gecon#

Functions

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

SGECON estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as 

rcond = 1 / ( norm(A) * norm(inv(A)) )

Parameters

in
norm

Specifies whether the 1-norm condition number or the infinity-norm condition number is required:

  • ’1’ or ‘O’: 1-norm

  • ’I’: Infinity-norm

in
n

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

in
A

Array of dimension (lda, n). The factors L and U from the factorization A = P*L*U as computed by sgetrf.

in
lda

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

in
anorm

If norm='1' or 'O', the 1-norm of the original matrix A. If norm='I', the infinity-norm of the original matrix A.

out
rcond

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

out
work

Workspace array of dimension (4*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. NaNs are illegal values for anorm, and they propagate to the output parameter rcond. Infinity is illegal for anorm, and it propagates to the output parameter rcond as 0.

  • info=1: if rcond = NaN, or rcond = Inf, or the computed norm of the inverse of A is 0. In the latter, rcond = 0.

Functions

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

DGECON estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as 

rcond = 1 / ( norm(A) * norm(inv(A)) )

Parameters

in
norm

Specifies whether the 1-norm condition number or the infinity-norm condition number is required:

  • ’1’ or ‘O’: 1-norm

  • ’I’: Infinity-norm

in
n

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

in
A

Array of dimension (lda, n). The factors L and U from the factorization A = P*L*U as computed by dgetrf.

in
lda

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

in
anorm

If norm='1' or 'O', the 1-norm of the original matrix A. If norm='I', the infinity-norm of the original matrix A.

out
rcond

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

out
work

Workspace array of dimension (4*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. NaNs are illegal values for anorm, and they propagate to the output parameter rcond. Infinity is illegal for anorm, and it propagates to the output parameter rcond as 0.

  • info=1: if rcond = NaN, or rcond = Inf, or the computed norm of the inverse of A is 0. In the latter, rcond = 0.

Functions

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

CGECON estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as 

rcond = 1 / ( norm(A) * norm(inv(A)) )

Parameters

in
norm

Specifies whether the 1-norm condition number or the infinity-norm condition number is required:

  • ’1’ or ‘O’: 1-norm

  • ’I’: Infinity-norm

in
n

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

in
A

Complex array of dimension (lda, n). The factors L and U from the factorization A = P*L*U as computed by cgetrf.

in
lda

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

in
anorm

If norm='1' or 'O', the 1-norm of the original matrix A. If norm='I', the infinity-norm of the original matrix A.

out
rcond

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

out
work

Complex workspace array of dimension (2*n).

out
rwork

Real 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. NaNs are illegal values for anorm, and they propagate to the output parameter rcond. Infinity is illegal for anorm, and it propagates to the output parameter rcond as 0.

  • info=1: if rcond = NaN, or rcond = Inf, or the computed norm of the inverse of A is 0. In the latter, rcond = 0.

Functions

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

ZGECON estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as 

rcond = 1 / ( norm(A) * norm(inv(A)) )

Parameters

in
norm

Specifies whether the 1-norm condition number or the infinity-norm condition number is required:

  • ’1’ or ‘O’: 1-norm

  • ’I’: Infinity-norm

in
n

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

in
A

Complex array of dimension (lda, n). The factors L and U from the factorization A = P*L*U as computed by zgetrf.

in
lda

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

in
anorm

If norm='1' or 'O', the 1-norm of the original matrix A. If norm='I', the infinity-norm of the original matrix A.

out
rcond

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

out
work

Complex workspace array of dimension (2*n).

out
rwork

Real 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. NaNs are illegal values for anorm, and they propagate to the output parameter rcond. Infinity is illegal for anorm, and it propagates to the output parameter rcond as 0.

  • info=1: if rcond = NaN, or rcond = Inf, or the computed norm of the inverse of A is 0. In the latter, rcond = 0.