hesv_rk#

Functions

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

CHESV_RK 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 = P*U*D*(U**H)*(P**T), if UPLO = ‘U’, or A = P*L*D*(L**H)*(P**T), if UPLO = ‘L’, where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

CHETRF_RK is called to compute the factorization of a complex Hermitian matrix. The factored form of A is then used to solve the system of equations A * X = B by calling BLAS3 routine CHETRS_3.

Parameters

in
uplo

Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = ‘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. On exit, if info = 0, diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK.

in
lda

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

out
E

Single complex array, dimension (n). On exit, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D.

out
ipiv

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

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. If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

  • < 0: if info = -k, the k-th argument had an illegal value

  • > 0: if info = k, the matrix A is singular.

Functions

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

ZHESV_RK 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 = P*U*D*(U**H)*(P**T), if UPLO = ‘U’, or A = P*L*D*(L**H)*(P**T), if UPLO = ‘L’, where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

ZHETRF_RK is called to compute the factorization of a complex Hermitian matrix. The factored form of A is then used to solve the system of equations A * X = B by calling BLAS3 routine ZHETRS_3.

Parameters

in
uplo

Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = ‘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. On exit, if info = 0, diagonal of the block diagonal matrix D and factors U or L as computed by ZHETRF_RK.

in
lda

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

out
E

Double complex array, dimension (n). On exit, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D.

out
ipiv

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

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. If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

  • < 0: if info = -k, the k-th argument had an illegal value

  • > 0: if info = k, the matrix A is singular.

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