---
name: "gbcon"
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/gbcon"
---

# gbcon(3)

gbcon: condition number estimate

## NAME

gbcon - gbcon: condition number estimate

## SYNOPSIS

### Functions

subroutine **cgbcon** (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, rwork, info)\
 **CGBCON**  subroutine **dgbcon** (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, iwork, info)\
 **DGBCON**  subroutine **sgbcon** (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, iwork, info)\
 **SGBCON**  subroutine **zgbcon** (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, rwork, info)\
 **ZGBCON**

## Detailed Description

## Function Documentation

### subroutine cgbcon (character norm, integer n, integer kl, integer ku, complex, dimension( ldab, \* ) ab, integer ldab, integer, dimension( \* ) ipiv, real anorm, real rcond, complex, dimension( \* ) work, real, dimension( \* ) rwork, integer info)

**CGBCON**

**Purpose:**

```
!>
!> CGBCON estimates the reciprocal of the condition number of a complex
!> general band matrix A, in either the 1-norm or the infinity-norm,
!> using the LU factorization computed by CGBTRF.
!>
!> An estimate is obtained for norm(inv(A)), and 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.
!>
```

*N*

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

*KL*

```
!>          KL is INTEGER
!>          The number of subdiagonals within the band of A.  KL >= 0.
!>
```

*KU*

```
!>          KU is INTEGER
!>          The number of superdiagonals within the band of A.  KU >= 0.
!>
```

*AB*

```
!>          AB is COMPLEX array, dimension (LDAB,N)
!>          Details of the LU factorization of the band matrix A, as
!>          computed by CGBTRF.  U is stored as an upper triangular band
!>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
!>          the multipliers used during the factorization are stored in
!>          rows KL+KU+2 to 2*KL+KU+1.
!>
```

*LDAB*

```
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
!>
```

*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).
!>
```

*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/(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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **145** of file **cgbcon.f**.

### subroutine dgbcon (character norm, integer n, integer kl, integer ku, double precision, dimension( ldab, \* ) ab, integer ldab, integer, dimension( \* ) ipiv, double precision anorm, double precision rcond, double precision, dimension( \* ) work, integer, dimension( \* ) iwork, integer info)

**DGBCON**

**Purpose:**

```
!>
!> DGBCON estimates the reciprocal of the condition number of a real
!> general band matrix A, in either the 1-norm or the infinity-norm,
!> using the LU factorization computed by DGBTRF.
!>
!> An estimate is obtained for norm(inv(A)), and 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.
!>
```

*N*

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

*KL*

```
!>          KL is INTEGER
!>          The number of subdiagonals within the band of A.  KL >= 0.
!>
```

*KU*

```
!>          KU is INTEGER
!>          The number of superdiagonals within the band of A.  KU >= 0.
!>
```

*AB*

```
!>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
!>          Details of the LU factorization of the band matrix A, as
!>          computed by DGBTRF.  U is stored as an upper triangular band
!>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
!>          the multipliers used during the factorization are stored in
!>          rows KL+KU+2 to 2*KL+KU+1.
!>
```

*LDAB*

```
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
!>
```

*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).
!>
```

*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/(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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **144** of file **dgbcon.f**.

### subroutine sgbcon (character norm, integer n, integer kl, integer ku, real, dimension( ldab, \* ) ab, integer ldab, integer, dimension( \* ) ipiv, real anorm, real rcond, real, dimension( \* ) work, integer, dimension( \* ) iwork, integer info)

**SGBCON**

**Purpose:**

```
!>
!> SGBCON estimates the reciprocal of the condition number of a real
!> general band matrix A, in either the 1-norm or the infinity-norm,
!> using the LU factorization computed by SGBTRF.
!>
!> An estimate is obtained for norm(inv(A)), and 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.
!>
```

*N*

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

*KL*

```
!>          KL is INTEGER
!>          The number of subdiagonals within the band of A.  KL >= 0.
!>
```

*KU*

```
!>          KU is INTEGER
!>          The number of superdiagonals within the band of A.  KU >= 0.
!>
```

*AB*

```
!>          AB is REAL array, dimension (LDAB,N)
!>          Details of the LU factorization of the band matrix A, as
!>          computed by SGBTRF.  U is stored as an upper triangular band
!>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
!>          the multipliers used during the factorization are stored in
!>          rows KL+KU+2 to 2*KL+KU+1.
!>
```

*LDAB*

```
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
!>
```

*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).
!>
```

*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/(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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **144** of file **sgbcon.f**.

### subroutine zgbcon (character norm, integer n, integer kl, integer ku, complex\*16, dimension( ldab, \* ) ab, integer ldab, integer, dimension( \* ) ipiv, double precision anorm, double precision rcond, complex\*16, dimension( \* ) work, double precision, dimension( \* ) rwork, integer info)

**ZGBCON**

**Purpose:**

```
!>
!> ZGBCON estimates the reciprocal of the condition number of a complex
!> general band matrix A, in either the 1-norm or the infinity-norm,
!> using the LU factorization computed by ZGBTRF.
!>
!> An estimate is obtained for norm(inv(A)), and 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.
!>
```

*N*

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

*KL*

```
!>          KL is INTEGER
!>          The number of subdiagonals within the band of A.  KL >= 0.
!>
```

*KU*

```
!>          KU is INTEGER
!>          The number of superdiagonals within the band of A.  KU >= 0.
!>
```

*AB*

```
!>          AB is COMPLEX*16 array, dimension (LDAB,N)
!>          Details of the LU factorization of the band matrix A, as
!>          computed by ZGBTRF.  U is stored as an upper triangular band
!>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
!>          the multipliers used during the factorization are stored in
!>          rows KL+KU+2 to 2*KL+KU+1.
!>
```

*LDAB*

```
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
!>
```

*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).
!>
```

*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/(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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **145** of file **zgbcon.f**.

## Author

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