sytri_3#

Functions

void ssytri_3(
    const char*          uplo,
    const INT            n,
          f32*  restrict A,
    const INT            lda,
    const f32*  restrict E,
    const INT*  restrict ipiv,
          f32*  restrict work,
    const INT            lwork,
          INT*           info
);
void ssytri_3(const char *uplo, const INT n, f32 *restrict A, const INT lda, const f32 *restrict E, const INT *restrict ipiv, f32 *restrict work, const INT lwork, INT *info)#

SSYTRI_3 computes the inverse of a real symmetric indefinite matrix A using the factorization computed by SSYTRF_RK or DSYTRF_BK: 

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.

SSYTRI_3 sets the leading dimension of the workspace before calling SSYTRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters

in
uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = ‘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, diagonal of the block diagonal matrix D and factors U or L as computed by SSYTRF_RK and DSYTRF_BK. On exit, if info = 0, the symmetric inverse of the original matrix.

in
lda

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

in
E

Double precision array, dimension (n). Contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D.

in
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. If n = 0, lwork >= 1, else lwork >= (n+nb+1)*(nb+3). 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) = 0; the matrix is singular.

Functions

void dsytri_3(
    const char*          uplo,
    const INT            n,
          f64*  restrict A,
    const INT            lda,
    const f64*  restrict E,
    const INT*  restrict ipiv,
          f64*  restrict work,
    const INT            lwork,
          INT*           info
);
void dsytri_3(const char *uplo, const INT n, f64 *restrict A, const INT lda, const f64 *restrict E, const INT *restrict ipiv, f64 *restrict work, const INT lwork, INT *info)#

DSYTRI_3 computes the inverse of a real symmetric indefinite matrix A using the factorization computed by DSYTRF_RK or DSYTRF_BK: 

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.

DSYTRI_3 sets the leading dimension of the workspace before calling DSYTRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters

in
uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = ‘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, diagonal of the block diagonal matrix D and factors U or L as computed by DSYTRF_RK and DSYTRF_BK. On exit, if info = 0, the symmetric inverse of the original matrix.

in
lda

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

in
E

Double precision array, dimension (n). Contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D.

in
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. If n = 0, lwork >= 1, else lwork >= (n+nb+1)*(nb+3). 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) = 0; the matrix is singular.

Functions

void csytri_3(
    const char*          uplo,
    const INT            n,
          c64*  restrict A,
    const INT            lda,
    const c64*  restrict E,
    const INT*  restrict ipiv,
          c64*  restrict work,
    const INT            lwork,
          INT*           info
);
void csytri_3(const char *uplo, const INT n, c64 *restrict A, const INT lda, const c64 *restrict E, const INT *restrict ipiv, c64 *restrict work, const INT lwork, INT *info)#

CSYTRI_3 computes the inverse of a complex symmetric indefinite matrix A using the factorization computed by CSYTRF_RK or ZSYTRF_BK: 

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.

CSYTRI_3 sets the leading dimension of the workspace before calling CSYTRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters

in
uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = ‘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

Complex*16 array, dimension (lda, n). On entry, diagonal of the block diagonal matrix D and factors U or L as computed by CSYTRF_RK and ZSYTRF_BK. On exit, if info = 0, the symmetric inverse of the original matrix.

in
lda

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

in
E

Complex*16 array, dimension (n). Contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D.

in
ipiv

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

out
work

Complex*16 array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The length of work. If n = 0, lwork >= 1, else lwork >= (n+nb+1)*(nb+3). 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) = 0; the matrix is singular.

Functions

void zsytri_3(
    const char*          uplo,
    const INT            n,
          c128* restrict A,
    const INT            lda,
    const c128* restrict E,
    const INT*  restrict ipiv,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);
void zsytri_3(const char *uplo, const INT n, c128 *restrict A, const INT lda, const c128 *restrict E, const INT *restrict ipiv, c128 *restrict work, const INT lwork, INT *info)#

ZSYTRI_3 computes the inverse of a complex symmetric indefinite matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK: 

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.

ZSYTRI_3 sets the leading dimension of the workspace before calling ZSYTRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters

in
uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = ‘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

Complex*16 array, dimension (lda, n). On entry, diagonal of the block diagonal matrix D and factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK. On exit, if info = 0, the symmetric inverse of the original matrix.

in
lda

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

in
E

Complex*16 array, dimension (n). Contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D.

in
ipiv

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

out
work

Complex*16 array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The length of work. If n = 0, lwork >= 1, else lwork >= (n+nb+1)*(nb+3). 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) = 0; the matrix is singular.