Provided by: liblapack-doc_3.12.0-3build1.1_all 
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, 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.
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, 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.
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.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.12.0 Fri Aug 9 2024 02:33:22 la_gercond(3)