sytrf_aa_2stage#

Functions

void ssytrf_aa_2stage(
    const char*          uplo,
    const INT            n,
          f32*  restrict A,
    const INT            lda,
          f32*  restrict TB,
    const INT            ltb,
          INT*  restrict ipiv,
          INT*  restrict ipiv2,
          f32*  restrict work,
    const INT            lwork,
          INT*           info
);
void ssytrf_aa_2stage(const char *uplo, const INT n, f32 *restrict A, const INT lda, f32 *restrict TB, const INT ltb, INT *restrict ipiv, INT *restrict ipiv2, f32 *restrict work, const INT lwork, INT *info)#

SSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A using the Aasen’s algorithm.

The form of the factorization is

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

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a symmetric 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

Double precision array, dimension (lda, n). On entry, the symmetric matrix A. On exit, L is stored below (or above) the subdiagonal blocks.

in
lda

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

out
TB

Double precision array, 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). If ltb = -1, then a workspace query is assumed.

out
ipiv

Integer array, dimension (n). On exit, details of the interchanges.

out
ipiv2

Integer array, dimension (n). On exit, details of the interchanges in T.

out
work

Double precision workspace of size (max(1, lwork)).

in
lwork

The size of work. lwork >= max(1, n). 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, band LU factorization failed on i-th column

Functions

void dsytrf_aa_2stage(
    const char*          uplo,
    const INT            n,
          f64*  restrict A,
    const INT            lda,
          f64*  restrict TB,
    const INT            ltb,
          INT*  restrict ipiv,
          INT*  restrict ipiv2,
          f64*  restrict work,
    const INT            lwork,
          INT*           info
);
void dsytrf_aa_2stage(const char *uplo, const INT n, f64 *restrict A, const INT lda, f64 *restrict TB, const INT ltb, INT *restrict ipiv, INT *restrict ipiv2, f64 *restrict work, const INT lwork, INT *info)#

DSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A using the Aasen’s algorithm.

The form of the factorization is

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

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a symmetric 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

Double precision array, dimension (lda, n). On entry, the symmetric matrix A. On exit, L is stored below (or above) the subdiagonal blocks.

in
lda

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

out
TB

Double precision array, 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). If ltb = -1, then a workspace query is assumed.

out
ipiv

Integer array, dimension (n). On exit, details of the interchanges.

out
ipiv2

Integer array, dimension (n). On exit, details of the interchanges in T.

out
work

Double precision workspace of size (max(1, lwork)).

in
lwork

The size of work. lwork >= max(1, n). 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, band LU factorization failed on i-th column

Functions

void csytrf_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 csytrf_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)#

CSYTRF_AA_2STAGE computes the factorization of a complex symmetric matrix A using the Aasen’s algorithm.

The form of the factorization is

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

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a complex symmetric 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

Single complex array, dimension (lda, n). On entry, the symmetric matrix A. On exit, L is stored below (or above) the subdiagonal blocks.

in
lda

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

out
TB

Single complex array, 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). If ltb = -1, then a workspace query is assumed.

out
ipiv

Integer array, dimension (n). On exit, details of the interchanges.

out
ipiv2

Integer array, dimension (n). On exit, details of the interchanges in T.

out
work

Single complex workspace of size (max(1, lwork)).

in
lwork

The size of work. lwork >= max(1, n). 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, band LU factorization failed on i-th column

Functions

void zsytrf_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 zsytrf_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)#

ZSYTRF_AA_2STAGE computes the factorization of a complex symmetric matrix A using the Aasen’s algorithm.

The form of the factorization is

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

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a complex symmetric 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

Double complex array, dimension (lda, n). On entry, the symmetric matrix A. On exit, L is stored below (or above) the subdiagonal blocks.

in
lda

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

out
TB

Double complex array, 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). If ltb = -1, then a workspace query is assumed.

out
ipiv

Integer array, dimension (n). On exit, details of the interchanges.

out
ipiv2

Integer array, dimension (n). On exit, details of the interchanges in T.

out
work

Double complex workspace of size (max(1, lwork)).

in
lwork

The size of work. lwork >= max(1, n). 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, band LU factorization failed on i-th column