hetrf_rk#

Functions

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

CHETRF_RK computes the factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman (rook) diagonal pivoting method:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

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.

This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters

in
uplo

Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = ‘U’: Upper triangular = ‘L’: Lower triangular

in
n

The order of the matrix A. n >= 0.

inout
A

Single complex array, dimension (lda, n). On entry, the Hermitian matrix A. On exit, contains: a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D are stored on exit in array E), and b) If UPLO = ‘U’: factor U in the superdiagonal part of A. If UPLO = ‘L’: factor L in the subdiagonal part of A.

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 with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = ‘U’: E(i) = D(i-1,i), i=2:N, E(1) is set to 0; If UPLO = ‘L’: E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

out
ipiv

Integer array, dimension (n). IPIV describes the permutation matrix P in the factorization.

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. For best performance lwork >= n*nb, where nb is the block size. If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

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

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

Functions

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

ZHETRF_RK computes the factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman (rook) diagonal pivoting method:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

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.

This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters

in
uplo

Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = ‘U’: Upper triangular = ‘L’: Lower triangular

in
n

The order of the matrix A. n >= 0.

inout
A

Double complex array, dimension (lda, n). On entry, the Hermitian matrix A. On exit, contains: a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D are stored on exit in array E), and b) If UPLO = ‘U’: factor U in the superdiagonal part of A. If UPLO = ‘L’: factor L in the subdiagonal part of A.

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 with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = ‘U’: E(i) = D(i-1,i), i=2:N, E(1) is set to 0; If UPLO = ‘L’: E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

out
ipiv

Integer array, dimension (n). IPIV describes the permutation matrix P in the factorization.

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. For best performance lwork >= n*nb, where nb is the block size. If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

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

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

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