# tpcon - Man Page

tpcon: condition number estimate

## Synopsis

### Functions

subroutine ctpcon (norm, uplo, diag, n, ap, rcond, work, rwork, info)
CTPCON
subroutine dtpcon (norm, uplo, diag, n, ap, rcond, work, iwork, info)
DTPCON
subroutine stpcon (norm, uplo, diag, n, ap, rcond, work, iwork, info)
STPCON
subroutine ztpcon (norm, uplo, diag, n, ap, rcond, work, rwork, info)
ZTPCON

## Function Documentation

### subroutine ctpcon (character norm, character uplo, character diag, integer n, complex, dimension( * ) ap, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CTPCON

Purpose:

``` CTPCON estimates the reciprocal of the condition number of a packed
triangular matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then the reciprocal of the condition number is
computed as
RCOND = 1 / ( norm(A) * 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.```

UPLO

```          UPLO is CHARACTER*1
= 'U':  A is upper triangular;
= 'L':  A is lower triangular.```

DIAG

```          DIAG is CHARACTER*1
= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.```

N

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

AP

```          AP is COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array.  The j-th column of A is stored in the array
AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.```

RCOND

```          RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).```

WORK

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

RWORK

`          RWORK is REAL 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

NAG Ltd.

Definition at line 128 of file ctpcon.f.

### subroutine dtpcon (character norm, character uplo, character diag, integer n, double precision, dimension( * ) ap, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DTPCON

Purpose:

``` DTPCON estimates the reciprocal of the condition number of a packed
triangular matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then the reciprocal of the condition number is
computed as
RCOND = 1 / ( norm(A) * 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.```

UPLO

```          UPLO is CHARACTER*1
= 'U':  A is upper triangular;
= 'L':  A is lower triangular.```

DIAG

```          DIAG is CHARACTER*1
= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.```

N

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

AP

```          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array.  The j-th column of A is stored in the array
AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.```

RCOND

```          RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).```

WORK

`          WORK is DOUBLE PRECISION array, dimension (3*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

NAG Ltd.

Definition at line 128 of file dtpcon.f.

### subroutine stpcon (character norm, character uplo, character diag, integer n, real, dimension( * ) ap, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

STPCON

Purpose:

``` STPCON estimates the reciprocal of the condition number of a packed
triangular matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then the reciprocal of the condition number is
computed as
RCOND = 1 / ( norm(A) * 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.```

UPLO

```          UPLO is CHARACTER*1
= 'U':  A is upper triangular;
= 'L':  A is lower triangular.```

DIAG

```          DIAG is CHARACTER*1
= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.```

N

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

AP

```          AP is REAL array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array.  The j-th column of A is stored in the array
AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.```

RCOND

```          RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).```

WORK

`          WORK is REAL array, dimension (3*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

NAG Ltd.

Definition at line 128 of file stpcon.f.

### subroutine ztpcon (character norm, character uplo, character diag, integer n, complex*16, dimension( * ) ap, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZTPCON

Purpose:

``` ZTPCON estimates the reciprocal of the condition number of a packed
triangular matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then the reciprocal of the condition number is
computed as
RCOND = 1 / ( norm(A) * 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.```

UPLO

```          UPLO is CHARACTER*1
= 'U':  A is upper triangular;
= 'L':  A is lower triangular.```

DIAG

```          DIAG is CHARACTER*1
= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.```

N

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

AP

```          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array.  The j-th column of A is stored in the array
AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.```

RCOND

```          RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).```

WORK

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

RWORK

`          RWORK is DOUBLE PRECISION 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