pocon#

Functions

void spocon(
    const char*          uplo,
    const INT            n,
    const f32*  restrict A,
    const INT            lda,
    const f32            anorm,
          f32*           rcond,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void spocon(const char *uplo, const INT n, const f32 *restrict A, const INT lda, const f32 anorm, f32 *rcond, f32 *restrict work, INT *restrict iwork, INT *info)#

SPOCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF.

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 triangle of A is stored = ‘L’: Lower triangle of A is stored

in
n

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

in
A

The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by spotrf. Array of dimension (lda, n).

in
lda

The leading dimension of the array A. lda >= max(1, n).

in
anorm

The 1-norm (or infinity-norm) of the symmetric matrix A.

out
rcond

The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM).

out
work

Double precision array, dimension (3*n).

out
iwork

Integer array, dimension (n).

out
info

  • = 0: successful exit

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

Functions

void dpocon(
    const char*          uplo,
    const INT            n,
    const f64*  restrict A,
    const INT            lda,
    const f64            anorm,
          f64*           rcond,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void dpocon(const char *uplo, const INT n, const f64 *restrict A, const INT lda, const f64 anorm, f64 *rcond, f64 *restrict work, INT *restrict iwork, INT *info)#

DPOCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF.

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 triangle of A is stored = ‘L’: Lower triangle of A is stored

in
n

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

in
A

The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by dpotrf. Array of dimension (lda, n).

in
lda

The leading dimension of the array A. lda >= max(1, n).

in
anorm

The 1-norm (or infinity-norm) of the symmetric matrix A.

out
rcond

The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM).

out
work

Double precision array, dimension (3*n).

out
iwork

Integer array, dimension (n).

out
info

  • = 0: successful exit

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

Functions

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

CPOCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.

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 triangle of A is stored = ‘L’: Lower triangle of A is stored

in
n

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

in
A

The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by cpotrf. Complex array of dimension (lda, n).

in
lda

The leading dimension of the array A. lda >= max(1, n).

in
anorm

The 1-norm (or infinity-norm) of the Hermitian matrix A.

out
rcond

The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM).

out
work

Complex array, dimension (2*n).

out
rwork

Single precision array, dimension (n).

out
info

  • = 0: successful exit

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

Functions

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

ZPOCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.

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 triangle of A is stored = ‘L’: Lower triangle of A is stored

in
n

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

in
A

The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by zpotrf. Complex array of dimension (lda, n).

in
lda

The leading dimension of the array A. lda >= max(1, n).

in
anorm

The 1-norm (or infinity-norm) of the Hermitian matrix A.

out
rcond

The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM).

out
work

Complex array, dimension (2*n).

out
rwork

Double precision array, dimension (n).

out
info

  • = 0: successful exit

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

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