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

NAME

spbcon - estimate 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

SYNOPSIS

  SUBROUTINE SPBCON( UPLO, N, NDIAG, A, LDA, ANORM, RCOND, WORK, 
 *      WORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, NDIAG, LDA, INFO
  INTEGER WORK2(*)
  REAL ANORM, RCOND
  REAL A(LDA,*), WORK(*)

  SUBROUTINE SPBCON_64( UPLO, N, NDIAG, A, LDA, ANORM, RCOND, WORK, 
 *      WORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, NDIAG, LDA, INFO
  INTEGER*8 WORK2(*)
  REAL ANORM, RCOND
  REAL A(LDA,*), WORK(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

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

void spbcon_64(char uplo, long n, long ndiag, float *a, long lda, float anorm, float *rcond, long *info);

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))).

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 subdiagonals if UPLO = 'L'. NDIAG > = 0.

• A (input)
  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 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 symmetric 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(3*N)

• WORK2 (workspace)
  dimension(N)

• INFO (output)
  

   = 0:  successful exit

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