ctfttr man page on Scientific

Man page or keyword search:  
man Server   26626 pages
apropos Keyword Search (all sections)
Output format
Scientific logo
[printable version]

CTFTTR(1LAPACK routine (version 3.2)				     CTFTTR(1)

NAME
       CTFTTR - copies a triangular matrix A from rectangular full packed for‐
       mat (TF) to standard full format (TR)

SYNOPSIS
       SUBROUTINE CTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )

	   CHARACTER	  TRANSR, UPLO

	   INTEGER	  INFO, N, LDA

	   COMPLEX	  A( 0: LDA-1, 0: * ), ARF( 0: * )

PURPOSE
       CTFTTR copies a triangular matrix A from rectangular full packed format
       (TF) to standard full format (TR).

ARGUMENTS
       TRANSR	(input) CHARACTER
		= 'N':	ARF is in Normal format;
		= 'C':	ARF is in Conjugate-transpose format;

       UPLO    (input) CHARACTER
	       = 'U':  A is upper triangular;
	       = 'L':  A is lower triangular.

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

       ARF     (input) COMPLEX array, dimension ( N*(N+1)/2 ),
	       On  entry, the upper or lower triangular matrix A stored in RFP
	       format. For a further discussion see Notes below.

       A       (output) COMPLEX array, dimension ( LDA, N )
	       On exit, the triangular matrix A.  If UPLO = 'U',  the  leading
	       N-by-N  upper triangular part of the array A contains the upper
	       triangular matrix, and the strictly lower triangular part of  A
	       is  not	referenced.   If  UPLO = 'L', the leading N-by-N lower
	       triangular part of the array A contains	the  lower  triangular
	       matrix, and the strictly upper triangular part of A is not ref‐
	       erenced.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS
       We first consider Standard Packed Format when N is even.
       We give an example where N = 6.
	   AP is Upper		   AP is Lower
	00 01 02 03 04 05	00
	   11 12 13 14 15	10 11
	      22 23 24 25	20 21 22
		 33 34 35	30 31 32 33
		    44 45	40 41 42 43 44
		       55	50 51 52 53 54 55
       Let TRANSR = 'N'. RFP holds AP as follows:
       For UPLO = 'U' the upper trapezoid  A(0:5,0:2)  consists	 of  the  last
       three  columns  of  AP upper. The lower triangle A(4:6,0:2) consists of
       conjugate-transpose of the first three columns of AP upper.  For UPLO =
       'L'  the lower trapezoid A(1:6,0:2) consists of the first three columns
       of AP lower. The upper triangle A(0:2,0:2) consists of conjugate-trans‐
       pose  of	 the  last  three columns of AP lower.	To denote conjugate we
       place -- above the element. This covers the case N even	and  TRANSR  =
       'N'.
	      RFP A		      RFP A
				     -- -- --
	     03 04 05		     33 43 53
					-- --
	     13 14 15		     00 44 54
					   --
	     23 24 25		     10 11 55
	     33 34 35		     20 21 22
	     --
	     00 44 45		     30 31 32
	     -- --
	     01 11 55		     40 41 42
	     -- -- --
	     02 12 22		     50 51 52
       Now  let	 TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
       transpose of RFP A above. One therefore gets:
		RFP A			RFP A
	  -- -- -- --		     -- -- -- -- -- --
	  03 13 23 33 00 01 02	  33 00 10 20 30 40 50
	  -- -- -- -- --		-- -- -- -- --
	  04 14 24 34 44 11 12	  43 44 11 21 31 41 51
	  -- -- -- -- -- --		   -- -- -- --
	  05 15 25 35 45 55 22	  53 54 55 22 32 42 52
       We next	consider Standard Packed Format when N is odd.
       We give an example where N = 5.
	  AP is Upper		      AP is Lower
	00 01 02 03 04		    00
	   11 12 13 14		    10 11
	      22 23 24		    20 21 22
		 33 34		    30 31 32 33
		    44		    40 41 42 43 44
       Let TRANSR = 'N'. RFP holds AP as follows:
       For UPLO = 'U' the upper trapezoid  A(0:4,0:2)  consists	 of  the  last
       three  columns  of  AP upper. The lower triangle A(3:4,0:1) consists of
       conjugate-transpose of the first two   columns of AP upper.  For UPLO =
       'L'  the lower trapezoid A(0:4,0:2) consists of the first three columns
       of AP lower. The upper triangle A(0:1,1:2) consists of conjugate-trans‐
       pose  of	 the  last  two	  columns of AP lower.	To denote conjugate we
       place -- above the element. This covers the case N odd	and  TRANSR  =
       'N'.
	      RFP A		      RFP A
					-- --
	     02 03 04		     00 33 43
					   --
	     12 13 14		     10 11 44
	     22 23 24		     20 21 22
	     --
	     00 33 34		     30 31 32
	     -- --
	     01 11 44		     40 41 42
       Now  let	 TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
       transpose of RFP A above. One therefore gets:
		RFP A			RFP A
	  -- -- --		     -- -- -- -- -- --
	  02 12 22 00 01	     00 10 20 30 40 50
	  -- -- -- --			-- -- -- -- --
	  03 13 23 33 11	     33 11 21 31 41 51
	  -- -- -- -- --		   -- -- -- --
	  04 14 24 34 44	     43 44 22 32 42 52

 LAPACK routine (version 3.2)	 November 2008			     CTFTTR(1)
[top]

List of man pages available for Scientific

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