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CentOS 7.0 - man page for ztrttf (centos section 3)

ztrttf.f(3)				      LAPACK				      ztrttf.f(3)

NAME
       ztrttf.f -

SYNOPSIS
   Functions/Subroutines
       subroutine ztrttf (TRANSR, UPLO, N, A, LDA, ARF, INFO)
	   ZTRTTF copies a triangular matrix from the standard full format (TR) to the
	   rectangular full packed format (TF).

Function/Subroutine Documentation
   subroutine ztrttf (characterTRANSR, characterUPLO, integerN, complex*16, dimension( 0: lda-1,
       0: * )A, integerLDA, complex*16, dimension( 0: * )ARF, integerINFO)
       ZTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular
       full packed format (TF).

       Purpose:

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

       Parameters:
	   TRANSR

		     TRANSR is CHARACTER*1
		     = 'N':  ARF in Normal mode is wanted;
		     = 'C':  ARF in Conjugate Transpose mode is wanted;

	   UPLO

		     UPLO is CHARACTER*1
		     = 'U':  A is upper triangular;
		     = 'L':  A is lower triangular.

	   N

		     N is INTEGER
		     The order of the matrix A.  N >= 0.

	   A

		     A is COMPLEX*16 array, dimension ( LDA, N )
		     On entry, 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 referenced.

	   LDA

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

	   ARF

		     ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
		     On exit, the upper or lower triangular matrix A stored in
		     RFP format. For a further discussion see Notes below.

	   INFO

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       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-transpose 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-transpose 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

       Definition at line 217 of file ztrttf.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      ztrttf.f(3)


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