Man page - la_gercond(3)

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Manual

la_gercond

NAME
SYNOPSIS
Functions
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)
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)
double precision function dla_gercond (character trans, integer n, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,integer cmode, double precision, dimension( * ) c, integer info, doubleprecision, dimension( * ) work, integer, dimension( * ) iwork)
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)
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, doubleprecision, dimension( * ) c, logical capply, integer info, complex*16,dimension( * ) work, double precision, dimension( * ) rwork)
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, doubleprecision, dimension( * ) rwork)
Author

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.

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.

double precision function dla_gercond (character trans, integer n, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,integer cmode, double precision, dimension( * ) c, integer info, doubleprecision, 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.

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.

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, doubleprecision, 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.

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, doubleprecision, 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.

Author

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