hetrf_aa_2stage#

Functions

void chetrf_aa_2stage(
    const char*          uplo,
    const INT            n,
          c64*  restrict A,
    const INT            lda,
          c64*  restrict TB,
    const INT            ltb,
          INT*  restrict ipiv,
          INT*  restrict ipiv2,
          c64*  restrict work,
    const INT            lwork,
          INT*           info
);
void chetrf_aa_2stage(const char *uplo, const INT n, c64 *restrict A, const INT lda, c64 *restrict TB, const INT ltb, INT *restrict ipiv, INT *restrict ipiv2, c64 *restrict work, const INT lwork, INT *info)#

CHETRF_AA_2STAGE 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 band matrix with the bandwidth of nb (nb is internally selected and stored in TB[0], and T is LU factorized with partial pivoting).

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, L is stored below (or above) the subdiagonal blocks, when uplo='L' (or 'U').

in
lda

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

out
TB

Array of dimension max(1,ltb). On exit, details of the LU factorization of the band matrix.

in
ltb

The size of the array TB. ltb>=max(1,4*n), internally used to select nb such that ltb>=(3*nb+1)*n. If ltb=-1, then a workspace query is assumed; the routine only calculates the optimal size of ltb, returns this value as the first entry of TB, and no error message related to ltb is issued.

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
ipiv2

Array of dimension n. On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column ipiv2[k].

out
work

Array of dimension max(1,lwork).

in
lwork

The size of work. lwork>=max(1,n), internally used to select nb such that lwork>=n*nb. 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

  • info>0: if info=i, band LU factorization failed on the i-th column

Functions

void zhetrf_aa_2stage(
    const char*          uplo,
    const INT            n,
          c128* restrict A,
    const INT            lda,
          c128* restrict TB,
    const INT            ltb,
          INT*  restrict ipiv,
          INT*  restrict ipiv2,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);
void zhetrf_aa_2stage(const char *uplo, const INT n, c128 *restrict A, const INT lda, c128 *restrict TB, const INT ltb, INT *restrict ipiv, INT *restrict ipiv2, c128 *restrict work, const INT lwork, INT *info)#

ZHETRF_AA_2STAGE 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 band matrix with the bandwidth of nb (nb is internally selected and stored in TB[0], and T is LU factorized with partial pivoting).

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, L is stored below (or above) the subdiagonal blocks, when uplo='L' (or 'U').

in
lda

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

out
TB

Array of dimension max(1,ltb). On exit, details of the LU factorization of the band matrix.

in
ltb

The size of the array TB. ltb>=max(1,4*n), internally used to select nb such that ltb>=(3*nb+1)*n. If ltb=-1, then a workspace query is assumed; the routine only calculates the optimal size of ltb, returns this value as the first entry of TB, and no error message related to ltb is issued.

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
ipiv2

Array of dimension n. On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column ipiv2[k].

out
work

Array of dimension max(1,lwork).

in
lwork

The size of work. lwork>=max(1,n), internally used to select nb such that lwork>=n*nb. 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

  • info>0: if info=i, band LU factorization failed on the i-th column