sytrf_rk#

Functions

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

SSYTRF_RK computes the factorization of a real symmetric matrix A using the bounded Bunch-Kaufman (rook) diagonal pivoting method:

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

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, 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

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

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, contains: a) ONLY diagonal elements of the symmetric 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 precision array, dimension (n). On exit, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D.

out
ipiv

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

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, the matrix A is singular.

Functions

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

DSYTRF_RK computes the factorization of a real symmetric matrix A using the bounded Bunch-Kaufman (rook) diagonal pivoting method:

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

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, 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

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

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, contains: a) ONLY diagonal elements of the symmetric 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 precision array, dimension (n). On exit, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D.

out
ipiv

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

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, the matrix A is singular.

Functions

void csytrf_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 csytrf_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)#

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

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

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, 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

Specifies whether the upper or lower triangular part of the symmetric 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 symmetric matrix A. On exit, contains: a) ONLY diagonal elements of the symmetric 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 symmetric block diagonal matrix D.

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 zsytrf_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 zsytrf_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)#

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

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

where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, 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

Specifies whether the upper or lower triangular part of the symmetric 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 symmetric matrix A. On exit, contains: a) ONLY diagonal elements of the symmetric 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 symmetric block diagonal matrix D.

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.