sytrf_rook#

Functions

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

SSYTRF_ROOK computes the factorization of a real symmetric matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method.

The form of the factorization is

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

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

= ‘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, the block diagonal matrix D and the multipliers used to obtain the factor U or L.

in
lda

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

out
ipiv

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

out
work

Double precision 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, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.

Functions

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

DSYTRF_ROOK computes the factorization of a real symmetric matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method.

The form of the factorization is

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

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

= ‘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, the block diagonal matrix D and the multipliers used to obtain the factor U or L.

in
lda

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

out
ipiv

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

out
work

Double precision 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, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.

Functions

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

CSYTRF_ROOK computes the factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method.

The form of the factorization is

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

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

= ‘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, the block diagonal matrix D and the multipliers used to obtain the factor U or L.

in
lda

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

out
ipiv

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

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, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.

Functions

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

ZSYTRF_ROOK computes the factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method.

The form of the factorization is

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

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

= ‘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, the block diagonal matrix D and the multipliers used to obtain the factor U or L.

in
lda

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

out
ipiv

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

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, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.