---
name: "hecon"
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/hecon"
---

# hecon(3)

{he,sy}con: condition number estimate

## NAME

hecon - {he,sy}con: condition number estimate

## SYNOPSIS

### Functions

subroutine **checon** (uplo, n, a, lda, ipiv, anorm, rcond, work, info)\
 **CHECON**  subroutine **csycon** (uplo, n, a, lda, ipiv, anorm, rcond, work, info)\
 **CSYCON**  subroutine **dsycon** (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info)\
 **DSYCON**  subroutine **ssycon** (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info)\
 **SSYCON**  subroutine **zhecon** (uplo, n, a, lda, ipiv, anorm, rcond, work, info)\
 **ZHECON**  subroutine **zsycon** (uplo, n, a, lda, ipiv, anorm, rcond, work, info)\
 **ZSYCON**

## Detailed Description

## Function Documentation

### subroutine checon (character uplo, integer n, complex, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, real anorm, real rcond, complex, dimension( \* ) work, integer info)

**CHECON**

**Purpose:**

```
!>
!> CHECON estimates the reciprocal of the condition number of a complex
!> Hermitian matrix A using the factorization A = U*D*U**H or
!> A = L*D*L**H computed by CHETRF.
!>
!> 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**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**H;
!>          = 'L':  Lower triangular, form is A = L*D*L**H.
!>
```

*N*

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

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by CHETRF.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by CHETRF.
!>
```

*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 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 **123** of file **checon.f**.

### subroutine csycon (character uplo, integer n, complex, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, real anorm, real rcond, complex, dimension( \* ) work, integer info)

**CSYCON**

**Purpose:**

```
!>
!> CSYCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a complex symmetric matrix A using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by CSYTRF.
!>
!> 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**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>
```

*N*

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

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by CSYTRF.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by CSYTRF.
!>
```

*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 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 **123** of file **csycon.f**.

### subroutine dsycon (character uplo, integer n, double precision, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, double precision anorm, double precision rcond, double precision, dimension( \* ) work, integer, dimension( \* ) iwork, integer info)

**DSYCON**

**Purpose:**

```
!>
!> DSYCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a real symmetric matrix A using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by DSYTRF.
!>
!> 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**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>
```

*N*

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

*A*

```
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by DSYTRF.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by DSYTRF.
!>
```

*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 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 **128** of file **dsycon.f**.

### subroutine ssycon (character uplo, integer n, real, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, real anorm, real rcond, real, dimension( \* ) work, integer, dimension( \* ) iwork, integer info)

**SSYCON**

**Purpose:**

```
!>
!> SSYCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a real symmetric matrix A using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by SSYTRF.
!>
!> 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**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>
```

*N*

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

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by SSYTRF.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by SSYTRF.
!>
```

*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 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 **128** of file **ssycon.f**.

### subroutine zhecon (character uplo, integer n, complex\*16, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, double precision anorm, double precision rcond, complex\*16, dimension( \* ) work, integer info)

**ZHECON**

**Purpose:**

```
!>
!> ZHECON estimates the reciprocal of the condition number of a complex
!> Hermitian matrix A using the factorization A = U*D*U**H or
!> A = L*D*L**H computed by ZHETRF.
!>
!> 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**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**H;
!>          = 'L':  Lower triangular, form is A = L*D*L**H.
!>
```

*N*

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

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by ZHETRF.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by ZHETRF.
!>
```

*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 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 **123** of file **zhecon.f**.

### subroutine zsycon (character uplo, integer n, complex\*16, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, double precision anorm, double precision rcond, complex\*16, dimension( \* ) work, integer info)

**ZSYCON**

**Purpose:**

```
!>
!> ZSYCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a complex symmetric matrix A using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by ZSYTRF.
!>
!> 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**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>
```

*N*

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

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by ZSYTRF.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by ZSYTRF.
!>
```

*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 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 **123** of file **zsycon.f**.

## Author

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