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 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.

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.

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 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; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

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_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 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.

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.

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 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; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

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.