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

.in +1c
.ti -1c
.RI "subroutine \fBcgtcon\fP (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info)"
.br
.RI "\fBCGTCON\fP "
.ti -1c
.RI "subroutine \fBdgtcon\fP (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info)"
.br
.RI "\fBDGTCON\fP "
.ti -1c
.RI "subroutine \fBsgtcon\fP (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info)"
.br
.RI "\fBSGTCON\fP "
.ti -1c
.RI "subroutine \fBzgtcon\fP (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info)"
.br
.RI "\fBZGTCON\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cgtcon (character norm, integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> CGTCON estimates the reciprocal of the condition number of a complex
!> tridiagonal matrix A using the LU factorization as computed by
!> CGTTRF\&.
!>
!> 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
\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
\fIDL\fP 
.PP
.nf
!>          DL is COMPLEX array, dimension (N-1)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A as computed by CGTTRF\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is COMPLEX array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A\&.
!> 
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
!>          DU is COMPLEX array, dimension (N-1)
!>          The (n-1) elements of the first superdiagonal of U\&.
!> 
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
!>          DU2 is COMPLEX array, dimension (N-2)
!>          The (n-2) elements of the second superdiagonal of U\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          The pivot indices; for 1 <= i <= n, row i of the matrix was
!>          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
!>          i or i+1; IPIV(i) = i indicates a row interchange was not
!>          required\&.
!> 
.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/(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 \fB139\fP of file \fBcgtcon\&.f\fP\&.
.SS "subroutine dgtcon (character norm, integer n, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

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

.PP
.nf
!>
!> DGTCON estimates the reciprocal of the condition number of a real
!> tridiagonal matrix A using the LU factorization as computed by
!> DGTTRF\&.
!>
!> 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
\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
\fIDL\fP 
.PP
.nf
!>          DL is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A as computed by DGTTRF\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is DOUBLE PRECISION array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A\&.
!> 
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
!>          DU is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) elements of the first superdiagonal of U\&.
!> 
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
!>          DU2 is DOUBLE PRECISION array, dimension (N-2)
!>          The (n-2) elements of the second superdiagonal of U\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          The pivot indices; for 1 <= i <= n, row i of the matrix was
!>          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
!>          i or i+1; IPIV(i) = i indicates a row interchange was not
!>          required\&.
!> 
.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/(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 \fB144\fP of file \fBdgtcon\&.f\fP\&.
.SS "subroutine sgtcon (character norm, integer n, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2, integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

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

.PP
.nf
!>
!> SGTCON estimates the reciprocal of the condition number of a real
!> tridiagonal matrix A using the LU factorization as computed by
!> SGTTRF\&.
!>
!> 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
\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
\fIDL\fP 
.PP
.nf
!>          DL is REAL array, dimension (N-1)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A as computed by SGTTRF\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is REAL array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A\&.
!> 
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
!>          DU is REAL array, dimension (N-1)
!>          The (n-1) elements of the first superdiagonal of U\&.
!> 
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
!>          DU2 is REAL array, dimension (N-2)
!>          The (n-2) elements of the second superdiagonal of U\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          The pivot indices; for 1 <= i <= n, row i of the matrix was
!>          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
!>          i or i+1; IPIV(i) = i indicates a row interchange was not
!>          required\&.
!> 
.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/(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 \fB144\fP of file \fBsgtcon\&.f\fP\&.
.SS "subroutine zgtcon (character norm, integer n, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> ZGTCON estimates the reciprocal of the condition number of a complex
!> tridiagonal matrix A using the LU factorization as computed by
!> ZGTTRF\&.
!>
!> 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
\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
\fIDL\fP 
.PP
.nf
!>          DL is COMPLEX*16 array, dimension (N-1)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A as computed by ZGTTRF\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is COMPLEX*16 array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A\&.
!> 
.fi
.PP
.br
\fIDU\fP 
.PP
.nf
!>          DU is COMPLEX*16 array, dimension (N-1)
!>          The (n-1) elements of the first superdiagonal of U\&.
!> 
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
!>          DU2 is COMPLEX*16 array, dimension (N-2)
!>          The (n-2) elements of the second superdiagonal of U\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          The pivot indices; for 1 <= i <= n, row i of the matrix was
!>          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
!>          i or i+1; IPIV(i) = i indicates a row interchange was not
!>          required\&.
!> 
.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/(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 \fB139\fP of file \fBzgtcon\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.