#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int spbtrf_(char *uplo, integer *n, integer *kd, real *ab, 
	integer *ldab, integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       March 31, 1993   


    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   

    =====================================================================   


       Test the input parameters.   

       Parameter adjustments */
    /* 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;
    
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
    /* Local variables */
    static real work[1056]	/* was [33][32] */;
    static integer i__, j;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    static integer i2, i3;
    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 *
	    ), spbtf2_(char *, integer *, integer *, real *, 
	    integer *, integer *);
    static integer ib;
    extern /* Subroutine */ int spotf2_(char *, integer *, real *, integer *, 
	    integer *);
    static integer nb, ii, jj;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
#define work_ref(a_1,a_2) work[(a_2)*33 + a_1 - 34]
#define ab_ref(a_1,a_2) ab[(a_2)*ab_dim1 + a_1]


    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1 * 1;
    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, (ftnlen)6, (
	    ftnlen)1);

/*     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_ref(i__, j) = 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_ref(*kd + 1, i__), &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_ref(*kd + 1, i__), &i__3, &
				ab_ref(*kd + 1 - ib, i__ + ib), &i__4);

/*                    Update A22 */

			i__3 = *ldab - 1;
			i__4 = *ldab - 1;
			ssyrk_("Upper", "Transpose", &i2, &ib, &c_b21, &
				ab_ref(*kd + 1 - ib, i__ + ib), &i__3, &c_b18,
				 &ab_ref(*kd + 1, i__ + ib), &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_ref(ii, jj) = ab_ref(ii - jj + 1, jj + 
					i__ + *kd - 1);
/* L30: */
			    }
/* L40: */
			}

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

			i__3 = *ldab - 1;
			strsm_("Left", "Upper", "Transpose", "Non-unit", &ib, 
				&i3, &c_b18, &ab_ref(*kd + 1, i__), &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_ref(*kd + 1 - ib, i__ + ib), 
				    &i__3, work, &c__33, &c_b18, &ab_ref(ib + 
				    1, i__ + *kd), &i__4);
			}

/*                    Update A33 */

			i__3 = *ldab - 1;
			ssyrk_("Upper", "Transpose", &i3, &ib, &c_b21, work, &
				c__33, &c_b18, &ab_ref(*kd + 1, i__ + *kd), &
				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_ref(ii - jj + 1, jj + i__ + *kd - 1) = 
					work_ref(ii, jj);
/* 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_ref(i__, j) = 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_ref(1, i__), &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_ref(1, i__), &i__3, &ab_ref(
				ib + 1, i__), &i__4);

/*                    Update A22 */

			i__3 = *ldab - 1;
			i__4 = *ldab - 1;
			ssyrk_("Lower", "No Transpose", &i2, &ib, &c_b21, &
				ab_ref(ib + 1, i__), &i__3, &c_b18, &ab_ref(1,
				 i__ + ib), &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_ref(ii, jj) = ab_ref(*kd + 1 - jj + ii, 
					jj + i__ - 1);
/* L100: */
			    }
/* L110: */
			}

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

			i__3 = *ldab - 1;
			strsm_("Right", "Lower", "Transpose", "Non-unit", &i3,
				 &ib, &c_b18, &ab_ref(1, i__), &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_ref(ib + 1, 
				    i__), &i__3, &c_b18, &ab_ref(*kd + 1 - ib,
				     i__ + ib), &i__4);
			}

/*                    Update A33 */

			i__3 = *ldab - 1;
			ssyrk_("Lower", "No Transpose", &i3, &ib, &c_b21, 
				work, &c__33, &c_b18, &ab_ref(1, i__ + *kd), &
				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_ref(*kd + 1 - jj + ii, jj + i__ - 1) = 
					work_ref(ii, jj);
/* L120: */
			    }
/* L130: */
			}
		    }
		}
/* L140: */
	    }
	}
    }
    return 0;

L150:
    return 0;

/*     End of SPBTRF */

} /* spbtrf_ */

#undef ab_ref
#undef work_ref


