---
name: "la_gercond"
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/la_gercond"
---

# la\_gercond(3)

la\_gercond: Skeel condition number estimate

## NAME

la\_gercond - la\_gercond: Skeel condition number estimate

## SYNOPSIS

### Functions

real function **cla\_gercond\_c** (trans, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)\
 **CLA\_GERCOND\_C** computes the infinity norm condition number of op(A)\*inv(diag(c)) for general matrices.  real function **cla\_gercond\_x** (trans, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)\
 **CLA\_GERCOND\_X** computes the infinity norm condition number of op(A)\*diag(x) for general matrices.  double precision function **dla\_gercond** (trans, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)\
 **DLA\_GERCOND** estimates the Skeel condition number for a general matrix.  real function **sla\_gercond** (trans, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)\
 **SLA\_GERCOND** estimates the Skeel condition number for a general matrix.  double precision function **zla\_gercond\_c** (trans, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)\
 **ZLA\_GERCOND\_C** computes the infinity norm condition number of op(A)\*inv(diag(c)) for general matrices.  double precision function **zla\_gercond\_x** (trans, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)\
 **ZLA\_GERCOND\_X** computes the infinity norm condition number of op(A)\*diag(x) for general matrices.

## Detailed Description

## Function Documentation

### real function cla\_gercond\_c (character trans, integer n, complex, dimension( lda, \* ) a, integer lda, complex, dimension( ldaf, \* ) af, integer ldaf, integer, dimension( \* ) ipiv, real, dimension( \* ) c, logical capply, integer info, complex, dimension( \* ) work, real, dimension( \* ) rwork)

**CLA\_GERCOND\_C** computes the infinity norm condition number of op(A)\*inv(diag(c)) for general matrices.

**Purpose:**

```
!>
!>
!>    CLA_GERCOND_C computes the infinity norm condition number of
!>    op(A) * inv(diag(C)) where C is a REAL vector.
!>
```

**Parameters**

*TRANS*

```
!>          TRANS is CHARACTER*1
!>     Specifies the form of the system of equations:
!>       = 'N':  A * X = B     (No transpose)
!>       = 'T':  A**T * X = B  (Transpose)
!>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
!>
```

*N*

```
!>          N is INTEGER
!>     The number of linear equations, i.e., the order of the
!>     matrix A.  N >= 0.
!>
```

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A
!>
```

*LDA*

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

*AF*

```
!>          AF is COMPLEX array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by CGETRF.
!>
```

*LDAF*

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

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by CGETRF; row i of the matrix was interchanged
!>     with row IPIV(i).
!>
```

*C*

```
!>          C is REAL array, dimension (N)
!>     The vector C in the formula op(A) * inv(diag(C)).
!>
```

*CAPPLY*

```
!>          CAPPLY is LOGICAL
!>     If .TRUE. then access the vector C in the formula above.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>       = 0:  Successful exit.
!>     i > 0:  The ith argument is invalid.
!>
```

*WORK*

```
!>          WORK is COMPLEX array, dimension (2*N).
!>     Workspace.
!>
```

*RWORK*

```
!>          RWORK is REAL array, dimension (N).
!>     Workspace.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **140** of file **cla\_gercond\_c.f**.

### real function cla\_gercond\_x (character trans, integer n, complex, dimension( lda, \* ) a, integer lda, complex, dimension( ldaf, \* ) af, integer ldaf, integer, dimension( \* ) ipiv, complex, dimension( \* ) x, integer info, complex, dimension( \* ) work, real, dimension( \* ) rwork)

**CLA\_GERCOND\_X** computes the infinity norm condition number of op(A)\*diag(x) for general matrices.

**Purpose:**

```
!>
!>
!>    CLA_GERCOND_X computes the infinity norm condition number of
!>    op(A) * diag(X) where X is a COMPLEX vector.
!>
```

**Parameters**

*TRANS*

```
!>          TRANS is CHARACTER*1
!>     Specifies the form of the system of equations:
!>       = 'N':  A * X = B     (No transpose)
!>       = 'T':  A**T * X = B  (Transpose)
!>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
!>
```

*N*

```
!>          N is INTEGER
!>     The number of linear equations, i.e., the order of the
!>     matrix A.  N >= 0.
!>
```

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A.
!>
```

*LDA*

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

*AF*

```
!>          AF is COMPLEX array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by CGETRF.
!>
```

*LDAF*

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

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by CGETRF; row i of the matrix was interchanged
!>     with row IPIV(i).
!>
```

*X*

```
!>          X is COMPLEX array, dimension (N)
!>     The vector X in the formula op(A) * diag(X).
!>
```

*INFO*

```
!>          INFO is INTEGER
!>       = 0:  Successful exit.
!>     i > 0:  The ith argument is invalid.
!>
```

*WORK*

```
!>          WORK is COMPLEX array, dimension (2*N).
!>     Workspace.
!>
```

*RWORK*

```
!>          RWORK is REAL array, dimension (N).
!>     Workspace.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **133** of file **cla\_gercond\_x.f**.

### double precision function dla\_gercond (character trans, integer n, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( ldaf, \* ) af, integer ldaf, integer, dimension( \* ) ipiv, integer cmode, double precision, dimension( \* ) c, integer info, double precision, dimension( \* ) work, integer, dimension( \* ) iwork)

**DLA\_GERCOND** estimates the Skeel condition number for a general matrix.

**Purpose:**

```
!>
!>    DLA_GERCOND estimates the Skeel condition number of op(A) * op2(C)
!>    where op2 is determined by CMODE as follows
!>    CMODE =  1    op2(C) = C
!>    CMODE =  0    op2(C) = I
!>    CMODE = -1    op2(C) = inv(C)
!>    The Skeel condition number cond(A) = norminf( |inv(A)||A| )
!>    is computed by computing scaling factors R such that
!>    diag(R)*A*op2(C) is row equilibrated and computing the standard
!>    infinity-norm condition number.
!>
```

**Parameters**

*TRANS*

```
!>          TRANS is CHARACTER*1
!>     Specifies the form of the system of equations:
!>       = 'N':  A * X = B     (No transpose)
!>       = 'T':  A**T * X = B  (Transpose)
!>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
!>
```

*N*

```
!>          N is INTEGER
!>     The number of linear equations, i.e., the order of the
!>     matrix A.  N >= 0.
!>
```

*A*

```
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A.
!>
```

*LDA*

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

*AF*

```
!>          AF is DOUBLE PRECISION array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by DGETRF.
!>
```

*LDAF*

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

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by DGETRF; row i of the matrix was interchanged
!>     with row IPIV(i).
!>
```

*CMODE*

```
!>          CMODE is INTEGER
!>     Determines op2(C) in the formula op(A) * op2(C) as follows:
!>     CMODE =  1    op2(C) = C
!>     CMODE =  0    op2(C) = I
!>     CMODE = -1    op2(C) = inv(C)
!>
```

*C*

```
!>          C is DOUBLE PRECISION array, dimension (N)
!>     The vector C in the formula op(A) * op2(C).
!>
```

*INFO*

```
!>          INFO is INTEGER
!>       = 0:  Successful exit.
!>     i > 0:  The ith argument is invalid.
!>
```

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (3*N).
!>     Workspace.
!>
```

*IWORK*

```
!>          IWORK is INTEGER array, dimension (N).
!>     Workspace.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **149** of file **dla\_gercond.f**.

### real function sla\_gercond (character trans, integer n, real, dimension( lda, \* ) a, integer lda, real, dimension( ldaf, \* ) af, integer ldaf, integer, dimension( \* ) ipiv, integer cmode, real, dimension( \* ) c, integer info, real, dimension( \* ) work, integer, dimension( \* ) iwork)

**SLA\_GERCOND** estimates the Skeel condition number for a general matrix.

**Purpose:**

```
!>
!>    SLA_GERCOND estimates the Skeel condition number of op(A) * op2(C)
!>    where op2 is determined by CMODE as follows
!>    CMODE =  1    op2(C) = C
!>    CMODE =  0    op2(C) = I
!>    CMODE = -1    op2(C) = inv(C)
!>    The Skeel condition number cond(A) = norminf( |inv(A)||A| )
!>    is computed by computing scaling factors R such that
!>    diag(R)*A*op2(C) is row equilibrated and computing the standard
!>    infinity-norm condition number.
!>
```

**Parameters**

*TRANS*

```
!>          TRANS is CHARACTER*1
!>     Specifies the form of the system of equations:
!>       = 'N':  A * X = B     (No transpose)
!>       = 'T':  A**T * X = B  (Transpose)
!>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
!>
```

*N*

```
!>          N is INTEGER
!>     The number of linear equations, i.e., the order of the
!>     matrix A.  N >= 0.
!>
```

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A.
!>
```

*LDA*

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

*AF*

```
!>          AF is REAL array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by SGETRF.
!>
```

*LDAF*

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

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by SGETRF; row i of the matrix was interchanged
!>     with row IPIV(i).
!>
```

*CMODE*

```
!>          CMODE is INTEGER
!>     Determines op2(C) in the formula op(A) * op2(C) as follows:
!>     CMODE =  1    op2(C) = C
!>     CMODE =  0    op2(C) = I
!>     CMODE = -1    op2(C) = inv(C)
!>
```

*C*

```
!>          C is REAL array, dimension (N)
!>     The vector C in the formula op(A) * op2(C).
!>
```

*INFO*

```
!>          INFO is INTEGER
!>       = 0:  Successful exit.
!>     i > 0:  The ith argument is invalid.
!>
```

*WORK*

```
!>          WORK is REAL array, dimension (3*N).
!>     Workspace.
!>
```

*IWORK*

```
!>          IWORK is INTEGER array, dimension (N).
!>     Workspace.2
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **148** of file **sla\_gercond.f**.

### double precision function zla\_gercond\_c (character trans, integer n, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( ldaf, \* ) af, integer ldaf, integer, dimension( \* ) ipiv, double precision, dimension( \* ) c, logical capply, integer info, complex\*16, dimension( \* ) work, double precision, dimension( \* ) rwork)

**ZLA\_GERCOND\_C** computes the infinity norm condition number of op(A)\*inv(diag(c)) for general matrices.

**Purpose:**

```
!>
!>    ZLA_GERCOND_C computes the infinity norm condition number of
!>    op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
!>
```

**Parameters**

*TRANS*

```
!>          TRANS is CHARACTER*1
!>     Specifies the form of the system of equations:
!>       = 'N':  A * X = B     (No transpose)
!>       = 'T':  A**T * X = B  (Transpose)
!>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
!>
```

*N*

```
!>          N is INTEGER
!>     The number of linear equations, i.e., the order of the
!>     matrix A.  N >= 0.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A
!>
```

*LDA*

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

*AF*

```
!>          AF is COMPLEX*16 array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by ZGETRF.
!>
```

*LDAF*

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

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by ZGETRF; row i of the matrix was interchanged
!>     with row IPIV(i).
!>
```

*C*

```
!>          C is DOUBLE PRECISION array, dimension (N)
!>     The vector C in the formula op(A) * inv(diag(C)).
!>
```

*CAPPLY*

```
!>          CAPPLY is LOGICAL
!>     If .TRUE. then access the vector C in the formula above.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>       = 0:  Successful exit.
!>     i > 0:  The ith argument is invalid.
!>
```

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension (2*N).
!>     Workspace.
!>
```

*RWORK*

```
!>          RWORK is DOUBLE PRECISION array, dimension (N).
!>     Workspace.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **140** of file **zla\_gercond\_c.f**.

### double precision function zla\_gercond\_x (character trans, integer n, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( ldaf, \* ) af, integer ldaf, integer, dimension( \* ) ipiv, complex\*16, dimension( \* ) x, integer info, complex\*16, dimension( \* ) work, double precision, dimension( \* ) rwork)

**ZLA\_GERCOND\_X** computes the infinity norm condition number of op(A)\*diag(x) for general matrices.

**Purpose:**

```
!>
!>    ZLA_GERCOND_X computes the infinity norm condition number of
!>    op(A) * diag(X) where X is a COMPLEX*16 vector.
!>
```

**Parameters**

*TRANS*

```
!>          TRANS is CHARACTER*1
!>     Specifies the form of the system of equations:
!>       = 'N':  A * X = B     (No transpose)
!>       = 'T':  A**T * X = B  (Transpose)
!>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
!>
```

*N*

```
!>          N is INTEGER
!>     The number of linear equations, i.e., the order of the
!>     matrix A.  N >= 0.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A.
!>
```

*LDA*

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

*AF*

```
!>          AF is COMPLEX*16 array, dimension (LDAF,N)
!>     The factors L and U from the factorization
!>     A = P*L*U as computed by ZGETRF.
!>
```

*LDAF*

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

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by ZGETRF; row i of the matrix was interchanged
!>     with row IPIV(i).
!>
```

*X*

```
!>          X is COMPLEX*16 array, dimension (N)
!>     The vector X in the formula op(A) * diag(X).
!>
```

*INFO*

```
!>          INFO is INTEGER
!>       = 0:  Successful exit.
!>     i > 0:  The ith argument is invalid.
!>
```

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension (2*N).
!>     Workspace.
!>
```

*RWORK*

```
!>          RWORK is DOUBLE PRECISION array, dimension (N).
!>     Workspace.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **133** of file **zla\_gercond\_x.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.