hpcon#

Functions

void chpcon(
    const char*          uplo,
    const INT            n,
    const c64*  restrict AP,
    const INT*  restrict ipiv,
    const f32            anorm,
          f32*           rcond,
          c64*  restrict work,
          INT*           info
);
void chpcon(const char *uplo, const INT n, const c64 *restrict AP, const INT *restrict ipiv, const f32 anorm, f32 *rcond, c64 *restrict work, INT *info)#

CHPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by chptrf.

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

Parameters

in
uplo

  • 'U': Upper triangular, form is A = U*D*U**H

  • 'L': Lower triangular, form is A = L*D*L**H

in
n

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

in
AP

Array of dimension n*(n+1)/2. The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by chptrf, stored as a packed triangular matrix.

in
ipiv

Array of dimension n. Details of the interchanges and the block structure of D as determined by chptrf.

in
anorm

The 1-norm of the original matrix A.

out
rcond

The reciprocal of the condition number of the matrix A.

out
work

Workspace array of dimension 2*n.

out
info

  • info=0: successful exit

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

Functions

void zhpcon(
    const char*          uplo,
    const INT            n,
    const c128* restrict AP,
    const INT*  restrict ipiv,
    const f64            anorm,
          f64*           rcond,
          c128* restrict work,
          INT*           info
);
void zhpcon(const char *uplo, const INT n, const c128 *restrict AP, const INT *restrict ipiv, const f64 anorm, f64 *rcond, c128 *restrict work, INT *info)#

ZHPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by zhptrf.

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

Parameters

in
uplo

  • 'U': Upper triangular, form is A = U*D*U**H

  • 'L': Lower triangular, form is A = L*D*L**H

in
n

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

in
AP

Array of dimension n*(n+1)/2. The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by zhptrf, stored as a packed triangular matrix.

in
ipiv

Array of dimension n. Details of the interchanges and the block structure of D as determined by zhptrf.

in
anorm

The 1-norm of the original matrix A.

out
rcond

The reciprocal of the condition number of the matrix A.

out
work

Workspace array of dimension 2*n.

out
info

  • info=0: successful exit

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