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man pages->IRIX man pages -> complib/ztpcon (3)
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### Contents

```
ZTPCON(3F)							    ZTPCON(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZTPCON(	NORM, UPLO, DIAG, N, AP, RCOND,	WORK, RWORK, INFO )

CHARACTER	DIAG, NORM, UPLO

INTEGER	INFO, N

DOUBLE		PRECISION RCOND

DOUBLE		PRECISION RWORK( * )

COMPLEX*16	AP( * ), WORK( * )
```

### PURPOSE[Toc][Back]

```     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)) ).

```

### ARGUMENTS[Toc][Back]

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

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

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

N	     (input) INTEGER
The order of the matrix A.	 N >= 0.

AP	     (input) 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.

Page 1

ZTPCON(3F)							    ZTPCON(3F)

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

WORK    (workspace) COMPLEX*16 array, dimension (2*N)

RWORK   (workspace) DOUBLE	PRECISION array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
ZTPCON(3F)							    ZTPCON(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZTPCON(	NORM, UPLO, DIAG, N, AP, RCOND,	WORK, RWORK, INFO )

CHARACTER	DIAG, NORM, UPLO

INTEGER	INFO, N

DOUBLE		PRECISION RCOND

DOUBLE		PRECISION RWORK( * )

COMPLEX*16	AP( * ), WORK( * )
```

### PURPOSE[Toc][Back]

```     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)) ).

```

### ARGUMENTS[Toc][Back]

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

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

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

N	     (input) INTEGER
The order of the matrix A.	 N >= 0.

AP	     (input) 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.

Page 1

ZTPCON(3F)							    ZTPCON(3F)

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

WORK    (workspace) COMPLEX*16 array, dimension (2*N)

RWORK   (workspace) DOUBLE	PRECISION array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

PPPPaaaaggggeeee 2222```
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