• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

zpbcon - 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 ZPBCON( UPLO, N, NDIAG, A, LDA, ANORM, RCOND, WORK, 
 *      WORK2, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX A(LDA,*), WORK(*)
  INTEGER N, NDIAG, LDA, INFO
  DOUBLE PRECISION ANORM, RCOND
  DOUBLE PRECISION WORK2(*)

  SUBROUTINE ZPBCON_64( UPLO, N, NDIAG, A, LDA, ANORM, RCOND, WORK, 
 *      WORK2, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX A(LDA,*), WORK(*)
  INTEGER*8 N, NDIAG, LDA, INFO
  DOUBLE PRECISION ANORM, RCOND
  DOUBLE PRECISION WORK2(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

void zpbcon(char uplo, int n, int ndiag, doublecomplex *a, int lda, double anorm, double *rcond, int *info);

void zpbcon_64(char uplo, long n, long ndiag, doublecomplex *a, long lda, double anorm, double *rcond, long *info);

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 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)
  

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

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

• 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)
  dimension(N)

• INFO (output)
  

   = 0:  successful exit

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