spbtrf (l)  Linux Man Pages
spbtrf: computes the Cholesky factorization of a real symmetric positive definite band matrix A
NAME
SPBTRF  computes the Cholesky factorization of a real symmetric positive definite band matrix ASYNOPSIS
 SUBROUTINE SPBTRF(
 UPLO, N, KD, AB, LDAB, INFO )
 CHARACTER UPLO
 INTEGER INFO, KD, LDAB, N
 REAL AB( LDAB, * )
PURPOSE
SPBTRF computes the Cholesky factorization of a real symmetric positive definite band matrix A. The factorization has the formA
A
where U is an upper triangular matrix and L is lower triangular.
ARGUMENTS
 UPLO (input) CHARACTER*1

= aqUaq: Upper triangle of A is stored;
= aqLaq: 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 = aqUaq, or the number of subdiagonals if UPLO = aqLaq. 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 jth column of A is stored in the jth column of the array AB as follows: if UPLO = aqUaq, AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j; if UPLO = aqLaq, AB(1+ij,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 ith 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 = aqUaq:On entry: On exit:
a11
On entry: On exit:
a11
a21
a31
Contributed by
Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989