#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int dpbstf_(char *uplo, integer *n, integer *kd, doublereal *
ab, integer *ldab, integer *info)
{
/* -- LAPACK routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
DPBSTF computes a split Cholesky factorization of a real
symmetric positive definite band matrix A.
This routine is designed to be used in conjunction with DSBGST.
The factorization has the form A = S**T*S where S is a band matrix
of the same bandwidth as A and the following structure:
S = ( U )
( M L )
where U is upper triangular of order m = (n+kd)/2, and L is lower
triangular of order n-m.
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) DOUBLE PRECISION 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 factor S from the split Cholesky
factorization A = S**T*S. See Further Details.
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 factorization could not be completed,
because the updated element a(i,i) was negative; the
matrix A is not positive definite.
Further Details
===============
The band storage scheme is illustrated by the following example, when
N = 7, KD = 2:
S = ( s11 s12 s13 )
( s22 s23 s24 )
( s33 s34 )
( s44 )
( s53 s54 s55 )
( s64 s65 s66 )
( s75 s76 s77 )
If UPLO = 'U', the array AB holds:
on entry: on exit:
* * a13 a24 a35 a46 a57 * * s13 s24 s53 s64 s75
* a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54 s65 s76
a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77
If UPLO = 'L', the array AB holds:
on entry: on exit:
a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77
a21 a32 a43 a54 a65 a76 * s12 s23 s34 s54 s65 s76 *
a31 a42 a53 a64 a64 * * s13 s24 s53 s64 s75 * *
Array elements marked * are not used by the routine.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static doublereal c_b9 = -1.;
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer j, m, km;
static doublereal ajj;
static integer kld;
extern /* Subroutine */ int dsyr_(char *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *), dscal_(
integer *, doublereal *, doublereal *, integer *);
extern logical lsame_(char *, char *);
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! 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_("DPBSTF", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Computing MAX */
i__1 = 1, i__2 = *ldab - 1;
kld = max(i__1,i__2);
/* Set the splitting point m. */
m = (*n + *kd) / 2;
if (upper) {
/* Factorize A(m+1:n,m+1:n) as L**T*L, and update A(1:m,1:m). */
i__1 = m + 1;
for (j = *n; j >= i__1; --j) {
/* Compute s(j,j) and test for non-positive-definiteness. */
ajj = ab[*kd + 1 + j * ab_dim1];
if (ajj <= 0.) {
goto L50;
}
ajj = sqrt(ajj);
ab[*kd + 1 + j * ab_dim1] = ajj;
/* Computing MIN */
i__2 = j - 1;
km = min(i__2,*kd);
/* Compute elements j-km:j-1 of the j-th column and update the
the leading submatrix within the band. */
d__1 = 1. / ajj;
dscal_(&km, &d__1, &ab[*kd + 1 - km + j * ab_dim1], &c__1);
dsyr_("Upper", &km, &c_b9, &ab[*kd + 1 - km + j * ab_dim1], &c__1,
&ab[*kd + 1 + (j - km) * ab_dim1], &kld);
/* L10: */
}
/* Factorize the updated submatrix A(1:m,1:m) as U**T*U. */
i__1 = m;
for (j = 1; j <= i__1; ++j) {
/* Compute s(j,j) and test for non-positive-definiteness. */
ajj = ab[*kd + 1 + j * ab_dim1];
if (ajj <= 0.) {
goto L50;
}
ajj = sqrt(ajj);
ab[*kd + 1 + j * ab_dim1] = ajj;
/* Computing MIN */
i__2 = *kd, i__3 = m - j;
km = min(i__2,i__3);
/* Compute elements j+1:j+km of the j-th row and update the
trailing submatrix within the band. */
if (km > 0) {
d__1 = 1. / ajj;
dscal_(&km, &d__1, &ab[*kd + (j + 1) * ab_dim1], &kld);
dsyr_("Upper", &km, &c_b9, &ab[*kd + (j + 1) * ab_dim1], &kld,
&ab[*kd + 1 + (j + 1) * ab_dim1], &kld);
}
/* L20: */
}
} else {
/* Factorize A(m+1:n,m+1:n) as L**T*L, and update A(1:m,1:m). */
i__1 = m + 1;
for (j = *n; j >= i__1; --j) {
/* Compute s(j,j) and test for non-positive-definiteness. */
ajj = ab[j * ab_dim1 + 1];
if (ajj <= 0.) {
goto L50;
}
ajj = sqrt(ajj);
ab[j * ab_dim1 + 1] = ajj;
/* Computing MIN */
i__2 = j - 1;
km = min(i__2,*kd);
/* Compute elements j-km:j-1 of the j-th row and update the
trailing submatrix within the band. */
d__1 = 1. / ajj;
dscal_(&km, &d__1, &ab[km + 1 + (j - km) * ab_dim1], &kld);
dsyr_("Lower", &km, &c_b9, &ab[km + 1 + (j - km) * ab_dim1], &kld,
&ab[(j - km) * ab_dim1 + 1], &kld);
/* L30: */
}
/* Factorize the updated submatrix A(1:m,1:m) as U**T*U. */
i__1 = m;
for (j = 1; j <= i__1; ++j) {
/* Compute s(j,j) and test for non-positive-definiteness. */
ajj = ab[j * ab_dim1 + 1];
if (ajj <= 0.) {
goto L50;
}
ajj = sqrt(ajj);
ab[j * ab_dim1 + 1] = ajj;
/* Computing MIN */
i__2 = *kd, i__3 = m - j;
km = min(i__2,i__3);
/* Compute elements j+1:j+km of the j-th column and update the
trailing submatrix within the band. */
if (km > 0) {
d__1 = 1. / ajj;
dscal_(&km, &d__1, &ab[j * ab_dim1 + 2], &c__1);
dsyr_("Lower", &km, &c_b9, &ab[j * ab_dim1 + 2], &c__1, &ab[(
j + 1) * ab_dim1 + 1], &kld);
}
/* L40: */
}
}
return 0;
L50:
*info = j;
return 0;
/* End of DPBSTF */
} /* dpbstf_ */