gbcon#

sgbcon

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

Array of dimension (ldab, n). 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.

in

ldab

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

in

ipiv

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

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

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

dgbcon

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

Array of dimension (ldab, n). 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.

in

ldab

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

in

ipiv

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

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

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

cgbcon

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

Array of dimension (ldab, n). 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.

in

ldab

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

in

ipiv

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

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

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

zgbcon

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

Array of dimension (ldab, n). 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.

in

ldab

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

in

ipiv

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

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

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