table of contents
| posv(3) | LAPACK | posv(3) |
NAME¶
posv - posv: factor and solve
SYNOPSIS¶
Functions¶
subroutine cposv (uplo, n, nrhs, a, lda, b, ldb, info)
CPOSV computes the solution to system of linear equations A * X = B for PO
matrices subroutine dposv (uplo, n, nrhs, a, lda, b, ldb, info)
DPOSV computes the solution to system of linear equations A * X = B for PO
matrices subroutine sposv (uplo, n, nrhs, a, lda, b, ldb, info)
SPOSV computes the solution to system of linear equations A * X = B for PO
matrices subroutine zposv (uplo, n, nrhs, a, lda, b, ldb, info)
ZPOSV computes the solution to system of linear equations A * X = B for PO
matrices
Detailed Description¶
Function Documentation¶
subroutine cposv (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, integer info)¶
CPOSV computes the solution to system of linear equations A * X = B for PO matrices
Purpose:
CPOSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix and X and B
are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
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 a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
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 number of linear equations, i.e., the order of the
matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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).
B
B is COMPLEX array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= 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
of A is not positive, so the factorization could not
be completed, and the solution has not been computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dposv (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, integer info)¶
DPOSV computes the solution to system of linear equations A * X = B for PO matrices
Purpose:
DPOSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix and X and B
are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
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 a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
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 number of linear equations, i.e., the order of the
matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= 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
of A is not positive, so the factorization could not
be completed, and the solution has not been computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine sposv (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, integer info)¶
SPOSV computes the solution to system of linear equations A * X = B for PO matrices
Purpose:
SPOSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix and X and B
are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
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 a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
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 number of linear equations, i.e., the order of the
matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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).
B
B is REAL array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= 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
of A is not positive, so the factorization could not
be completed, and the solution has not been computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zposv (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, integer info)¶
ZPOSV computes the solution to system of linear equations A * X = B for PO matrices
Purpose:
ZPOSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix and X and B
are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
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 a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
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 number of linear equations, i.e., the order of the
matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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).
B
B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= 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
of A is not positive, so the factorization could not
be completed, and the solution has not been computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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