table of contents
| la_gercond(3) | LAPACK | la_gercond(3) |
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 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 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 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 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 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 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 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 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 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 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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