hesv_rook#

Functions

void chesv_rook(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
          c64*  restrict A,
    const INT            lda,
          INT*  restrict ipiv,
          c64*  restrict B,
    const INT            ldb,
          c64*  restrict work,
    const INT            lwork,
          INT*           info
);
void chesv_rook(const char *uplo, const INT n, const INT nrhs, c64 *restrict A, const INT lda, INT *restrict ipiv, c64 *restrict B, const INT ldb, c64 *restrict work, const INT lwork, INT *info)#

CHESV_ROOK 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.

The bounded Bunch-Kaufman (“rook”) 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.

CHETRF_ROOK is called to compute the factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method.

The factored form of A is then used to solve the system of equations A * X = B by calling CHETRS_ROOK (uses BLAS 2).

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_ROOK.

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.

Parameters

in
uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in
n

The number of linear equations, i.e., the order of the matrix A. n >= 0.

in
nrhs

The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0.

inout
A

Single 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.

in
lda

The leading dimension of the array A. lda >= max(1, n).

out
ipiv

Integer array, dimension (n). Details of the interchanges and the block structure of D, as determined by CHETRF_ROOK.

inout
B

Single 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.

in
ldb

The leading dimension of the array B. ldb >= max(1, n).

out
work

Single complex array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The length of work. lwork >= 1, and for best performance lwork >= max(1, n*NB), where NB is the optimal blocksize for CHETRF_ROOK. for lwork < n, TRS will be done with Level BLAS 2 for lwork >= n, TRS will be done with Level BLAS 3

out
info

  • = 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.

Functions

void zhesv_rook(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
          c128* restrict A,
    const INT            lda,
          INT*  restrict ipiv,
          c128* restrict B,
    const INT            ldb,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);
void zhesv_rook(const char *uplo, const INT n, const INT nrhs, c128 *restrict A, const INT lda, INT *restrict ipiv, c128 *restrict B, const INT ldb, c128 *restrict work, const INT lwork, INT *info)#

ZHESV_ROOK 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.

The bounded Bunch-Kaufman (“rook”) 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.

ZHETRF_ROOK is called to compute the factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method.

The factored form of A is then used to solve the system of equations A * X = B by calling ZHETRS_ROOK (uses BLAS 2).

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 ZHETRF_ROOK.

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.

Parameters

in
uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in
n

The number of linear equations, i.e., the order of the matrix A. n >= 0.

in
nrhs

The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0.

inout
A

Double 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.

in
lda

The leading dimension of the array A. lda >= max(1, n).

out
ipiv

Integer array, dimension (n). Details of the interchanges and the block structure of D, as determined by ZHETRF_ROOK.

inout
B

Double 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.

in
ldb

The leading dimension of the array B. ldb >= max(1, n).

out
work

Double complex array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The length of work. lwork >= 1, and for best performance lwork >= max(1, n*NB), where NB is the optimal blocksize for ZHETRF_ROOK. for lwork < n, TRS will be done with Level BLAS 2 for lwork >= n, TRS will be done with Level BLAS 3

out
info

  • = 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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