spbcon (3p)

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, KD, A, LDA, ANORM, RCOND, WORK, WORK2,
INFO)

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

SUBROUTINE SPBCON_64(UPLO, N, KD, A, LDA, ANORM, RCOND, WORK,
WORK2, INFO)

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




F95 INTERFACE
SUBROUTINE PBCON(UPLO, N, KD, A, LDA, ANORM, RCOND, WORK,
WORK2, INFO)

CHARACTER(LEN=1) :: UPLO
INTEGER :: N, KD, LDA, INFO
INTEGER, DIMENSION(:) :: WORK2
REAL :: ANORM, RCOND
REAL, DIMENSION(:) :: WORK
REAL, DIMENSION(:,:) :: A

SUBROUTINE PBCON_64(UPLO, N, KD, A, LDA, ANORM, RCOND, WORK,
WORK2, INFO)

CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, KD, 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 kd, float *a, int lda, float anorm,
float *rcond, int *info);

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

Description

Oracle Solaris Studio Performance Library                           spbcon(3P)



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, KD, A, LDA, ANORM, RCOND, WORK, WORK2,
             INFO)

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

       SUBROUTINE SPBCON_64(UPLO, N, KD, A, LDA, ANORM, RCOND, WORK,
             WORK2, INFO)

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




   F95 INTERFACE
       SUBROUTINE PBCON(UPLO, N, KD, A, LDA, ANORM, RCOND, WORK,
              WORK2, INFO)

       CHARACTER(LEN=1) :: UPLO
       INTEGER :: N, KD, LDA, INFO
       INTEGER, DIMENSION(:) :: WORK2
       REAL :: ANORM, RCOND
       REAL, DIMENSION(:) :: WORK
       REAL, DIMENSION(:,:) :: A

       SUBROUTINE PBCON_64(UPLO, N, KD, A, LDA, ANORM, RCOND, WORK,
              WORK2, INFO)

       CHARACTER(LEN=1) :: UPLO
       INTEGER(8) :: N, KD, 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 kd, float *a, int lda, float anorm,
                 float *rcond, int *info);

       void spbcon_64(char uplo, long n, long kd, 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.


       KD (input)
                 The number of superdiagonals of the matrix A if UPLO  =  'U',
                 or the number of subdiagonals if UPLO = 'L'.  KD >= 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  KD+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 >= KD+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, com-
                 puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti-
                 mate 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




                                  7 Nov 2015                        spbcon(3P)