.TH "gecon" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
gecon \- gecon: condition number estimate
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcgecon\fP (norm, n, a, lda, anorm, rcond, work, rwork, info)"
.br
.RI "\fBCGECON\fP "
.ti -1c
.RI "subroutine \fBdgecon\fP (norm, n, a, lda, anorm, rcond, work, iwork, info)"
.br
.RI "\fBDGECON\fP "
.ti -1c
.RI "subroutine \fBsgecon\fP (norm, n, a, lda, anorm, rcond, work, iwork, info)"
.br
.RI "\fBSGECON\fP "
.ti -1c
.RI "subroutine \fBzgecon\fP (norm, n, a, lda, anorm, rcond, work, rwork, info)"
.br
.RI "\fBZGECON\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cgecon (character norm, integer n, complex, dimension( lda, * ) a, integer lda, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)"

.PP
\fBCGECON\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)) )\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fINORM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX array, dimension (LDA,N)
!>          The factors L and U from the factorization A = P*L*U
!>          as computed by CGETRF\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIRCOND\fP 
.PP
.nf
!>          RCOND is REAL
!>          The reciprocal of the condition number of the matrix A,
!>          computed as RCOND = 1/(norm(A) * norm(inv(A)))\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX array, dimension (2*N)
!> 
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
!>          RWORK is REAL array, dimension (2*N)
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB130\fP of file \fBcgecon\&.f\fP\&.
.SS "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)"

.PP
\fBDGECON\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)) )\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fINORM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The factors L and U from the factorization A = P*L*U
!>          as computed by DGETRF\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIRCOND\fP 
.PP
.nf
!>          RCOND is DOUBLE PRECISION
!>          The reciprocal of the condition number of the matrix A,
!>          computed as RCOND = 1/(norm(A) * norm(inv(A)))\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension (4*N)
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (N)
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB130\fP of file \fBdgecon\&.f\fP\&.
.SS "subroutine sgecon (character norm, integer n, real, dimension( lda, * ) a, integer lda, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

.PP
\fBSGECON\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)) )\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fINORM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is REAL array, dimension (LDA,N)
!>          The factors L and U from the factorization A = P*L*U
!>          as computed by SGETRF\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIRCOND\fP 
.PP
.nf
!>          RCOND is REAL
!>          The reciprocal of the condition number of the matrix A,
!>          computed as RCOND = 1/(norm(A) * norm(inv(A)))\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (4*N)
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (N)
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB130\fP of file \fBsgecon\&.f\fP\&.
.SS "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)"

.PP
\fBZGECON\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)) )\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fINORM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The factors L and U from the factorization A = P*L*U
!>          as computed by ZGETRF\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIRCOND\fP 
.PP
.nf
!>          RCOND is DOUBLE PRECISION
!>          The reciprocal of the condition number of the matrix A,
!>          computed as RCOND = 1/(norm(A) * norm(inv(A)))\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (2*N)
!> 
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
!>          RWORK is DOUBLE PRECISION array, dimension (2*N)
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB130\fP of file \fBzgecon\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.