hetri_3x#

Functions

void chetri_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 chetri_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)#

CHETRI_3X 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.

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 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

Single complex 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

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 zhetri_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 zhetri_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)#

ZHETRI_3X 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.

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 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

Double complex 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

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.

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