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 CHETRF_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 transpose 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.

On exit, if info=0, the Hermitian inverse of the original matrix. If uplo='U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; If uplo='L': the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.

Parameters

in
uplo

  • '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

Array of dimension (lda,n). On entry, diagonal of the block diagonal matrix D and factors U or L as computed by chetrf_rk or chetrf_bk:

  • Only diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k)=A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and

  • 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).

in
E

Array of dimension n. On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where if uplo='U': E[i]=D(i-1,i), i=1:n-1, E[0] not referenced; if uplo='L': E[i]=D(i+1,i), i=0:n-2, E[n-1] not referenced. For a 1-by-1 diagonal block D(k), the element E[k] is not referenced in both uplo='U' or uplo='L' cases.

in
ipiv

Array of dimension n. Details of the interchanges and the block structure of D as determined by chetrf_rk or chetrf_bk.

out
work

Array of dimension (n+nb+1,nb+3).

in
nb

Block size.

out
info

  • info=0: successful exit

  • info<0: if info=-i, the i-th argument had an illegal value

  • info>0: if info=i, D(i,i)=0; the matrix is singular and its inverse could not be computed.

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 transpose 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.

On exit, if info=0, the Hermitian inverse of the original matrix. If uplo='U': the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; If uplo='L': the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.

Parameters

in
uplo

  • '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

Array of dimension (lda,n). On entry, diagonal of the block diagonal matrix D and factors U or L as computed by zhetrf_rk or zhetrf_bk:

  • Only diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k)=A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and

  • 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).

in
E

Array of dimension n. On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where if uplo='U': E[i]=D(i-1,i), i=1:n-1, E[0] not referenced; if uplo='L': E[i]=D(i+1,i), i=0:n-2, E[n-1] not referenced. For a 1-by-1 diagonal block D(k), the element E[k] is not referenced in both uplo='U' or uplo='L' cases.

in
ipiv

Array of dimension n. Details of the interchanges and the block structure of D as determined by zhetrf_rk or zhetrf_bk.

out
work

Array of dimension (n+nb+1,nb+3).

in
nb

Block size.

out
info

  • info=0: successful exit

  • info<0: if info=-i, the i-th argument had an illegal value

  • info>0: if info=i, D(i,i)=0; the matrix is singular and its inverse could not be computed.