb + (j + jb) * ab_dim1], &i__4, 
                                 &c_b31, &ab[kv + 1 + (j + jb) * ab_dim1], &
                                i__5);
                    }

                    if (i3 > 0) {

/*                    Update A32 */

                        i__3 = *ldab - 1;
                        i__4 = *ldab - 1;
                        sgemm_("No transpose", "No transpose", &i3, &j2, &jb, 
                                &c_b18, work31, &c__65, &ab[kv + 1 - jb + (j 
                                + jb) * ab_dim1], &i__3, &c_b31, &ab[kv + *kl 
                                + 1 - jb + (j + jb) * ab_dim1], &i__4);
                    }
                }

                if (j3 > 0) {

/*                 Copy the lower triangle of A13 into the work array */
/*                 WORK13 */

                    i__3 = j3;
                    for (jj = 1; jj <= i__3; ++jj) {
                        i__4 = jb;
                        for (ii = jj; ii <= i__4; ++ii) {
                            work13[ii + jj * 65 - 66] = ab[ii - jj + 1 + (jj 
                                    + j + kv - 1) * ab_dim1];
/* L120: */
                        }
/* L130: */
                    }

/*                 Update A13 in the work array */

                    i__3 = *ldab - 1;
                    strsm_("Left", "Lower", "No transpose", "Unit", &jb, &j3, 
                            &c_b31, &ab[kv + 1 + j * ab_dim1], &i__3, work13, 
                            &c__65);

                    if (i2 > 0) {

/*                    Update A23 */

                        i__3 = *ldab - 1;
                        i__4 = *ldab - 1;
                        sgemm_("No transpose", "No transpose", &i2, &j3, &jb, 
                                &c_b18, &ab[kv + 1 + jb + j * ab_dim1], &i__3, 
                                 work13, &c__65, &c_b31, &ab[jb + 1 + (j + kv)
                                 * ab_dim1], &i__4);
                    }

                    if (i3 > 0) {

/*                    Update A33 */

                        i__3 = *ldab - 1;
                        sgemm_("No transpose", "No transpose", &i3, &j3, &jb, 
                                &c_b18, work31, &c__65, work13, &c__65, &
                                c_b31, &ab[*kl + 1 + (j + kv) * ab_dim1], &
                                i__3);
                    }

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

                    i__3 = j3;
                    for (jj = 1; jj <= i__3; ++jj) {
                        i__4 = jb;
                        for (ii = jj; ii <= i__4; ++ii) {
                            ab[ii - jj + 1 + (jj + j + kv - 1) * ab_dim1] = 
                                    work13[ii + jj * 65 - 66];
/* L140: */
                        }
/* L150: */
                    }
                }
            } else {

/*              Adjust the pivot indices. */

                i__3 = j + jb - 1;
                for (i__ = j; i__ <= i__3; ++i__) {
                    ipiv[i__] = ipiv[i__] + j - 1;
/* L160: */
                }
            }

/*           Partially undo the interchanges in the current block to */
/*           restore the upper triangular form of A31 and copy the upper */
/*           triangle of A31 back into place */

            i__3 = j;
            for (jj = j + jb - 1; jj >= i__3; --jj) {
                jp = ipiv[jj] - jj + 1;
                if (jp != 1) {

/*                 Apply interchange to columns J to JJ-1 */

                    if (jp + jj - 1 < j + *kl) {

/*                    The interchange does not affect A31 */

                        i__4 = jj - j;
                        i__5 = *ldab - 1;
                        i__6 = *ldab - 1;
                        sswap_(&i__4, &ab[kv + 1 + jj - j + j * ab_dim1], &
                                i__5, &ab[kv + jp + jj - j + j * ab_dim1], &
                                i__6);
                    } else {

/*                    The interchange does affect A31 */

                        i__4 = jj - j;
                        i__5 = *ldab - 1;
                        sswap_(&i__4, &ab[kv + 1 + jj - j + j * ab_dim1], &
                                i__5, &work31[jp + jj - j - *kl - 1], &c__65);
                    }
                }

/*              Copy the current column of A31 back into place */

/* Computing MIN */
                i__4 = i3, i__5 = jj - j + 1;
                nw = min(i__4,i__5);
                if (nw > 0) {
                    scopy_(&nw, &work31[(jj - j + 1) * 65 - 65], &c__1, &ab[
                            kv + *kl + 1 - jj + j + jj * ab_dim1], &c__1);
                }
/* L170: */
            }
/* L180: */
        }
    }

    return 0;

/*     End of SGBTRF */

} /* sgbtrf_ */