cpbstf(3P) Sun Performance Library cpbstf(3P)NAMEcpbstf - compute a split Cholesky factorization of a complex Hermitian
positive definite band matrix A
SYNOPSIS
SUBROUTINE CPBSTF(UPLO, N, KD, AB, LDAB, INFO)
CHARACTER * 1 UPLO
COMPLEX AB(LDAB,*)
INTEGER N, KD, LDAB, INFO
SUBROUTINE CPBSTF_64(UPLO, N, KD, AB, LDAB, INFO)
CHARACTER * 1 UPLO
COMPLEX AB(LDAB,*)
INTEGER*8 N, KD, LDAB, INFO
F95 INTERFACE
SUBROUTINE PBSTF(UPLO, [N], KD, AB, [LDAB], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:,:) :: AB
INTEGER :: N, KD, LDAB, INFO
SUBROUTINE PBSTF_64(UPLO, [N], KD, AB, [LDAB], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:,:) :: AB
INTEGER(8) :: N, KD, LDAB, INFO
C INTERFACE
#include <sunperf.h>
void cpbstf(char uplo, int n, int kd, complex *ab, int ldab, int
*info);
void cpbstf_64(char uplo, long n, long kd, complex *ab, long ldab, long
*info);
PURPOSEcpbstf computes a split Cholesky factorization of a complex Hermitian
positive definite band matrix A.
This routine is designed to be used in conjunction with CHBGST.
The factorization has the form A = S**H*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 tri‐
angular of order n-m.
ARGUMENTS
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
KD (input)
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.
AB (input/output)
On entry, the upper or lower triangle of the Hermitian 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**H*S. See Further Details.
LDAB (input)
The leading dimension of the array AB. LDAB >= KD+1.
INFO (output)
= 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; s12' denotes
conjg(s12); the diagonal elements of S are real.
6 Mar 2009 cpbstf(3P)
