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

.in +1c
.ti -1c
.RI "subroutine \fBcgbcon\fP (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, rwork, info)"
.br
.RI "\fBCGBCON\fP "
.ti -1c
.RI "subroutine \fBdgbcon\fP (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, iwork, info)"
.br
.RI "\fBDGBCON\fP "
.ti -1c
.RI "subroutine \fBsgbcon\fP (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, iwork, info)"
.br
.RI "\fBSGBCON\fP "
.ti -1c
.RI "subroutine \fBzgbcon\fP (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, rwork, info)"
.br
.RI "\fBZGBCON\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cgbcon (character norm, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)"

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

.PP
.nf
 CGBCON estimates the reciprocal of the condition number of a complex
 general band matrix A, in either the 1-norm or the infinity-norm,
 using the LU factorization computed by CGBTRF\&.

 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
\fIKL\fP 
.PP
.nf
          KL is INTEGER
          The number of subdiagonals within the band of A\&.  KL >= 0\&.
.fi
.PP
.br
\fIKU\fP 
.PP
.nf
          KU is INTEGER
          The number of superdiagonals within the band of A\&.  KU >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is COMPLEX array, dimension (LDAB,N)
          Details of the LU factorization of the band matrix A, as
          computed by CGBTRF\&.  U is stored as an upper triangular band
          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
          the multipliers used during the factorization are stored in
          rows KL+KU+2 to 2*KL+KU+1\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= 2*KL+KU+1\&.
.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)\&.
.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 (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 \fB145\fP of file \fBcgbcon\&.f\fP\&.
.SS "subroutine dgbcon (character norm, integer n, integer kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

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

.PP
.nf
 DGBCON estimates the reciprocal of the condition number of a real
 general band matrix A, in either the 1-norm or the infinity-norm,
 using the LU factorization computed by DGBTRF\&.

 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
\fIKL\fP 
.PP
.nf
          KL is INTEGER
          The number of subdiagonals within the band of A\&.  KL >= 0\&.
.fi
.PP
.br
\fIKU\fP 
.PP
.nf
          KU is INTEGER
          The number of superdiagonals within the band of A\&.  KU >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          Details of the LU factorization of the band matrix A, as
          computed by DGBTRF\&.  U is stored as an upper triangular band
          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
          the multipliers used during the factorization are stored in
          rows KL+KU+2 to 2*KL+KU+1\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= 2*KL+KU+1\&.
.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)\&.
.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 (3*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 \fBdgbcon\&.f\fP\&.
.SS "subroutine sgbcon (character norm, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

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

.PP
.nf
 SGBCON estimates the reciprocal of the condition number of a real
 general band matrix A, in either the 1-norm or the infinity-norm,
 using the LU factorization computed by SGBTRF\&.

 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
\fIKL\fP 
.PP
.nf
          KL is INTEGER
          The number of subdiagonals within the band of A\&.  KL >= 0\&.
.fi
.PP
.br
\fIKU\fP 
.PP
.nf
          KU is INTEGER
          The number of superdiagonals within the band of A\&.  KU >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is REAL array, dimension (LDAB,N)
          Details of the LU factorization of the band matrix A, as
          computed by SGBTRF\&.  U is stored as an upper triangular band
          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
          the multipliers used during the factorization are stored in
          rows KL+KU+2 to 2*KL+KU+1\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= 2*KL+KU+1\&.
.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)\&.
.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 (3*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 \fBsgbcon\&.f\fP\&.
.SS "subroutine zgbcon (character norm, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)"

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

.PP
.nf
 ZGBCON estimates the reciprocal of the condition number of a complex
 general band matrix A, in either the 1-norm or the infinity-norm,
 using the LU factorization computed by ZGBTRF\&.

 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
\fIKL\fP 
.PP
.nf
          KL is INTEGER
          The number of subdiagonals within the band of A\&.  KL >= 0\&.
.fi
.PP
.br
\fIKU\fP 
.PP
.nf
          KU is INTEGER
          The number of superdiagonals within the band of A\&.  KU >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is COMPLEX*16 array, dimension (LDAB,N)
          Details of the LU factorization of the band matrix A, as
          computed by ZGBTRF\&.  U is stored as an upper triangular band
          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
          the multipliers used during the factorization are stored in
          rows KL+KU+2 to 2*KL+KU+1\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= 2*KL+KU+1\&.
.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)\&.
.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 (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 \fB145\fP of file \fBzgbcon\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.