table of contents
| gecon(3) | LAPACK | gecon(3) |
NAME¶
gecon - gecon: condition number estimate
SYNOPSIS¶
Functions¶
subroutine cgecon (norm, n, a, lda, anorm, rcond, work,
rwork, info)
CGECON subroutine dgecon (norm, n, a, lda, anorm, rcond, work,
iwork, info)
DGECON subroutine sgecon (norm, n, a, lda, anorm, rcond, work,
iwork, info)
SGECON subroutine zgecon (norm, n, a, lda, anorm, rcond, work,
rwork, info)
ZGECON
Detailed Description¶
Function Documentation¶
subroutine cgecon (character norm, integer n, complex, dimension( lda, * ) a, integer lda, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)¶
CGECON
Purpose:
CGECON estimates the reciprocal of the condition number of a general
complex matrix A, in either the 1-norm or the infinity-norm, using
the LU factorization computed by CGETRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).
Parameters
NORM
NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
N
N is INTEGER
The order of the matrix A. N >= 0.
A
A is COMPLEX array, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U
as computed by CGETRF.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
ANORM
ANORM is REAL
If NORM = '1' or 'O', the 1-norm of the original matrix A.
If NORM = 'I', the infinity-norm of the original matrix A.
RCOND
RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).
WORK
WORK is COMPLEX array, dimension (2*N)
RWORK
RWORK is REAL array, dimension (2*N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
NaNs are illegal values for ANORM, and they propagate to
the output parameter RCOND.
Infinity is illegal for ANORM, and it propagates to the output
parameter RCOND as 0.
= 1: if RCOND = NaN, or
RCOND = Inf, or
the computed norm of the inverse of A is 0.
In the latter, RCOND = 0 is returned.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dgecon (character norm, integer n, double precision, dimension( lda, * ) a, integer lda, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)¶
DGECON
Purpose:
DGECON estimates the reciprocal of the condition number of a general
real matrix A, in either the 1-norm or the infinity-norm, using
the LU factorization computed by DGETRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).
Parameters
NORM
NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
N
N is INTEGER
The order of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U
as computed by DGETRF.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
ANORM
ANORM is DOUBLE PRECISION
If NORM = '1' or 'O', the 1-norm of the original matrix A.
If NORM = 'I', the infinity-norm of the original matrix A.
RCOND
RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).
WORK
WORK is DOUBLE PRECISION array, dimension (4*N)
IWORK
IWORK is INTEGER array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
NaNs are illegal values for ANORM, and they propagate to
the output parameter RCOND.
Infinity is illegal for ANORM, and it propagates to the output
parameter RCOND as 0.
= 1: if RCOND = NaN, or
RCOND = Inf, or
the computed norm of the inverse of A is 0.
In the latter, RCOND = 0 is returned.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine sgecon (character norm, integer n, real, dimension( lda, * ) a, integer lda, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)¶
SGECON
Purpose:
SGECON estimates the reciprocal of the condition number of a general
real matrix A, in either the 1-norm or the infinity-norm, using
the LU factorization computed by SGETRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).
Parameters
NORM
NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
N
N is INTEGER
The order of the matrix A. N >= 0.
A
A is REAL array, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U
as computed by SGETRF.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
ANORM
ANORM is REAL
If NORM = '1' or 'O', the 1-norm of the original matrix A.
If NORM = 'I', the infinity-norm of the original matrix A.
RCOND
RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).
WORK
WORK is REAL array, dimension (4*N)
IWORK
IWORK is INTEGER array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
NaNs are illegal values for ANORM, and they propagate to
the output parameter RCOND.
Infinity is illegal for ANORM, and it propagates to the output
parameter RCOND as 0.
= 1: if RCOND = NaN, or
RCOND = Inf, or
the computed norm of the inverse of A is 0.
In the latter, RCOND = 0 is returned.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zgecon (character norm, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision anorm, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)¶
ZGECON
Purpose:
ZGECON estimates the reciprocal of the condition number of a general
complex matrix A, in either the 1-norm or the infinity-norm, using
the LU factorization computed by ZGETRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).
Parameters
NORM
NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
N
N is INTEGER
The order of the matrix A. N >= 0.
A
A is COMPLEX*16 array, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U
as computed by ZGETRF.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
ANORM
ANORM is DOUBLE PRECISION
If NORM = '1' or 'O', the 1-norm of the original matrix A.
If NORM = 'I', the infinity-norm of the original matrix A.
RCOND
RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).
WORK
WORK is COMPLEX*16 array, dimension (2*N)
RWORK
RWORK is DOUBLE PRECISION array, dimension (2*N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
NaNs are illegal values for ANORM, and they propagate to
the output parameter RCOND.
Infinity is illegal for ANORM, and it propagates to the output
parameter RCOND as 0.
= 1: if RCOND = NaN, or
RCOND = Inf, or
the computed norm of the inverse of A is 0.
In the latter, RCOND = 0 is returned.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |