table of contents
/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/cpbtf2.f(3) | Library Functions Manual | /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/cpbtf2.f(3) |
NAME¶
/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/cpbtf2.f
SYNOPSIS¶
Functions/Subroutines¶
subroutine CPBTF2 (uplo, n, kd, ab, ldab, info)
CPBTF2 computes the Cholesky factorization of a symmetric/Hermitian
positive definite band matrix (unblocked algorithm).
Function/Subroutine Documentation¶
subroutine CPBTF2 (character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, integer info)¶
CPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).
Purpose:
!> !> CPBTF2 computes the Cholesky factorization of a complex Hermitian !> positive definite band matrix A. !> !> The factorization has the form !> A = U**H * U , if UPLO = 'U', or !> A = L * L**H, if UPLO = 'L', !> where U is an upper triangular matrix, U**H is the conjugate transpose !> of U, and L is lower triangular. !> !> This is the unblocked version of the algorithm, calling Level 2 BLAS. !>
Parameters
UPLO
!> UPLO is CHARACTER*1 !> Specifies whether the upper or lower triangular part of the !> Hermitian matrix A is stored: !> = 'U': Upper triangular !> = 'L': Lower triangular !>
N
!> N is INTEGER !> The order of the matrix A. N >= 0. !>
KD
!> KD is INTEGER !> The number of super-diagonals of the matrix A if UPLO = 'U', !> or the number of sub-diagonals if UPLO = 'L'. KD >= 0. !>
AB
!> AB is COMPLEX 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 triangular factor U or L from the !> Cholesky factorization A = U**H *U or A = L*L**H of the band !> matrix A, in the same storage format as A. !>
LDAB
!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !>
INFO
!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -k, the k-th argument had an illegal value !> > 0: if INFO = k, the leading principal minor of order k !> is not positive, and the factorization could not be !> completed. !>
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 = 6, KD = 2, and UPLO = 'U': !> !> On entry: On exit: !> !> * * a13 a24 a35 a46 * * u13 u24 u35 u46 !> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 !> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 !> !> Similarly, if UPLO = 'L' the format of A is as follows: !> !> On entry: On exit: !> !> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 !> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * !> a31 a42 a53 a64 * * l31 l42 l53 l64 * * !> !> Array elements marked * are not used by the routine. !>
Definition at line 141 of file cpbtf2.f.
Author¶
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