NAME

pbcon - pbcon: condition number estimate

SYNOPSIS

Functions

subroutine cpbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, rwork, info)
CPBCON subroutine dpbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, iwork, info)
DPBCON subroutine spbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, iwork, info)
SPBCON subroutine zpbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, rwork, info)
ZPBCON

Detailed Description

Function Documentation

subroutine cpbcon (character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CPBCON

Purpose:



 CPBCON estimates the reciprocal of the condition number (in the


 1-norm) of a complex Hermitian positive definite band matrix using


 the Cholesky factorization A = U**H*U or A = L*L**H computed by


 CPBTRF.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO



          UPLO is CHARACTER*1


          = 'U':  Upper triangular factor stored in AB;


          = 'L':  Lower triangular factor stored in AB.



          N is INTEGER


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



          KD is INTEGER


          The number of superdiagonals of the matrix A if UPLO = 'U',


          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.



          AB is COMPLEX array, dimension (LDAB,N)


          The triangular factor U or L from the Cholesky factorization


          A = U**H*U or A = L*L**H of the band matrix A, stored in the


          first KD+1 rows of the array.  The j-th column of U or L is


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


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


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

LDAB



          LDAB is INTEGER


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

ANORM



          ANORM is REAL


          The 1-norm (or infinity-norm) of the Hermitian band matrix A.

RCOND



          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.

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 131 of file cpbcon.f.

subroutine dpbcon (character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DPBCON

Purpose:



 DPBCON estimates the reciprocal of the condition number (in the


 1-norm) of a real symmetric positive definite band matrix using the


 Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO



          UPLO is CHARACTER*1


          = 'U':  Upper triangular factor stored in AB;


          = 'L':  Lower triangular factor stored in AB.



          N is INTEGER


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



          KD is INTEGER


          The number of superdiagonals of the matrix A if UPLO = 'U',


          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.



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


          The triangular factor U or L from the Cholesky factorization


          A = U**T*U or A = L*L**T of the band matrix A, stored in the


          first KD+1 rows of the array.  The j-th column of U or L is


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


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


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

LDAB



          LDAB is INTEGER


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

ANORM



          ANORM is DOUBLE PRECISION


          The 1-norm (or infinity-norm) of the symmetric band matrix A.

RCOND



          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.

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 130 of file dpbcon.f.

subroutine spbcon (character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SPBCON

Purpose:



 SPBCON estimates the reciprocal of the condition number (in the


 1-norm) of a real symmetric positive definite band matrix using the


 Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO



          UPLO is CHARACTER*1


          = 'U':  Upper triangular factor stored in AB;


          = 'L':  Lower triangular factor stored in AB.



          N is INTEGER


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



          KD is INTEGER


          The number of superdiagonals of the matrix A if UPLO = 'U',


          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.



          AB is REAL array, dimension (LDAB,N)


          The triangular factor U or L from the Cholesky factorization


          A = U**T*U or A = L*L**T of the band matrix A, stored in the


          first KD+1 rows of the array.  The j-th column of U or L is


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


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


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

LDAB



          LDAB is INTEGER


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

ANORM



          ANORM is REAL


          The 1-norm (or infinity-norm) of the symmetric band matrix A.

RCOND



          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.

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 130 of file spbcon.f.

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

ZPBCON

Purpose:



 ZPBCON estimates the reciprocal of the condition number (in the


 1-norm) of a complex Hermitian positive definite band matrix using


 the Cholesky factorization A = U**H*U or A = L*L**H computed by


 ZPBTRF.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters

UPLO



          UPLO is CHARACTER*1


          = 'U':  Upper triangular factor stored in AB;


          = 'L':  Lower triangular factor stored in AB.



          N is INTEGER


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



          KD is INTEGER


          The number of superdiagonals of the matrix A if UPLO = 'U',


          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.



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


          The triangular factor U or L from the Cholesky factorization


          A = U**H*U or A = L*L**H of the band matrix A, stored in the


          first KD+1 rows of the array.  The j-th column of U or L is


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


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


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

LDAB



          LDAB is INTEGER


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

ANORM



          ANORM is DOUBLE PRECISION


          The 1-norm (or infinity-norm) of the Hermitian band matrix A.

RCOND



          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.

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 131 of file zpbcon.f.

Author

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