hetrf_aa#

Functions

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

CHETRF_AA computes the factorization of a complex Hermitian matrix A using the Aasen’s algorithm.

The form of the factorization is 

A = U**H*T*U  or  A = L*T*L**H

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a Hermitian tridiagonal matrix.

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

Parameters

in
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

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

inout
A

Array of 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, the tridiagonal matrix is stored in the diagonals and the subdiagonals of A just below (or above) the diagonals, and L is stored below (or above) the subdiagonals, when uplo='L' (or 'U').

in
lda

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

out
ipiv

Array of 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].

out
work

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

in
lwork

The length of work. lwork>=1, if n<=1, and lwork>=2*n, otherwise. For optimum performance lwork>=n*(1+nb), where nb is the optimal block size, returned by ILAENV. 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.

out
info

  • info=0: successful exit

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

Functions

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

ZHETRF_AA computes the factorization of a complex Hermitian matrix A using the Aasen’s algorithm.

The form of the factorization is 

A = U**H*T*U  or  A = L*T*L**H

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a Hermitian tridiagonal matrix.

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

Parameters

in
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

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

inout
A

Array of 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, the tridiagonal matrix is stored in the diagonals and the subdiagonals of A just below (or above) the diagonals, and L is stored below (or above) the subdiagonals, when uplo='L' (or 'U').

in
lda

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

out
ipiv

Array of 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].

out
work

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

in
lwork

The length of work. lwork>=1, if n<=1, and lwork>=2*n, otherwise. For optimum performance lwork>=n*(1+nb), where nb is the optimal block size, returned by ILAENV. 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.

out
info

  • info=0: successful exit

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