NAME

gbcon - gbcon: condition number estimate

SYNOPSIS

Functions

subroutine cgbcon (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, rwork, info)
CGBCON subroutine dgbcon (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, iwork, info)
DGBCON subroutine sgbcon (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, iwork, info)
SGBCON subroutine zgbcon (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, rwork, info)
ZGBCON

Detailed Description

Function Documentation

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)

CGBCON

Purpose:



 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)) ).

Parameters

NORM



          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.



          N is INTEGER


          The order of the matrix A.  N >= 0.



          KL is INTEGER


          The number of subdiagonals within the band of A.  KL >= 0.



          KU is INTEGER


          The number of superdiagonals within the band of A.  KU >= 0.



          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.

LDAB



          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

IPIV



          IPIV is INTEGER array, dimension (N)


          The pivot indices; for 1 <= i <= N, row i of the matrix was


          interchanged with row IPIV(i).

ANORM



          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.

RCOND



          RCOND is REAL


          The reciprocal of the condition number of the matrix A,


          computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK



          WORK is COMPLEX array, dimension (2*N)

RWORK



          RWORK is REAL array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 145 of file cgbcon.f.

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)

DGBCON

Purpose:



 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)) ).

Parameters

NORM



          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.



          N is INTEGER


          The order of the matrix A.  N >= 0.



          KL is INTEGER


          The number of subdiagonals within the band of A.  KL >= 0.



          KU is INTEGER


          The number of superdiagonals within the band of A.  KU >= 0.



          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.

LDAB



          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

IPIV



          IPIV is INTEGER array, dimension (N)


          The pivot indices; for 1 <= i <= N, row i of the matrix was


          interchanged with row IPIV(i).

ANORM



          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.

RCOND



          RCOND is DOUBLE PRECISION


          The reciprocal of the condition number of the matrix A,


          computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK



          WORK is DOUBLE PRECISION array, dimension (3*N)

IWORK



          IWORK is INTEGER array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 144 of file dgbcon.f.

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)

SGBCON

Purpose:



 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)) ).

Parameters

NORM



          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.



          N is INTEGER


          The order of the matrix A.  N >= 0.



          KL is INTEGER


          The number of subdiagonals within the band of A.  KL >= 0.



          KU is INTEGER


          The number of superdiagonals within the band of A.  KU >= 0.



          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.

LDAB



          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

IPIV



          IPIV is INTEGER array, dimension (N)


          The pivot indices; for 1 <= i <= N, row i of the matrix was


          interchanged with row IPIV(i).

ANORM



          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.

RCOND



          RCOND is REAL


          The reciprocal of the condition number of the matrix A,


          computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK



          WORK is REAL array, dimension (3*N)

IWORK



          IWORK is INTEGER array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 144 of file sgbcon.f.

subroutine zgbcon (character norm, integer n, integer kl, integer ku, complex16, dimension( ldab, ) ab, integer ldab, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex16, dimension( ) work, double precision, dimension( * ) rwork, integer info)

ZGBCON

Purpose:



 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)) ).

Parameters

NORM



          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.



          N is INTEGER


          The order of the matrix A.  N >= 0.



          KL is INTEGER


          The number of subdiagonals within the band of A.  KL >= 0.



          KU is INTEGER


          The number of superdiagonals within the band of A.  KU >= 0.



          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.

LDAB



          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

IPIV



          IPIV is INTEGER array, dimension (N)


          The pivot indices; for 1 <= i <= N, row i of the matrix was


          interchanged with row IPIV(i).

ANORM



          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.

RCOND



          RCOND is DOUBLE PRECISION


          The reciprocal of the condition number of the matrix A,


          computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK



          WORK is COMPLEX*16 array, dimension (2*N)

RWORK



          RWORK is DOUBLE PRECISION array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 145 of file zgbcon.f.

Author

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