---
name: "ptcon"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/ptcon"
---

# ptcon(3)

ptcon: condition number estimate

## NAME

ptcon - ptcon: condition number estimate

## SYNOPSIS

### Functions

subroutine **cptcon** (n, d, e, anorm, rcond, rwork, info)\
 **CPTCON**  subroutine **dptcon** (n, d, e, anorm, rcond, work, info)\
 **DPTCON**  subroutine **sptcon** (n, d, e, anorm, rcond, work, info)\
 **SPTCON**  subroutine **zptcon** (n, d, e, anorm, rcond, rwork, info)\
 **ZPTCON**

## Detailed Description

## Function Documentation

### subroutine cptcon (integer n, real, dimension( \* ) d, complex, dimension( \* ) e, real anorm, real rcond, real, dimension( \* ) rwork, integer info)

**CPTCON**

**Purpose:**

```
!>
!> CPTCON computes the reciprocal of the condition number (in the
!> 1-norm) of a complex Hermitian positive definite tridiagonal matrix
!> using the factorization A = L*D*L**H or A = U**H*D*U computed by
!> CPTTRF.
!>
!> Norm(inv(A)) is computed by a direct method, and the reciprocal of
!> the condition number is computed as
!>                  RCOND = 1 / (ANORM * norm(inv(A))).
!>
```

**Parameters**

*N*

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

*D*

```
!>          D is REAL array, dimension (N)
!>          The n diagonal elements of the diagonal matrix D from the
!>          factorization of A, as computed by CPTTRF.
!>
```

*E*

```
!>          E is COMPLEX array, dimension (N-1)
!>          The (n-1) off-diagonal elements of the unit bidiagonal factor
!>          U or L from the factorization of A, as computed by CPTTRF.
!>
```

*ANORM*

```
!>          ANORM is REAL
!>          The 1-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 the
!>          1-norm of inv(A) computed in this routine.
!>
```

*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

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  The method used is described in Nicholas J. Higham, , SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
!>
```

Definition at line **118** of file **cptcon.f**.

### subroutine dptcon (integer n, double precision, dimension( \* ) d, double precision, dimension( \* ) e, double precision anorm, double precision rcond, double precision, dimension( \* ) work, integer info)

**DPTCON**

**Purpose:**

```
!>
!> DPTCON computes the reciprocal of the condition number (in the
!> 1-norm) of a real symmetric positive definite tridiagonal matrix
!> using the factorization A = L*D*L**T or A = U**T*D*U computed by
!> DPTTRF.
!>
!> Norm(inv(A)) is computed by a direct method, and the reciprocal of
!> the condition number is computed as
!>              RCOND = 1 / (ANORM * norm(inv(A))).
!>
```

**Parameters**

*N*

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

*D*

```
!>          D is DOUBLE PRECISION array, dimension (N)
!>          The n diagonal elements of the diagonal matrix D from the
!>          factorization of A, as computed by DPTTRF.
!>
```

*E*

```
!>          E is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) off-diagonal elements of the unit bidiagonal factor
!>          U or L from the factorization of A,  as computed by DPTTRF.
!>
```

*ANORM*

```
!>          ANORM is DOUBLE PRECISION
!>          The 1-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 the
!>          1-norm of inv(A) computed in this routine.
!>
```

*WORK*

```
!>          WORK 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

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  The method used is described in Nicholas J. Higham, , SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
!>
```

Definition at line **117** of file **dptcon.f**.

### subroutine sptcon (integer n, real, dimension( \* ) d, real, dimension( \* ) e, real anorm, real rcond, real, dimension( \* ) work, integer info)

**SPTCON**

**Purpose:**

```
!>
!> SPTCON computes the reciprocal of the condition number (in the
!> 1-norm) of a real symmetric positive definite tridiagonal matrix
!> using the factorization A = L*D*L**T or A = U**T*D*U computed by
!> SPTTRF.
!>
!> Norm(inv(A)) is computed by a direct method, and the reciprocal of
!> the condition number is computed as
!>              RCOND = 1 / (ANORM * norm(inv(A))).
!>
```

**Parameters**

*N*

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

*D*

```
!>          D is REAL array, dimension (N)
!>          The n diagonal elements of the diagonal matrix D from the
!>          factorization of A, as computed by SPTTRF.
!>
```

*E*

```
!>          E is REAL array, dimension (N-1)
!>          The (n-1) off-diagonal elements of the unit bidiagonal factor
!>          U or L from the factorization of A,  as computed by SPTTRF.
!>
```

*ANORM*

```
!>          ANORM is REAL
!>          The 1-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 the
!>          1-norm of inv(A) computed in this routine.
!>
```

*WORK*

```
!>          WORK 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

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  The method used is described in Nicholas J. Higham, , SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
!>
```

Definition at line **117** of file **sptcon.f**.

### subroutine zptcon (integer n, double precision, dimension( \* ) d, complex\*16, dimension( \* ) e, double precision anorm, double precision rcond, double precision, dimension( \* ) rwork, integer info)

**ZPTCON**

**Purpose:**

```
!>
!> ZPTCON computes the reciprocal of the condition number (in the
!> 1-norm) of a complex Hermitian positive definite tridiagonal matrix
!> using the factorization A = L*D*L**H or A = U**H*D*U computed by
!> ZPTTRF.
!>
!> Norm(inv(A)) is computed by a direct method, and the reciprocal of
!> the condition number is computed as
!>                  RCOND = 1 / (ANORM * norm(inv(A))).
!>
```

**Parameters**

*N*

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

*D*

```
!>          D is DOUBLE PRECISION array, dimension (N)
!>          The n diagonal elements of the diagonal matrix D from the
!>          factorization of A, as computed by ZPTTRF.
!>
```

*E*

```
!>          E is COMPLEX*16 array, dimension (N-1)
!>          The (n-1) off-diagonal elements of the unit bidiagonal factor
!>          U or L from the factorization of A, as computed by ZPTTRF.
!>
```

*ANORM*

```
!>          ANORM is DOUBLE PRECISION
!>          The 1-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 the
!>          1-norm of inv(A) computed in this routine.
!>
```

*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

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  The method used is described in Nicholas J. Higham, , SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
!>
```

Definition at line **118** of file **zptcon.f**.

## Author

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