cpbstf man page on IRIX

Man page or keyword search:  
man Server   31559 pages
apropos Keyword Search (all sections)
Output format
IRIX logo
[printable version]



CPBSTF(3F)							    CPBSTF(3F)

NAME
     CPBSTF - compute a split Cholesky factorization of a complex Hermitian
     positive definite band matrix A

SYNOPSIS
     SUBROUTINE CPBSTF( UPLO, N, KD, AB, LDAB, INFO )

	 CHARACTER	UPLO

	 INTEGER	INFO, KD, LDAB, N

	 COMPLEX	AB( LDAB, * )

PURPOSE
     CPBSTF computes a split Cholesky factorization of a complex Hermitian
     positive definite band matrix A.

     This routine is designed to be used in conjunction with CHBGST.

     The factorization has the form  A = S**H*S	 where S is a band matrix of
     the same bandwidth as A and the following structure:

       S = ( U	  )
	   ( M	L )

     where U is upper triangular of order m = (n+kd)/2, and L is lower
     triangular of order n-m.

ARGUMENTS
     UPLO    (input) CHARACTER*1
	     = 'U':  Upper triangle of A is stored;
	     = 'L':  Lower triangle of A is stored.

     N	     (input) INTEGER
	     The order of the matrix A.	 N >= 0.

     KD	     (input) INTEGER
	     The number of superdiagonals of the matrix A if UPLO = 'U', or
	     the number of subdiagonals if UPLO = 'L'.	KD >= 0.

     AB	     (input/output) COMPLEX array, dimension (LDAB,N)
	     On entry, the upper or lower triangle of the Hermitian band
	     matrix A, stored in the first kd+1 rows of the array.  The j-th
	     column of A is stored in the j-th column of the array AB as
	     follows:  if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
	     kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for
	     j<=i<=min(n,j+kd).

	     On exit, if INFO = 0, the factor S from the split Cholesky
	     factorization A = S**H*S. See Further Details.  LDAB    (input)
	     INTEGER The leading dimension of the array AB.  LDAB >= KD+1.

									Page 1

CPBSTF(3F)							    CPBSTF(3F)

     INFO    (output) INTEGER
	     = 0: successful exit
	     < 0: if INFO = -i, the i-th argument had an illegal value
	     > 0: if INFO = i, the factorization could not be completed,
	     because the updated element a(i,i) was negative; the matrix A is
	     not positive definite.

FURTHER DETAILS
     The band storage scheme is illustrated by the following example, when N =
     7, KD = 2:

     S = ( s11	s12  s13		     )
	 (	s22  s23  s24		     )
	 (	     s33  s34		     )
	 (		  s44		     )
	 (	     s53  s54  s55	     )
	 (		  s64  s65  s66	     )
	 (		       s75  s76	 s77 )

     If UPLO = 'U', the array AB holds:

     on entry:				on exit:

      *	   *   a13  a24	 a35  a46  a57	 *    *	  s13  s24  s53' s64' s75'
      *	  a12  a23  a34	 a45  a56  a67	 *   s12  s23  s34  s54' s65' s76' a11
     a22  a33  a44  a55	 a66  a77  s11	s22  s33  s44  s55  s66	 s77

     If UPLO = 'L', the array AB holds:

     on entry:				on exit:

     a11  a22  a33  a44	 a55  a66  a77	s11  s22  s33  s44  s55	 s66  s77 a21
     a32  a43  a54  a65	 a76   *   s12' s23' s34' s54  s65  s76	  * a31	 a42
     a53  a64  a64   *	  *   s13' s24' s53  s64  s75	*    *

     Array elements marked * are not used by the routine; s12' denotes
     conjg(s12); the diagonal elements of S are real.

									Page 2

[top]

List of man pages available for IRIX

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net