hecon_3#

Functions

void checon_3(
    const char*          uplo,
    const INT            n,
    const c64*  restrict A,
    const INT            lda,
    const c64*  restrict E,
    const INT*  restrict ipiv,
    const f32            anorm,
          f32*           rcond,
          c64*  restrict work,
          INT*           info
);
void checon_3(const char *uplo, const INT n, const c64 *restrict A, const INT lda, const c64 *restrict E, const INT *restrict ipiv, const f32 anorm, f32 *rcond, c64 *restrict work, INT *info)#

CHECON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian 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.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). This routine uses BLAS3 solver CHETRS_3.

Parameters

in
uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = ‘U’: Upper triangular, form is A = P*U*D*(U**H)*(P**T); = ‘L’: Lower triangular, form is A = P*L*D*(L**H)*(P**T).

in
n

The order of the matrix A. n >= 0.

in
A

Single complex array, dimension (lda, n). Diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK and ZHETRF_BK: a) 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 b) 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

Single complex array, dimension (n). Contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks.

in
ipiv

Integer array, dimension (n). Details of the interchanges and the block structure of D as determined by CHETRF_RK or ZHETRF_BK.

in
anorm

The 1-norm of the original matrix A.

out
rcond

The reciprocal of the condition number of the matrix A, computed as rcond = 1/(anorm * ainvnm).

out
work

Single complex array, dimension (2*n).

out
info

  • = 0: successful exit

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

Functions

void zhecon_3(
    const char*          uplo,
    const INT            n,
    const c128* restrict A,
    const INT            lda,
    const c128* restrict E,
    const INT*  restrict ipiv,
    const f64            anorm,
          f64*           rcond,
          c128* restrict work,
          INT*           info
);
void zhecon_3(const char *uplo, const INT n, const c128 *restrict A, const INT lda, const c128 *restrict E, const INT *restrict ipiv, const f64 anorm, f64 *rcond, c128 *restrict work, INT *info)#

ZHECON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian 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.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). This routine uses BLAS3 solver ZHETRS_3.

Parameters

in
uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = ‘U’: Upper triangular, form is A = P*U*D*(U**H)*(P**T); = ‘L’: Lower triangular, form is A = P*L*D*(L**H)*(P**T).

in
n

The order of the matrix A. n >= 0.

in
A

Double complex array, dimension (lda, n). Diagonal of the block diagonal matrix D and factors U or L as computed by ZHETRF_RK and ZHETRF_BK: a) 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 b) 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

Double complex array, dimension (n). Contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks.

in
ipiv

Integer array, dimension (n). Details of the interchanges and the block structure of D as determined by ZHETRF_RK or ZHETRF_BK.

in
anorm

The 1-norm of the original matrix A.

out
rcond

The reciprocal of the condition number of the matrix A, computed as rcond = 1/(anorm * ainvnm).

out
work

Double complex array, dimension (2*n).

out
info

  • = 0: successful exit

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

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