gtcon

sgtcon

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

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

in

D

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

in

DU

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

in

DU2

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

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/(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

• info=0: successful exit

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

dgtcon

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

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

in

D

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

in

DU

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

in

DU2

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

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/(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

• info=0: successful exit

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

cgtcon

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

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

in

D

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

in

DU

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

in

DU2

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

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/(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

• info=0: successful exit

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

zgtcon

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

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

in

D

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

in

DU

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

in

DU2

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

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/(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

• info=0: successful exit

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