table of contents
| potrf2(3) | LAPACK | potrf2(3) |
NAME¶
potrf2 - potrf2: triangular factor panel, recursive?
SYNOPSIS¶
Functions¶
recursive subroutine cpotrf2 (uplo, n, a, lda, info)
CPOTRF2 recursive subroutine dpotrf2 (uplo, n, a, lda, info)
DPOTRF2 recursive subroutine spotrf2 (uplo, n, a, lda, info)
SPOTRF2 recursive subroutine zpotrf2 (uplo, n, a, lda, info)
ZPOTRF2
Detailed Description¶
Function Documentation¶
recursive subroutine cpotrf2 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer info)¶
CPOTRF2
Purpose:
CPOTRF2 computes the Cholesky factorization of a Hermitian
positive definite matrix A using the recursive algorithm.
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 and L is lower triangular.
This is the recursive version of the algorithm. It divides
the matrix into four submatrices:
[ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
A = [ -----|----- ] with n1 = n/2
[ A21 | A22 ] n2 = n-n1
The subroutine calls itself to factor A11. Update and scale A21
or A12, update A22 then calls itself to factor A22.
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.
A
A is COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading principal minor of order i
is not positive, and the factorization could not be
completed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
recursive subroutine dpotrf2 (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer info)¶
DPOTRF2
Purpose:
DPOTRF2 computes the Cholesky factorization of a real symmetric
positive definite matrix A using the recursive algorithm.
The factorization has the form
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the recursive version of the algorithm. It divides
the matrix into four submatrices:
[ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
A = [ -----|----- ] with n1 = n/2
[ A21 | A22 ] n2 = n-n1
The subroutine calls itself to factor A11. Update and scale A21
or A12, update A22 then calls itself to factor A22.
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.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading principal minor of order i
is not positive, and the factorization could not be
completed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
recursive subroutine spotrf2 (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer info)¶
SPOTRF2
Purpose:
SPOTRF2 computes the Cholesky factorization of a real symmetric
positive definite matrix A using the recursive algorithm.
The factorization has the form
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the recursive version of the algorithm. It divides
the matrix into four submatrices:
[ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
A = [ -----|----- ] with n1 = n/2
[ A21 | A22 ] n2 = n-n1
The subroutine calls itself to factor A11. Update and scale A21
or A12, update A22 then call itself to factor A22.
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.
A
A is REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading principal minor of order i
is not positive, and the factorization could not be
completed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
recursive subroutine zpotrf2 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer info)¶
ZPOTRF2
Purpose:
ZPOTRF2 computes the Cholesky factorization of a Hermitian
positive definite matrix A using the recursive algorithm.
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 and L is lower triangular.
This is the recursive version of the algorithm. It divides
the matrix into four submatrices:
[ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2
A = [ -----|----- ] with n1 = n/2
[ A21 | A22 ] n2 = n-n1
The subroutine calls itself to factor A11. Update and scale A21
or A12, update A22 then call itself to factor A22.
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.
A
A is COMPLEX*16 array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading principal minor of order i
is not positive, and the factorization could not be
completed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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