table of contents
/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/zpbstf.f(3) | Library Functions Manual | /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/zpbstf.f(3) |
NAME¶
/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/zpbstf.f
SYNOPSIS¶
Functions/Subroutines¶
subroutine ZPBSTF (uplo, n, kd, ab, ldab, info)
ZPBSTF
Function/Subroutine Documentation¶
subroutine ZPBSTF (character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, integer info)¶
ZPBSTF
Purpose:
!> !> ZPBSTF computes a split Cholesky factorization of a complex !> Hermitian positive definite band matrix A. !> !> This routine is designed to be used in conjunction with ZHBGST. !> !> 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 !> triangular of order n-m. !>
Parameters
UPLO
!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
N
!> N is INTEGER !> The order of the matrix A. N >= 0. !>
KD
!> KD is INTEGER !> The number of superdiagonals of the matrix A if UPLO = 'U', !> or the number of subdiagonals if UPLO = 'L'. KD >= 0. !>
AB
!> AB is COMPLEX*16 array, dimension (LDAB,N) !> 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
!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !>
INFO
!> INFO is 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. !>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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**H s64**H s75**H !> * a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54**H s65**H s76**H !> 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**H s23**H s34**H s54 s65 s76 * !> a31 a42 a53 a64 a64 * * s13**H s24**H s53 s64 s75 * * !> !> Array elements marked * are not used by the routine; s12**H denotes !> conjg(s12); the diagonal elements of S are real. !>
Definition at line 152 of file zpbstf.f.
Author¶
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