sytri_3x#

Functions

void ssytri_3x(
    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            nb,
          INT*           info
);
void ssytri_3x(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 nb, INT *info)#

SSYTRI_3X 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.

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 (n+nb+1, nb+3).

in
nb

Block size.

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_3x(
    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            nb,
          INT*           info
);
void dsytri_3x(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 nb, INT *info)#

DSYTRI_3X 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.

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 (n+nb+1, nb+3).

in
nb

Block size.

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_3x(
    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            nb,
          INT*           info
);
void csytri_3x(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 nb, INT *info)#

CSYTRI_3X 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.

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

Single complex 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

Single complex 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

Single complex array, dimension (n+nb+1, nb+3).

in
nb

Block size.

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_3x(
    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            nb,
          INT*           info
);
void zsytri_3x(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 nb, INT *info)#

ZSYTRI_3X 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.

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 complex 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

Double complex 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 complex array, dimension (n+nb+1, nb+3).

in
nb

Block size.

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.