.TH "ptcon" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
ptcon \- ptcon: condition number estimate
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcptcon\fP (n, d, e, anorm, rcond, rwork, info)"
.br
.RI "\fBCPTCON\fP "
.ti -1c
.RI "subroutine \fBdptcon\fP (n, d, e, anorm, rcond, work, info)"
.br
.RI "\fBDPTCON\fP "
.ti -1c
.RI "subroutine \fBsptcon\fP (n, d, e, anorm, rcond, work, info)"
.br
.RI "\fBSPTCON\fP "
.ti -1c
.RI "subroutine \fBzptcon\fP (n, d, e, anorm, rcond, rwork, info)"
.br
.RI "\fBZPTCON\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cptcon (integer n, real, dimension( * ) d, complex, dimension( * ) e, real anorm, real rcond, real, dimension( * ) rwork, integer info)"

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

.PP
.nf
 CPTCON computes the reciprocal of the condition number (in the
 1-norm) of a complex Hermitian positive definite tridiagonal matrix
 using the factorization A = L*D*L**H or A = U**H*D*U computed by
 CPTTRF\&.

 Norm(inv(A)) is computed by a direct method, and the reciprocal of
 the condition number is computed as
                  RCOND = 1 / (ANORM * norm(inv(A)))\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          factorization of A, as computed by CPTTRF\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is COMPLEX array, dimension (N-1)
          The (n-1) off-diagonal elements of the unit bidiagonal factor
          U or L from the factorization of A, as computed by CPTTRF\&.
.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 the
          1-norm of inv(A) computed in this routine\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is REAL 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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  The method used is described in Nicholas J\&. Higham, 'Efficient
  Algorithms for Computing the Condition Number of a Tridiagonal
  Matrix', SIAM J\&. Sci\&. Stat\&. Comput\&., Vol\&. 7, No\&. 1, January 1986\&.
.fi
.PP
 
.RE
.PP

.SS "subroutine dptcon (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer info)"

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

.PP
.nf
 DPTCON computes the reciprocal of the condition number (in the
 1-norm) of a real symmetric positive definite tridiagonal matrix
 using the factorization A = L*D*L**T or A = U**T*D*U computed by
 DPTTRF\&.

 Norm(inv(A)) is computed by a direct method, and the reciprocal of
 the condition number is computed as
              RCOND = 1 / (ANORM * norm(inv(A)))\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          factorization of A, as computed by DPTTRF\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) off-diagonal elements of the unit bidiagonal factor
          U or L from the factorization of A,  as computed by DPTTRF\&.
.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 the
          1-norm of inv(A) computed in this routine\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION 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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  The method used is described in Nicholas J\&. Higham, 'Efficient
  Algorithms for Computing the Condition Number of a Tridiagonal
  Matrix', SIAM J\&. Sci\&. Stat\&. Comput\&., Vol\&. 7, No\&. 1, January 1986\&.
.fi
.PP
 
.RE
.PP

.SS "subroutine sptcon (integer n, real, dimension( * ) d, real, dimension( * ) e, real anorm, real rcond, real, dimension( * ) work, integer info)"

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

.PP
.nf
 SPTCON computes the reciprocal of the condition number (in the
 1-norm) of a real symmetric positive definite tridiagonal matrix
 using the factorization A = L*D*L**T or A = U**T*D*U computed by
 SPTTRF\&.

 Norm(inv(A)) is computed by a direct method, and the reciprocal of
 the condition number is computed as
              RCOND = 1 / (ANORM * norm(inv(A)))\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          factorization of A, as computed by SPTTRF\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is REAL array, dimension (N-1)
          The (n-1) off-diagonal elements of the unit bidiagonal factor
          U or L from the factorization of A,  as computed by SPTTRF\&.
.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 the
          1-norm of inv(A) computed in this routine\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL 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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  The method used is described in Nicholas J\&. Higham, 'Efficient
  Algorithms for Computing the Condition Number of a Tridiagonal
  Matrix', SIAM J\&. Sci\&. Stat\&. Comput\&., Vol\&. 7, No\&. 1, January 1986\&.
.fi
.PP
 
.RE
.PP

.SS "subroutine zptcon (integer n, double precision, dimension( * ) d, complex*16, dimension( * ) e, double precision anorm, double precision rcond, double precision, dimension( * ) rwork, integer info)"

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

.PP
.nf
 ZPTCON computes the reciprocal of the condition number (in the
 1-norm) of a complex Hermitian positive definite tridiagonal matrix
 using the factorization A = L*D*L**H or A = U**H*D*U computed by
 ZPTTRF\&.

 Norm(inv(A)) is computed by a direct method, and the reciprocal of
 the condition number is computed as
                  RCOND = 1 / (ANORM * norm(inv(A)))\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          factorization of A, as computed by ZPTTRF\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is COMPLEX*16 array, dimension (N-1)
          The (n-1) off-diagonal elements of the unit bidiagonal factor
          U or L from the factorization of A, as computed by ZPTTRF\&.
.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 the
          1-norm of inv(A) computed in this routine\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is DOUBLE PRECISION 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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  The method used is described in Nicholas J\&. Higham, 'Efficient
  Algorithms for Computing the Condition Number of a Tridiagonal
  Matrix', SIAM J\&. Sci\&. Stat\&. Comput\&., Vol\&. 7, No\&. 1, January 1986\&.
.fi
.PP
 
.RE
.PP

.SH "Author"
.PP 
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