# la_gercond - Man Page

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.

## 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

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

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

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

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

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

NAG Ltd.

Definition at line 133 of file zla_gercond_x.f.

## Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK