.TH "hecon" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
hecon \- {he,sy}con: condition number estimate
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBchecon\fP (uplo, n, a, lda, ipiv, anorm, rcond, work, info)"
.br
.RI "\fBCHECON\fP "
.ti -1c
.RI "subroutine \fBcsycon\fP (uplo, n, a, lda, ipiv, anorm, rcond, work, info)"
.br
.RI "\fBCSYCON\fP "
.ti -1c
.RI "subroutine \fBdsycon\fP (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info)"
.br
.RI "\fBDSYCON\fP "
.ti -1c
.RI "subroutine \fBssycon\fP (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info)"
.br
.RI "\fBSSYCON\fP "
.ti -1c
.RI "subroutine \fBzhecon\fP (uplo, n, a, lda, ipiv, anorm, rcond, work, info)"
.br
.RI "\fBZHECON\fP "
.ti -1c
.RI "subroutine \fBzsycon\fP (uplo, n, a, lda, ipiv, anorm, rcond, work, info)"
.br
.RI "\fBZSYCON\fP "
.in -1c
.SH "Detailed Description"
.PP 

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

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

.PP
.nf
!>
!> CHECON estimates the reciprocal of the condition number of a complex
!> Hermitian matrix A using the factorization A = U*D*U**H or
!> A = L*D*L**H computed by CHETRF\&.
!>
!> An estimate is obtained for norm(inv(A)), and the reciprocal of the
!> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix\&.
!>          = 'U':  Upper triangular, form is A = U*D*U**H;
!>          = 'L':  Lower triangular, form is A = L*D*L**H\&.
!> 
.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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by CHETRF\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by CHETRF\&.
!> 
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
!>          ANORM is REAL
!>          The 1-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/(ANORM * AINVNM), where AINVNM is an
!>          estimate of the 1-norm of inv(A) computed in this routine\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX 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
!> 
.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 \fB123\fP of file \fBchecon\&.f\fP\&.
.SS "subroutine csycon (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> CSYCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a complex symmetric matrix A using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by CSYTRF\&.
!>
!> An estimate is obtained for norm(inv(A)), and the reciprocal of the
!> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix\&.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T\&.
!> 
.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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by CSYTRF\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by CSYTRF\&.
!> 
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
!>          ANORM is REAL
!>          The 1-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/(ANORM * AINVNM), where AINVNM is an
!>          estimate of the 1-norm of inv(A) computed in this routine\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX 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
!> 
.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 \fB123\fP of file \fBcsycon\&.f\fP\&.
.SS "subroutine dsycon (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

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

.PP
.nf
!>
!> DSYCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a real symmetric matrix A using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by DSYTRF\&.
!>
!> An estimate is obtained for norm(inv(A)), and the reciprocal of the
!> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix\&.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T\&.
!> 
.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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by DSYTRF\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by DSYTRF\&.
!> 
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
!>          ANORM is DOUBLE PRECISION
!>          The 1-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/(ANORM * AINVNM), where AINVNM is an
!>          estimate of the 1-norm of inv(A) computed in this routine\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension (2*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
!> 
.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 \fB128\fP of file \fBdsycon\&.f\fP\&.
.SS "subroutine ssycon (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

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

.PP
.nf
!>
!> SSYCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a real symmetric matrix A using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by SSYTRF\&.
!>
!> An estimate is obtained for norm(inv(A)), and the reciprocal of the
!> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix\&.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T\&.
!> 
.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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by SSYTRF\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by SSYTRF\&.
!> 
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
!>          ANORM is REAL
!>          The 1-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/(ANORM * AINVNM), where AINVNM is an
!>          estimate of the 1-norm of inv(A) computed in this routine\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (2*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
!> 
.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 \fB128\fP of file \fBssycon\&.f\fP\&.
.SS "subroutine zhecon (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> ZHECON estimates the reciprocal of the condition number of a complex
!> Hermitian matrix A using the factorization A = U*D*U**H or
!> A = L*D*L**H computed by ZHETRF\&.
!>
!> An estimate is obtained for norm(inv(A)), and the reciprocal of the
!> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix\&.
!>          = 'U':  Upper triangular, form is A = U*D*U**H;
!>          = 'L':  Lower triangular, form is A = L*D*L**H\&.
!> 
.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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by ZHETRF\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by ZHETRF\&.
!> 
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
!>          ANORM is DOUBLE PRECISION
!>          The 1-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/(ANORM * AINVNM), where AINVNM is an
!>          estimate of the 1-norm of inv(A) computed in this routine\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 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
!> 
.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 \fB123\fP of file \fBzhecon\&.f\fP\&.
.SS "subroutine zsycon (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> ZSYCON estimates the reciprocal of the condition number (in the
!> 1-norm) of a complex symmetric matrix A using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by ZSYTRF\&.
!>
!> An estimate is obtained for norm(inv(A)), and the reciprocal of the
!> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix\&.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T\&.
!> 
.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 block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by ZSYTRF\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by ZSYTRF\&.
!> 
.fi
.PP
.br
\fIANORM\fP 
.PP
.nf
!>          ANORM is DOUBLE PRECISION
!>          The 1-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/(ANORM * AINVNM), where AINVNM is an
!>          estimate of the 1-norm of inv(A) computed in this routine\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 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
!> 
.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 \fB123\fP of file \fBzsycon\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.