spcon#

Functions

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

SSPCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF.

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**T

  • 'L': Lower triangular, form is A = L*D*L**T

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 ssptrf, 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 ssptrf.

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
iwork

Integer workspace array of dimension n.

out
info

  • info=0: successful exit

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

Functions

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

DSPCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF.

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**T

  • 'L': Lower triangular, form is A = L*D*L**T

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 dsptrf, 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 dsptrf.

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
iwork

Integer workspace array of dimension n.

out
info

  • info=0: successful exit

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

Functions

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

CSPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF.

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**T

  • 'L': Lower triangular, form is A = L*D*L**T

in
n

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

in
AP

Complex 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 csptrf, 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 csptrf.

in
anorm

The 1-norm of the original matrix A.

out
rcond

The reciprocal of the condition number of the matrix A.

out
work

Complex 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 zspcon(
    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 zspcon(const char *uplo, const INT n, const c128 *restrict AP, const INT *restrict ipiv, const f64 anorm, f64 *rcond, c128 *restrict work, INT *info)#

ZSPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF.

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**T

  • 'L': Lower triangular, form is A = L*D*L**T

in
n

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

in
AP

Complex 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 zsptrf, 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 zsptrf.

in
anorm

The 1-norm of the original matrix A.

out
rcond

The reciprocal of the condition number of the matrix A.

out
work

Complex 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