NAME

tbcon - tbcon: condition number estimate

SYNOPSIS

Functions

subroutine ctbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, rwork, info)
CTBCON subroutine dtbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, iwork, info)
DTBCON subroutine stbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, iwork, info)
STBCON subroutine ztbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, rwork, info)
ZTBCON

Detailed Description

Function Documentation

subroutine ctbcon (character norm, character uplo, character diag, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CTBCON

Purpose:



 CTBCON estimates the reciprocal of the condition number of a


 triangular band matrix A, in either the 1-norm or the infinity-norm.


 The norm of A is computed and an estimate is obtained for


 norm(inv(A)), then 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.

UPLO



          UPLO is CHARACTER*1


          = 'U':  A is upper triangular;


          = 'L':  A is lower triangular.

DIAG



          DIAG is CHARACTER*1


          = 'N':  A is non-unit triangular;


          = 'U':  A is unit triangular.



          N is INTEGER


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



          KD is INTEGER


          The number of superdiagonals or subdiagonals of the


          triangular band matrix A.  KD >= 0.



          AB is COMPLEX array, dimension (LDAB,N)


          The upper or lower triangular band matrix A, stored in the


          first kd+1 rows of the array. The j-th column of A is stored


          in the j-th column of the array AB as follows:


          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;


          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).


          If DIAG = 'U', the diagonal elements of A are not referenced


          and are assumed to be 1.

LDAB



          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

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 141 of file ctbcon.f.

subroutine dtbcon (character norm, character uplo, character diag, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DTBCON

Purpose:



 DTBCON estimates the reciprocal of the condition number of a


 triangular band matrix A, in either the 1-norm or the infinity-norm.


 The norm of A is computed and an estimate is obtained for


 norm(inv(A)), then 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.

UPLO



          UPLO is CHARACTER*1


          = 'U':  A is upper triangular;


          = 'L':  A is lower triangular.

DIAG



          DIAG is CHARACTER*1


          = 'N':  A is non-unit triangular;


          = 'U':  A is unit triangular.



          N is INTEGER


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



          KD is INTEGER


          The number of superdiagonals or subdiagonals of the


          triangular band matrix A.  KD >= 0.



          AB is DOUBLE PRECISION array, dimension (LDAB,N)


          The upper or lower triangular band matrix A, stored in the


          first kd+1 rows of the array. The j-th column of A is stored


          in the j-th column of the array AB as follows:


          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;


          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).


          If DIAG = 'U', the diagonal elements of A are not referenced


          and are assumed to be 1.

LDAB



          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

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 141 of file dtbcon.f.

subroutine stbcon (character norm, character uplo, character diag, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

STBCON

Purpose:



 STBCON estimates the reciprocal of the condition number of a


 triangular band matrix A, in either the 1-norm or the infinity-norm.


 The norm of A is computed and an estimate is obtained for


 norm(inv(A)), then 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.

UPLO



          UPLO is CHARACTER*1


          = 'U':  A is upper triangular;


          = 'L':  A is lower triangular.

DIAG



          DIAG is CHARACTER*1


          = 'N':  A is non-unit triangular;


          = 'U':  A is unit triangular.



          N is INTEGER


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



          KD is INTEGER


          The number of superdiagonals or subdiagonals of the


          triangular band matrix A.  KD >= 0.



          AB is REAL array, dimension (LDAB,N)


          The upper or lower triangular band matrix A, stored in the


          first kd+1 rows of the array. The j-th column of A is stored


          in the j-th column of the array AB as follows:


          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;


          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).


          If DIAG = 'U', the diagonal elements of A are not referenced


          and are assumed to be 1.

LDAB



          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

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 141 of file stbcon.f.

subroutine ztbcon (character norm, character uplo, character diag, integer n, integer kd, complex16, dimension( ldab, ) ab, integer ldab, double precision rcond, complex16, dimension( ) work, double precision, dimension( * ) rwork, integer info)

ZTBCON

Purpose:



 ZTBCON estimates the reciprocal of the condition number of a


 triangular band matrix A, in either the 1-norm or the infinity-norm.


 The norm of A is computed and an estimate is obtained for


 norm(inv(A)), then 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.

UPLO



          UPLO is CHARACTER*1


          = 'U':  A is upper triangular;


          = 'L':  A is lower triangular.

DIAG



          DIAG is CHARACTER*1


          = 'N':  A is non-unit triangular;


          = 'U':  A is unit triangular.



          N is INTEGER


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



          KD is INTEGER


          The number of superdiagonals or subdiagonals of the


          triangular band matrix A.  KD >= 0.



          AB is COMPLEX*16 array, dimension (LDAB,N)


          The upper or lower triangular band matrix A, stored in the


          first kd+1 rows of the array. The j-th column of A is stored


          in the j-th column of the array AB as follows:


          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;


          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).


          If DIAG = 'U', the diagonal elements of A are not referenced


          and are assumed to be 1.

LDAB



          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

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 141 of file ztbcon.f.

Author

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