trcon#

Functions

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

STRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for norm(inv(A)), then 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
uplo

‘U’: A is upper triangular; ‘L’: A is lower triangular.

in
diag

‘N’: A is non-unit triangular; ‘U’: A is unit triangular.

in
n

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

in
A

The triangular matrix A. Array of dimension (lda, n). If uplo = ‘U’, the leading n-by-n upper triangular part contains the upper triangular matrix. If uplo = ‘L’, the leading n-by-n lower triangular part contains the lower triangular matrix. If diag = ‘U’, the diagonal elements are not referenced and are assumed to be 1.

in
lda

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

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 (3*n).

out
iwork

Integer workspace array of dimension (n).

out
info

Exit status:

  • = 0: successful exit

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

Functions

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

DTRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for norm(inv(A)), then 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
uplo

‘U’: A is upper triangular; ‘L’: A is lower triangular.

in
diag

‘N’: A is non-unit triangular; ‘U’: A is unit triangular.

in
n

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

in
A

The triangular matrix A. Array of dimension (lda, n). If uplo = ‘U’, the leading n-by-n upper triangular part contains the upper triangular matrix. If uplo = ‘L’, the leading n-by-n lower triangular part contains the lower triangular matrix. If diag = ‘U’, the diagonal elements are not referenced and are assumed to be 1.

in
lda

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

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 (3*n).

out
iwork

Integer workspace array of dimension (n).

out
info

Exit status:

  • = 0: successful exit

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

Functions

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

CTRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for norm(inv(A)), then 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
uplo

‘U’: A is upper triangular; ‘L’: A is lower triangular.

in
diag

‘N’: A is non-unit triangular; ‘U’: A is unit triangular.

in
n

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

in
A

The triangular matrix A. Array of dimension (lda, n). If uplo = ‘U’, the leading n-by-n upper triangular part contains the upper triangular matrix. If uplo = ‘L’, the leading n-by-n lower triangular part contains the lower triangular matrix. If diag = ‘U’, the diagonal elements are not referenced and are assumed to be 1.

in
lda

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

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 (n).

out
info

Exit status:

  • = 0: successful exit

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

Functions

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

ZTRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for norm(inv(A)), then 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
uplo

‘U’: A is upper triangular; ‘L’: A is lower triangular.

in
diag

‘N’: A is non-unit triangular; ‘U’: A is unit triangular.

in
n

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

in
A

The triangular matrix A. Array of dimension (lda, n). If uplo = ‘U’, the leading n-by-n upper triangular part contains the upper triangular matrix. If uplo = ‘L’, the leading n-by-n lower triangular part contains the lower triangular matrix. If diag = ‘U’, the diagonal elements are not referenced and are assumed to be 1.

in
lda

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

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 (n).

out
info

Exit status:

  • = 0: successful exit

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

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