cpbcon

NAME

cpbcon - estimate 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

SYNOPSIS

  SUBROUTINE CPBCON( UPLO, N, NDIAG, A, LDA, ANORM, RCOND, WORK, 
 *      WORK2, INFO)
  CHARACTER * 1 UPLO
  COMPLEX A(LDA,*), WORK(*)
  INTEGER N, NDIAG, LDA, INFO
  REAL ANORM, RCOND
  REAL WORK2(*)
 
  SUBROUTINE CPBCON_64( UPLO, N, NDIAG, A, LDA, ANORM, RCOND, WORK, 
 *      WORK2, INFO)
  CHARACTER * 1 UPLO
  COMPLEX A(LDA,*), WORK(*)
  INTEGER*8 N, NDIAG, LDA, INFO
  REAL ANORM, RCOND
  REAL WORK2(*)

F95 INTERFACE

  SUBROUTINE PBCON( UPLO, [N], NDIAG, A, [LDA], ANORM, RCOND, [WORK], 
 *       [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A
  INTEGER :: N, NDIAG, LDA, INFO
  REAL :: ANORM, RCOND
  REAL, DIMENSION(:) :: WORK2
 
  SUBROUTINE PBCON_64( UPLO, [N], NDIAG, A, [LDA], ANORM, RCOND, [WORK], 
 *       [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A
  INTEGER(8) :: N, NDIAG, LDA, INFO
  REAL :: ANORM, RCOND
  REAL, DIMENSION(:) :: WORK2

C INTERFACE

#include <sunperf.h>

void cpbcon(char uplo, int n, int ndiag, complex *a, int lda, float anorm, float *rcond, int *info);

void cpbcon_64(char uplo, long n, long ndiag, complex *a, long lda, float anorm, float *rcond, long *info);

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))).

ARGUMENTS

* UPLO (input)
* N (input): The order of the matrix A. N >= 0.
* NDIAG (input): The number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. NDIAG >= 0.
* A (input): 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 NDIAG+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array A as follows: if UPLO ='U', A(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', A(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
* LDA (input): The leading dimension of the array A. LDA >= NDIAG+1.
* ANORM (input): The 1-norm (or infinity-norm) of the Hermitian band matrix A.
* RCOND (output): 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 (workspace): dimension(2*N)
* WORK2 (workspace)
* INFO (output)