# gtcon - Man Page

gtcon: condition number estimate

## Synopsis

### Functions

subroutine cgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info)
CGTCON
subroutine dgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info)
DGTCON
subroutine sgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info)
SGTCON
subroutine zgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info)
ZGTCON

## Function Documentation

### subroutine cgtcon (character norm, integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info)

CGTCON

Purpose:

``` 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

NORM

```          NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= '1' or 'O':  1-norm;
= 'I':         Infinity-norm.```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.```

DL

```          DL is COMPLEX array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A as computed by CGTTRF.```

D

```          D is COMPLEX array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.```

DU

```          DU is COMPLEX array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.```

DU2

```          DU2 is COMPLEX array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.```

IPIV

```          IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i).  IPIV(i) will always be either
i or i+1; IPIV(i) = i indicates a row interchange was not
required.```

ANORM

```          ANORM is REAL
If NORM = '1' or 'O', the 1-norm of the original matrix A.
If NORM = 'I', the infinity-norm of the original matrix A.```

RCOND

```          RCOND is REAL
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.```

WORK

`          WORK is COMPLEX array, dimension (2*N)`

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 139 of file cgtcon.f.

### subroutine dgtcon (character norm, integer n, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DGTCON

Purpose:

``` 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

NORM

```          NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= '1' or 'O':  1-norm;
= 'I':         Infinity-norm.```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.```

DL

```          DL is DOUBLE PRECISION array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A as computed by DGTTRF.```

D

```          D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.```

DU

```          DU is DOUBLE PRECISION array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.```

DU2

```          DU2 is DOUBLE PRECISION array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.```

IPIV

```          IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i).  IPIV(i) will always be either
i or i+1; IPIV(i) = i indicates a row interchange was not
required.```

ANORM

```          ANORM is DOUBLE PRECISION
If NORM = '1' or 'O', the 1-norm of the original matrix A.
If NORM = 'I', the infinity-norm of the original matrix A.```

RCOND

```          RCOND is DOUBLE PRECISION
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.```

WORK

`          WORK is DOUBLE PRECISION array, dimension (2*N)`

IWORK

`          IWORK is INTEGER array, dimension (N)`

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 144 of file dgtcon.f.

### subroutine sgtcon (character norm, integer n, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2, integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SGTCON

Purpose:

``` 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

NORM

```          NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= '1' or 'O':  1-norm;
= 'I':         Infinity-norm.```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.```

DL

```          DL is REAL array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A as computed by SGTTRF.```

D

```          D is REAL array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.```

DU

```          DU is REAL array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.```

DU2

```          DU2 is REAL array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.```

IPIV

```          IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i).  IPIV(i) will always be either
i or i+1; IPIV(i) = i indicates a row interchange was not
required.```

ANORM

```          ANORM is REAL
If NORM = '1' or 'O', the 1-norm of the original matrix A.
If NORM = 'I', the infinity-norm of the original matrix A.```

RCOND

```          RCOND is REAL
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.```

WORK

`          WORK is REAL array, dimension (2*N)`

IWORK

`          IWORK is INTEGER array, dimension (N)`

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 144 of file sgtcon.f.

### subroutine zgtcon (character norm, integer n, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, integer info)

ZGTCON

Purpose:

``` 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

NORM

```          NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= '1' or 'O':  1-norm;
= 'I':         Infinity-norm.```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.```

DL

```          DL is COMPLEX*16 array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the
LU factorization of A as computed by ZGTTRF.```

D

```          D is COMPLEX*16 array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.```

DU

```          DU is COMPLEX*16 array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.```

DU2

```          DU2 is COMPLEX*16 array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.```

IPIV

```          IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i).  IPIV(i) will always be either
i or i+1; IPIV(i) = i indicates a row interchange was not
required.```

ANORM

```          ANORM is DOUBLE PRECISION
If NORM = '1' or 'O', the 1-norm of the original matrix A.
If NORM = 'I', the infinity-norm of the original matrix A.```

RCOND

```          RCOND is DOUBLE PRECISION
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.```

WORK

`          WORK is COMPLEX*16 array, dimension (2*N)`

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 139 of file zgtcon.f.

## Author

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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK