pbcon#

Functions

void spbcon(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const f32*  restrict AB,
    const INT            ldab,
    const f32            anorm,
          f32*           rcond,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void spbcon(const char *uplo, const INT n, const INT kd, const f32 *restrict AB, const INT ldab, const f32 anorm, f32 *rcond, f32 *restrict work, INT *restrict iwork, INT *info)#

SPBCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF.

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 factor stored in AB = ‘L’: Lower triangular factor stored in AB

in
n

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

in
kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in
AB

The triangular factor from SPBTRF. Array of dimension (ldab, n).

in
ldab

The leading dimension of AB. ldab >= kd+1.

in
anorm

The 1-norm of the original matrix A.

out
rcond

The reciprocal condition number.

out
work

Workspace array of dimension (3*n).

out
iwork

Integer workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

void dpbcon(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const f64*  restrict AB,
    const INT            ldab,
    const f64            anorm,
          f64*           rcond,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void dpbcon(const char *uplo, const INT n, const INT kd, const f64 *restrict AB, const INT ldab, const f64 anorm, f64 *rcond, f64 *restrict work, INT *restrict iwork, INT *info)#

DPBCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF.

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 factor stored in AB = ‘L’: Lower triangular factor stored in AB

in
n

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

in
kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in
AB

The triangular factor from DPBTRF. Array of dimension (ldab, n).

in
ldab

The leading dimension of AB. ldab >= kd+1.

in
anorm

The 1-norm of the original matrix A.

out
rcond

The reciprocal condition number.

out
work

Workspace array of dimension (3*n).

out
iwork

Integer workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

void cpbcon(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const c64*  restrict AB,
    const INT            ldab,
    const f32            anorm,
          f32*           rcond,
          c64*  restrict work,
          f32*  restrict rwork,
          INT*           info
);
void cpbcon(const char *uplo, const INT n, const INT kd, const c64 *restrict AB, const INT ldab, const f32 anorm, f32 *rcond, c64 *restrict work, f32 *restrict rwork, INT *info)#

CPBCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF.

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 factor stored in AB = ‘L’: Lower triangular factor stored in AB

in
n

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

in
kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in
AB

The triangular factor from CPBTRF. Array of dimension (ldab, n).

in
ldab

The leading dimension of AB. ldab >= kd+1.

in
anorm

The 1-norm (or infinity-norm) of the Hermitian band matrix A.

out
rcond

The reciprocal condition number.

out
work

Complex workspace array of dimension (2*n).

out
rwork

Real workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

void zpbcon(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const c128* restrict AB,
    const INT            ldab,
    const f64            anorm,
          f64*           rcond,
          c128* restrict work,
          f64*  restrict rwork,
          INT*           info
);
void zpbcon(const char *uplo, const INT n, const INT kd, const c128 *restrict AB, const INT ldab, const f64 anorm, f64 *rcond, c128 *restrict work, f64 *restrict rwork, INT *info)#

ZPBCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF.

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 factor stored in AB = ‘L’: Lower triangular factor stored in AB

in
n

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

in
kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in
AB

The triangular factor from ZPBTRF. Array of dimension (ldab, n).

in
ldab

The leading dimension of AB. ldab >= kd+1.

in
anorm

The 1-norm (or infinity-norm) of the Hermitian band matrix A.

out
rcond

The reciprocal condition number.

out
work

Complex workspace array of dimension (2*n).

out
rwork

Real workspace array of dimension (n).

out
info

  • = 0: successful exit

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

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