table of contents
| hesv_aa_2stage(3) | LAPACK | hesv_aa_2stage(3) |
NAME¶
hesv_aa_2stage - {he,sy}sv_aa_2stage: Aasen, blocked 2-stage
SYNOPSIS¶
Functions¶
subroutine chesv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb,
ipiv, ipiv2, b, ldb, work, lwork, info)
CHESV_AA_2STAGE computes the solution to system of linear equations A * X
= B for HE matrices subroutine csysv_aa_2stage (uplo, n, nrhs, a,
lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
CSYSV_AA_2STAGE computes the solution to system of linear equations A * X
= B for SY matrices subroutine dsysv_aa_2stage (uplo, n, nrhs, a,
lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
DSYSV_AA_2STAGE computes the solution to system of linear equations A * X
= B for SY matrices subroutine ssysv_aa_2stage (uplo, n, nrhs, a,
lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
SSYSV_AA_2STAGE computes the solution to system of linear equations A * X
= B for SY matrices subroutine zhesv_aa_2stage (uplo, n, nrhs, a,
lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
ZHESV_AA_2STAGE computes the solution to system of linear equations A * X
= B for HE matrices subroutine zsysv_aa_2stage (uplo, n, nrhs, a,
lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X
= B for SY matrices
Detailed Description¶
Function Documentation¶
subroutine chesv_aa_2stage (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)¶
CHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices
Purpose:
CHESV_AA_2STAGE computes the solution to a complex system of
linear equations
A * X = B,
where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
matrices.
Aasen's 2-stage algorithm is used to factor A as
A = U**H * T * U, if UPLO = 'U', or
A = L * T * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is Hermitian and band. The matrix T is
then LU-factored with partial pivoting. The factored form of A
is then used to solve the system of equations A * X = B.
This is the blocked version of the algorithm, calling Level 3 BLAS.
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.
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, L is stored below (or above) the subdiagonal blocks,
when UPLO is 'L' (or 'U').
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TB
TB is COMPLEX array, dimension (LTB)
On exit, details of the LU factorization of the band matrix.
LTB
LTB is INTEGER
The size of the array TB. LTB >= 4*N, internally
used to select NB such that LTB >= (3*NB+1)*N.
If LTB = -1, then a workspace query is assumed; the
routine only calculates the optimal size of LTB,
returns this value as the first entry of TB, and
no error message related to LTB is issued by XERBLA.
IPIV
IPIV is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).
IPIV2
IPIV2 is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of T were interchanged with the
row and column IPIV(k).
B
B is COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is COMPLEX workspace of size LWORK
LWORK
LWORK is INTEGER
The size of WORK. LWORK >= N, internally used to select NB
such that LWORK >= N*NB.
If LWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the WORK array,
returns this value as the first entry of the WORK array, and
no error message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, band LU factorization failed on i-th column
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine csysv_aa_2stage (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)¶
CSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices
Purpose:
CSYSV_AA_2STAGE computes the solution to a complex system of
linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
Aasen's 2-stage algorithm is used to factor A as
A = U**T * T * U, if UPLO = 'U', or
A = L * T * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is symmetric and band. The matrix T is
then LU-factored with partial pivoting. The factored form of A
is then used to solve the system of equations A * X = B.
This is the blocked version of the algorithm, calling Level 3 BLAS.
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.
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 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, L is stored below (or above) the subdiagonal blocks,
when UPLO is 'L' (or 'U').
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TB
TB is COMPLEX array, dimension (LTB)
On exit, details of the LU factorization of the band matrix.
LTB
LTB is INTEGER
The size of the array TB. LTB >= 4*N, internally
used to select NB such that LTB >= (3*NB+1)*N.
If LTB = -1, then a workspace query is assumed; the
routine only calculates the optimal size of LTB,
returns this value as the first entry of TB, and
no error message related to LTB is issued by XERBLA.
IPIV
IPIV is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).
IPIV2
IPIV2 is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of T were interchanged with the
row and column IPIV(k).
B
B is COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is COMPLEX workspace of size LWORK
LWORK
LWORK is INTEGER
The size of WORK. LWORK >= N, internally used to select NB
such that LWORK >= N*NB.
If LWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the WORK array,
returns this value as the first entry of the WORK array, and
no error message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, band LU factorization failed on i-th column
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dsysv_aa_2stage (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer lwork, integer info)¶
DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices
Purpose:
DSYSV_AA_2STAGE computes the solution to a real system of
linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
Aasen's 2-stage algorithm is used to factor A as
A = U**T * T * U, if UPLO = 'U', or
A = L * T * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is symmetric and band. The matrix T is
then LU-factored with partial pivoting. The factored form of A
is then used to solve the system of equations A * X = B.
This is the blocked version of the algorithm, calling Level 3 BLAS.
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.
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, L is stored below (or above) the subdiagonal blocks,
when UPLO is 'L' (or 'U').
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TB
TB is DOUBLE PRECISION array, dimension (LTB)
On exit, details of the LU factorization of the band matrix.
LTB
LTB is INTEGER
The size of the array TB. LTB >= 4*N, internally
used to select NB such that LTB >= (3*NB+1)*N.
If LTB = -1, then a workspace query is assumed; the
routine only calculates the optimal size of LTB,
returns this value as the first entry of TB, and
no error message related to LTB is issued by XERBLA.
IPIV
IPIV is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).
IPIV2
IPIV2 is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of T were interchanged with the
row and column IPIV(k).
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is DOUBLE PRECISION workspace of size LWORK
LWORK
LWORK is INTEGER
The size of WORK. LWORK >= N, internally used to select NB
such that LWORK >= N*NB.
If LWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the WORK array,
returns this value as the first entry of the WORK array, and
no error message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, band LU factorization failed on i-th column
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine ssysv_aa_2stage (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)¶
SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices
Purpose:
SSYSV_AA_2STAGE computes the solution to a real system of
linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
Aasen's 2-stage algorithm is used to factor A as
A = U**T * T * U, if UPLO = 'U', or
A = L * T * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is symmetric and band. The matrix T is
then LU-factored with partial pivoting. The factored form of A
is then used to solve the system of equations A * X = B.
This is the blocked version of the algorithm, calling Level 3 BLAS.
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.
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, L is stored below (or above) the subdiagonal blocks,
when UPLO is 'L' (or 'U').
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TB
TB is REAL array, dimension (LTB)
On exit, details of the LU factorization of the band matrix.
LTB
LTB is INTEGER
The size of the array TB. LTB >= 4*N, internally
used to select NB such that LTB >= (3*NB+1)*N.
If LTB = -1, then a workspace query is assumed; the
routine only calculates the optimal size of LTB,
returns this value as the first entry of TB, and
no error message related to LTB is issued by XERBLA.
IPIV
IPIV is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).
IPIV2
IPIV2 is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of T were interchanged with the
row and column IPIV(k).
B
B is REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is REAL workspace of size LWORK
LWORK
LWORK is INTEGER
The size of WORK. LWORK >= N, internally used to select NB
such that LWORK >= N*NB.
If LWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the WORK array,
returns this value as the first entry of the WORK array, and
no error message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, band LU factorization failed on i-th column
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zhesv_aa_2stage (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)¶
ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices
Purpose:
ZHESV_AA_2STAGE computes the solution to a complex system of
linear equations
A * X = B,
where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
matrices.
Aasen's 2-stage algorithm is used to factor A as
A = U**H * T * U, if UPLO = 'U', or
A = L * T * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is Hermitian and band. The matrix T is
then LU-factored with partial pivoting. The factored form of A
is then used to solve the system of equations A * X = B.
This is the blocked version of the algorithm, calling Level 3 BLAS.
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.
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, L is stored below (or above) the subdiagonal blocks,
when UPLO is 'L' (or 'U').
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TB
TB is COMPLEX*16 array, dimension (LTB)
On exit, details of the LU factorization of the band matrix.
LTB
LTB is INTEGER
The size of the array TB. LTB >= 4*N, internally
used to select NB such that LTB >= (3*NB+1)*N.
If LTB = -1, then a workspace query is assumed; the
routine only calculates the optimal size of LTB,
returns this value as the first entry of TB, and
no error message related to LTB is issued by XERBLA.
IPIV
IPIV is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).
IPIV2
IPIV2 is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of T were interchanged with the
row and column IPIV(k).
B
B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is COMPLEX*16 workspace of size LWORK
LWORK
LWORK is INTEGER
The size of WORK. LWORK >= N, internally used to select NB
such that LWORK >= N*NB.
If LWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the WORK array,
returns this value as the first entry of the WORK array, and
no error message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, band LU factorization failed on i-th column
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zsysv_aa_2stage (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)¶
ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices
Purpose:
ZSYSV_AA_2STAGE computes the solution to a complex system of
linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
Aasen's 2-stage algorithm is used to factor A as
A = U**T * T * U, if UPLO = 'U', or
A = L * T * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is symmetric and band. The matrix T is
then LU-factored with partial pivoting. The factored form of A
is then used to solve the system of equations A * X = B.
This is the blocked version of the algorithm, calling Level 3 BLAS.
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.
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 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, L is stored below (or above) the subdiagonal blocks,
when UPLO is 'L' (or 'U').
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TB
TB is COMPLEX*16 array, dimension (LTB)
On exit, details of the LU factorization of the band matrix.
LTB
LTB is INTEGER
The size of the array TB. LTB >= 4*N, internally
used to select NB such that LTB >= (3*NB+1)*N.
If LTB = -1, then a workspace query is assumed; the
routine only calculates the optimal size of LTB,
returns this value as the first entry of TB, and
no error message related to LTB is issued by XERBLA.
IPIV
IPIV is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).
IPIV2
IPIV2 is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of T were interchanged with the
row and column IPIV(k).
B
B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK
WORK is COMPLEX*16 workspace of size LWORK
LWORK
LWORK is INTEGER
The size of WORK. LWORK >= N, internally used to select NB
such that LWORK >= N*NB.
If LWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the WORK array,
returns this value as the first entry of the WORK array, and
no error message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, band LU factorization failed on i-th column
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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