hetri_3#

Functions

void chetri_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 chetri_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)#

CHETRI_3 computes the inverse of a complex Hermitian indefinite matrix A using the factorization computed by CHETRF_RK or ZHETRF_BK: 

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),
where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

CHETRI_3 sets the leading dimension of the workspace before calling CHETRI_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 CHETRF_RK and ZHETRF_BK. On exit, if info = 0, the Hermitian 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 Hermitian 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 zhetri_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 zhetri_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)#

ZHETRI_3 computes the inverse of a complex Hermitian indefinite matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK: 

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),
where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

ZHETRI_3 sets the leading dimension of the workspace before calling ZHETRI_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 ZHETRF_RK and ZHETRF_BK. On exit, if info = 0, the Hermitian 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 Hermitian 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.

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