gbcon#

Functions

void sgbcon(
    const char*          norm,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const f32*  restrict AB,
    const INT            ldab,
    const INT*  restrict ipiv,
    const f32            anorm,
          f32*           rcond,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void sgbcon(const char *norm, const INT n, const INT kl, const INT ku, const f32 *restrict AB, const INT ldab, const INT *restrict ipiv, const f32 anorm, f32 *rcond, f32 *restrict work, INT *restrict iwork, INT *info)#

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

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
kl

The number of subdiagonals within the band of A (kl >= 0).

in
ku

The number of superdiagonals within the band of A (ku >= 0).

in
AB

The LU factorization of the band matrix A, as computed by sgbtrf. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku, and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku. Array of dimension (ldab, n).

in
ldab

The leading dimension of the array AB (ldab >= 2*kl+ku+1).

in
ipiv

The pivot indices; for 0 <= i < n, row i of the matrix was interchanged with row ipiv[i]. Array of dimension 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 (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 dgbcon(
    const char*          norm,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const f64*  restrict AB,
    const INT            ldab,
    const INT*  restrict ipiv,
    const f64            anorm,
          f64*           rcond,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void dgbcon(const char *norm, const INT n, const INT kl, const INT ku, const f64 *restrict AB, const INT ldab, const INT *restrict ipiv, const f64 anorm, f64 *rcond, f64 *restrict work, INT *restrict iwork, INT *info)#

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

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
kl

The number of subdiagonals within the band of A (kl >= 0).

in
ku

The number of superdiagonals within the band of A (ku >= 0).

in
AB

The LU factorization of the band matrix A, as computed by dgbtrf. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku, and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku. Array of dimension (ldab, n).

in
ldab

The leading dimension of the array AB (ldab >= 2*kl+ku+1).

in
ipiv

The pivot indices; for 0 <= i < n, row i of the matrix was interchanged with row ipiv[i]. Array of dimension 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 (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 cgbcon(
    const char*          norm,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const c64*  restrict AB,
    const INT            ldab,
    const INT*  restrict ipiv,
    const f32            anorm,
          f32*           rcond,
          c64*  restrict work,
          f32*  restrict rwork,
          INT*           info
);
void cgbcon(const char *norm, const INT n, const INT kl, const INT ku, const c64 *restrict AB, const INT ldab, const INT *restrict ipiv, const f32 anorm, f32 *rcond, c64 *restrict work, f32 *restrict rwork, INT *info)#

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

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
kl

The number of subdiagonals within the band of A (kl >= 0).

in
ku

The number of superdiagonals within the band of A (ku >= 0).

in
AB

The LU factorization of the band matrix A, as computed by cgbtrf. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku, and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku. Array of dimension (ldab, n).

in
ldab

The leading dimension of the array AB (ldab >= 2*kl+ku+1).

in
ipiv

The pivot indices; for 0 <= i < n, row i of the matrix was interchanged with row ipiv[i]. Array of dimension 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 (n).

out
info

Exit status:

  • = 0: successful exit

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

Functions

void zgbcon(
    const char*          norm,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const c128* restrict AB,
    const INT            ldab,
    const INT*  restrict ipiv,
    const f64            anorm,
          f64*           rcond,
          c128* restrict work,
          f64*  restrict rwork,
          INT*           info
);
void zgbcon(const char *norm, const INT n, const INT kl, const INT ku, const c128 *restrict AB, const INT ldab, const INT *restrict ipiv, const f64 anorm, f64 *rcond, c128 *restrict work, f64 *restrict rwork, INT *info)#

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

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
kl

The number of subdiagonals within the band of A (kl >= 0).

in
ku

The number of superdiagonals within the band of A (ku >= 0).

in
AB

The LU factorization of the band matrix A, as computed by zgbtrf. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku, and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku. Array of dimension (ldab, n).

in
ldab

The leading dimension of the array AB (ldab >= 2*kl+ku+1).

in
ipiv

The pivot indices; for 0 <= i < n, row i of the matrix was interchanged with row ipiv[i]. Array of dimension 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 (n).

out
info

Exit status:

  • = 0: successful exit

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

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