CHESV(3F) CHESV(3F)
CHESV - compute the solution to a complex system of linear equations A *
X = B,
SUBROUTINE CHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO
)
CHARACTER UPLO
INTEGER INFO, LDA, LDB, LWORK, N, NRHS
INTEGER IPIV( * )
COMPLEX A( LDA, * ), B( LDB, * ), WORK( LWORK )
CHESV 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 Nby-NRHS
matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is Hermitian and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to solve
the system of equations A * X = B.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The number of linear equations, i.e., the order of the matrix A.
N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrix B. NRHS >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading Nby-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.
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CHESV(3F) CHESV(3F)
On exit, if INFO = 0, the block diagonal matrix D and the
multipliers used to obtain the factor U or L from the
factorization A = U*D*U**H or A = L*D*L**H as computed by CHETRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV (output) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as
determined by CHETRF. If IPIV(k) > 0, then rows and columns k
and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal
block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is
a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) <
0, then rows and columns k+1 and -IPIV(k) were interchanged and
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
B (input/output) 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 (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of WORK. LWORK >= 1, and for best performance LWORK
>= N*NB, where NB is the optimal blocksize for CHETRF.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) is exactly zero. The factorization has
been completed, but the block diagonal matrix D is exactly
singular, so the solution could not be computed.
CHESV(3F) CHESV(3F)
CHESV - compute the solution to a complex system of linear equations A *
X = B,
SUBROUTINE CHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO
)
CHARACTER UPLO
INTEGER INFO, LDA, LDB, LWORK, N, NRHS
INTEGER IPIV( * )
COMPLEX A( LDA, * ), B( LDB, * ), WORK( LWORK )
CHESV 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 Nby-NRHS
matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is Hermitian and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to solve
the system of equations A * X = B.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The number of linear equations, i.e., the order of the matrix A.
N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrix B. NRHS >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading Nby-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.
Page 1
CHESV(3F) CHESV(3F)
On exit, if INFO = 0, the block diagonal matrix D and the
multipliers used to obtain the factor U or L from the
factorization A = U*D*U**H or A = L*D*L**H as computed by CHETRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV (output) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as
determined by CHETRF. If IPIV(k) > 0, then rows and columns k
and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal
block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is
a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) <
0, then rows and columns k+1 and -IPIV(k) were interchanged and
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
B (input/output) 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 (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of WORK. LWORK >= 1, and for best performance LWORK
>= N*NB, where NB is the optimal blocksize for CHETRF.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) is exactly zero. The factorization has
been completed, but the block diagonal matrix D is exactly
singular, so the solution could not be computed.
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