CHPTRF man page on IRIX

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



CHPTRF(3F)							    CHPTRF(3F)

NAME
     CHPTRF - compute the factorization of a complex Hermitian packed matrix A
     using the Bunch-Kaufman diagonal pivoting method

SYNOPSIS
     SUBROUTINE CHPTRF( UPLO, N, AP, IPIV, INFO )

	 CHARACTER	UPLO

	 INTEGER	INFO, N

	 INTEGER	IPIV( * )

	 COMPLEX	AP( * )

PURPOSE
     CHPTRF computes the factorization of a complex Hermitian packed matrix A
     using the Bunch-Kaufman diagonal pivoting method:

	A = U*D*U**H  or  A = L*D*L**H

     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, and D is Hermitian and block diagonal with 1-by-1
     and 2-by-2 diagonal blocks.

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.

     AP	     (input/output) COMPLEX array, dimension (N*(N+1)/2)
	     On entry, the upper or lower triangle of the Hermitian matrix A,
	     packed columnwise in a linear array.  The j-th column of A is
	     stored in the array AP as follows:	 if UPLO = 'U', AP(i + (j-
	     1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-
	     j)/2) = A(i,j) for j<=i<=n.

	     On exit, the block diagonal matrix D and the multipliers used to
	     obtain the factor U or L, stored as a packed triangular matrix
	     overwriting A (see below for further details).

     IPIV    (output) INTEGER array, dimension (N)
	     Details of the interchanges and the block structure of D.	If
	     IPIV(k) > 0, then rows and columns k and IPIV(k) were
	     interchanged and D(k,k) is a 1-by-1 diagonal block.  If UPLO =
	     'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and
	     -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2
	     diagonal block.  If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then

									Page 1

CHPTRF(3F)							    CHPTRF(3F)

	     rows and columns k+1 and -IPIV(k) were interchanged and
	     D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

     INFO    (output) INTEGER
	     = 0: successful exit
	     < 0: if INFO = -i, the i-th argument had an illegal value
	     > 0: if INFO = i, D(i,i) is exactly zero.	The factorization has
	     been completed, but the block diagonal matrix D is exactly
	     singular, and division by zero will occur if it is used to solve
	     a system of equations.

FURTHER DETAILS
     If UPLO = 'U', then A = U*D*U', where
	U = P(n)*U(n)* ... *P(k)U(k)* ...,
     i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in
     steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2
     diagonal blocks D(k).  P(k) is a permutation matrix as defined by
     IPIV(k), and U(k) is a unit upper triangular matrix, such that if the
     diagonal block D(k) is of order s (s = 1 or 2), then

		(   I	 v    0	  )   k-s
	U(k) =	(   0	 I    0	  )   s
		(   0	 0    I	  )   n-k
		   k-s	 s   n-k

     If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).  If s = 2,
     the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k),
     and v overwrites A(1:k-2,k-1:k).

     If UPLO = 'L', then A = L*D*L', where
	L = P(1)*L(1)* ... *P(k)*L(k)* ...,
     i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in
     steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2
     diagonal blocks D(k).  P(k) is a permutation matrix as defined by
     IPIV(k), and L(k) is a unit lower triangular matrix, such that if the
     diagonal block D(k) is of order s (s = 1 or 2), then

		(   I	 0     0   )  k-1
	L(k) =	(   0	 I     0   )  s
		(   0	 v     I   )  n-k-s+1
		   k-1	 s  n-k-s+1

     If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).  If s = 2,
     the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1),
     and v overwrites A(k+2:n,k:k+1).

									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