ctfttp.f(3)							      LAPACK							       ctfttp.f(3)

NAME

       ctfttp.f -

SYNOPSIS

   Functions/Subroutines
       subroutine ctfttp (TRANSR, UPLO, N, ARF, AP, INFO)
	   CTFTTP

Function/Subroutine Documentation
   subroutine ctfttp (characterTRANSR, characterUPLO, integerN, complex, dimension( 0: * )ARF, complex, dimension( 0: * )AP, integerINFO)
       CTFTTP

       Purpose:

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

       Parameters:
	   TRANSR

		     TRANSR is CHARACTER*1
		     = 'N':  ARF is in Normal format;
		     = 'C':  ARF is in Conjugate-transpose format;

	   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.

	   ARF

		     ARF is 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.

	   AP

		     AP is COMPLEX array, dimension ( N*(N+1)/2 ),
		     On exit, the upper or lower triangular 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.

	   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:
	   November 2011

       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 209 of file ctfttp.f.

Author
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Version 3.4.1							  Sun May 26 2013						       ctfttp.f(3)