gtcon#

Functions

void sgtcon(
    const char*          norm,
    const INT            n,
    const f32*  restrict DL,
    const f32*  restrict D,
    const f32*  restrict DU,
    const f32*  restrict DU2,
    const INT*  restrict ipiv,
    const f32            anorm,
          f32*           rcond,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void sgtcon(const char *norm, const INT n, const f32 *restrict DL, const f32 *restrict D, const f32 *restrict DU, const f32 *restrict DU2, const INT *restrict ipiv, const f32 anorm, f32 *rcond, f32 *restrict work, INT *restrict iwork, INT *info)#

SGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF.

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
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
DL

The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF. Array of dimension (n-1).

in
D

The n diagonal elements of the upper triangular matrix U from the LU factorization of A. Array of dimension (n).

in
DU

The (n-1) elements of the first superdiagonal of U. Array of dimension (n-1).

in
DU2

The (n-2) elements of the second superdiagonal of U. Array of dimension (n-2).

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/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.

out
work

Workspace array of dimension (2*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 dgtcon(
    const char*          norm,
    const INT            n,
    const f64*  restrict DL,
    const f64*  restrict D,
    const f64*  restrict DU,
    const f64*  restrict DU2,
    const INT*  restrict ipiv,
    const f64            anorm,
          f64*           rcond,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void dgtcon(const char *norm, const INT n, const f64 *restrict DL, const f64 *restrict D, const f64 *restrict DU, const f64 *restrict DU2, const INT *restrict ipiv, const f64 anorm, f64 *rcond, f64 *restrict work, INT *restrict iwork, INT *info)#

DGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF.

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
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
DL

The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by DGTTRF. Array of dimension (n-1).

in
D

The n diagonal elements of the upper triangular matrix U from the LU factorization of A. Array of dimension (n).

in
DU

The (n-1) elements of the first superdiagonal of U. Array of dimension (n-1).

in
DU2

The (n-2) elements of the second superdiagonal of U. Array of dimension (n-2).

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/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.

out
work

Workspace array of dimension (2*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 cgtcon(
    const char*          norm,
    const INT            n,
    const c64*  restrict DL,
    const c64*  restrict D,
    const c64*  restrict DU,
    const c64*  restrict DU2,
    const INT*  restrict ipiv,
    const f32            anorm,
          f32*           rcond,
          c64*  restrict work,
          INT*           info
);
void cgtcon(const char *norm, const INT n, const c64 *restrict DL, const c64 *restrict D, const c64 *restrict DU, const c64 *restrict DU2, const INT *restrict ipiv, const f32 anorm, f32 *rcond, c64 *restrict work, INT *info)#

CGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF.

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
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
DL

The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF. Array of dimension (n-1).

in
D

The n diagonal elements of the upper triangular matrix U from the LU factorization of A. Array of dimension (n).

in
DU

The (n-1) elements of the first superdiagonal of U. Array of dimension (n-1).

in
DU2

The (n-2) elements of the second superdiagonal of U. Array of dimension (n-2).

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/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.

out
work

Workspace array of dimension (2*n).

out
info

  • = 0: successful exit

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

Functions

void zgtcon(
    const char*          norm,
    const INT            n,
    const c128* restrict DL,
    const c128* restrict D,
    const c128* restrict DU,
    const c128* restrict DU2,
    const INT*  restrict ipiv,
    const f64            anorm,
          f64*           rcond,
          c128* restrict work,
          INT*           info
);
void zgtcon(const char *norm, const INT n, const c128 *restrict DL, const c128 *restrict D, const c128 *restrict DU, const c128 *restrict DU2, const INT *restrict ipiv, const f64 anorm, f64 *rcond, c128 *restrict work, INT *info)#

ZGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF.

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
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
DL

The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF. Array of dimension (n-1).

in
D

The n diagonal elements of the upper triangular matrix U from the LU factorization of A. Array of dimension (n).

in
DU

The (n-1) elements of the first superdiagonal of U. Array of dimension (n-1).

in
DU2

The (n-2) elements of the second superdiagonal of U. Array of dimension (n-2).

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/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.

out
work

Workspace array of dimension (2*n).

out
info

  • = 0: successful exit

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

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