clarzt man page on IRIX

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



CLARZT(3S)							    CLARZT(3S)

NAME
     CLARZT - form the triangular factor T of a complex block reflector H of
     order > n, which is defined as a product of k elementary reflectors

SYNOPSIS
     SUBROUTINE CLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )

	 CHARACTER	DIRECT, STOREV

	 INTEGER	K, LDT, LDV, N

	 COMPLEX	T( LDT, * ), TAU( * ), V( LDV, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CLARZT forms the triangular factor T of a complex block reflector H of
     order > n, which is defined as a product of k elementary reflectors. If
     DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;

     If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.

     If STOREV = 'C', the vector which defines the elementary reflector H(i)
     is stored in the i-th column of the array V, and

	H  =  I - V * T * V'

     If STOREV = 'R', the vector which defines the elementary reflector H(i)
     is stored in the i-th row of the array V, and

	H  =  I - V' * T * V

     Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

ARGUMENTS
     DIRECT  (input) CHARACTER*1
	     Specifies the order in which the elementary reflectors are
	     multiplied to form the block reflector:
	     = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
	     = 'B': H = H(k) . . . H(2) H(1) (Backward)

									Page 1

CLARZT(3S)							    CLARZT(3S)

     STOREV  (input) CHARACTER*1
	     Specifies how the vectors which define the elementary reflectors
	     are stored (see also Further Details):
	     = 'R': rowwise

     N	     (input) INTEGER
	     The order of the block reflector H. N >= 0.

     K	     (input) INTEGER
	     The order of the triangular factor T (= the number of elementary
	     reflectors). K >= 1.

     V	     (input/output) COMPLEX array, dimension
	     (LDV,K) if STOREV = 'C' (LDV,N) if STOREV = 'R' The matrix V. See
	     further details.

     LDV     (input) INTEGER
	     The leading dimension of the array V.  If STOREV = 'C', LDV >=
	     max(1,N); if STOREV = 'R', LDV >= K.

     TAU     (input) COMPLEX array, dimension (K)
	     TAU(i) must contain the scalar factor of the elementary reflector
	     H(i).

     T	     (output) COMPLEX array, dimension (LDT,K)
	     The k by k triangular factor T of the block reflector.  If DIRECT
	     = 'F', T is upper triangular; if DIRECT = 'B', T is lower
	     triangular. The rest of the array is not used.

     LDT     (input) INTEGER
	     The leading dimension of the array T. LDT >= K.

FURTHER DETAILS
     Based on contributions by
       A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

     The shape of the matrix V and the storage of the vectors which define the
     H(i) is best illustrated by the following example with n = 5 and k = 3.
     The elements equal to 1 are not stored; the corresponding array elements
     are modified but restored on exit. The rest of the array is not used.

     DIRECT = 'F' and STOREV = 'C':	    DIRECT = 'F' and STOREV = 'R':

						 ______V_____
	    ( v1 v2 v3 )			/		    ( v1 v2 v3
     )			    ( v1 v1 v1 v1 v1 . . . . 1 )
	V = ( v1 v2 v3 )		      ( v2 v2 v2 v2 v2 . . . 1	 )
	    ( v1 v2 v3 )		      ( v3 v3 v3 v3 v3 . . 1	 )
	    ( v1 v2 v3 )
	       .  .  .
	       .  .  .
	       1  .  .

									Page 2

CLARZT(3S)							    CLARZT(3S)

		  1  .
		     1

     DIRECT = 'B' and STOREV = 'C':	    DIRECT = 'B' and STOREV = 'R':

							   ______V_____
	       1					  /
     .	1			    ( 1 . . . . v1 v1 v1 v1 v1 )
	       .  .  1			      ( . 1 . . . v2 v2 v2 v2 v2 )
	       .  .  .			      ( . . 1 . . v3 v3 v3 v3 v3 )
	       .  .  .
	    ( v1 v2 v3 )
	    ( v1 v2 v3 )
	V = ( v1 v2 v3 )
	    ( v1 v2 v3 )
	    ( v1 v2 v3 )

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.

									Page 3

[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