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?pbstf
Computes a split Cholesky factorization of a real symmetric or complex Hermitian positive-definite banded matrix used in ?sbgst/?hbgst .
Syntax
call spbstf(uplo, n, kb, bb, ldbb, info)
call dpbstf(uplo, n, kb, bb, ldbb, info)
call cpbstf(uplo, n, kb, bb, ldbb, info)
call zpbstf(uplo, n, kb, bb, ldbb, info)
call pbstf(bb [, uplo] [,info])
Include Files
- mkl.fi, lapack.f90
Description
The routine computes a split Cholesky factorization of a real symmetric or complex Hermitian positive-definite band matrix B. It is to be used in conjunction with sbgst/hbgst.
The factorization has the form B = ST*S (or B = SH*S for complex flavors), where S is a band matrix of the same bandwidth as B and the following structure: S is upper triangular in the first (n+kb)/2 rows and lower triangular in the remaining rows.
Input Parameters
- uplo
-
CHARACTER*1. Must be 'U' or 'L'.
If uplo = 'U', bb stores the upper triangular part of B.
If uplo = 'L', bb stores the lower triangular part of B.
- n
-
INTEGER. The order of the matrix B (n≥ 0).
- kb
-
INTEGER. The number of super- or sub-diagonals in B
(kb≥ 0).
- bb
-
REAL for spbstf
DOUBLE PRECISION for dpbstf
COMPLEX for cpbstf
DOUBLE COMPLEX for zpbstf.
bb(ldbb,*) is an array containing either upper or lower triangular part of the matrix B (as specified by uplo) in band storage format.
The second dimension of the array bb must be at least max(1, n).
- ldbb
-
INTEGER. The leading dimension of bb; must be at least kb+1.
Output Parameters
- bb
-
On exit, this array is overwritten by the elements of the split Cholesky factor S.
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = i, then the factorization could not be completed, because the updated element bii would be the square root of a negative number; hence the matrix B is not positive-definite.
If info = -i, the i-th parameter had an illegal value.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine pbstf interface are the following:
- bb
-
Holds the array B of size (kb+1,n).
- uplo
-
Must be 'U' or 'L'. The default value is 'U'.
Application Notes
The computed factor S is the exact factor of a perturbed matrix B + E, where
c(n) is a modest linear function of n, and ε is the machine precision.
The total number of floating-point operations for real flavors is approximately n(kb+1)2. The number of operations for complex flavors is 4 times greater. All these estimates assume that kb is much less than n.
After calling this routine, you can call sbgst/hbgst to solve the generalized eigenproblem Az = λBz, where A and B are banded and B is positive-definite.