ppcon#

Functions

void sppcon(
    const char*          uplo,
    const INT            n,
    const f32*  restrict AP,
    const f32            anorm,
          f32*           rcond,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void sppcon(const char *uplo, const INT n, const f32 *restrict AP, const f32 anorm, f32 *rcond, f32 *restrict work, INT *restrict iwork, INT *info)#

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

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
AP

The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise in a linear array. Array of dimension (n*(n+1)/2).

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

Workspace array of dimension (3*n).

out
iwork

Integer workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

void dppcon(
    const char*          uplo,
    const INT            n,
    const f64*  restrict AP,
    const f64            anorm,
          f64*           rcond,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void dppcon(const char *uplo, const INT n, const f64 *restrict AP, const f64 anorm, f64 *rcond, f64 *restrict work, INT *restrict iwork, INT *info)#

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

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
AP

The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise in a linear array. Array of dimension (n*(n+1)/2).

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

Workspace array of dimension (3*n).

out
iwork

Integer workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

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

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

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
AP

The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise in a linear array. Array of dimension (n*(n+1)/2).

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 workspace array of dimension (2*n).

out
rwork

Single precision workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

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

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

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
AP

The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise in a linear array. Array of dimension (n*(n+1)/2).

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 workspace array of dimension (2*n).

out
rwork

Double precision workspace array of dimension (n).

out
info

  • = 0: successful exit

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

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