dtpttf.f(3)							      LAPACK							       dtpttf.f(3)

NAME

       dtpttf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dtpttf (TRANSR, UPLO, N, AP, ARF, INFO)
	   DTPTTF

Function/Subroutine Documentation
   subroutine dtpttf (characterTRANSR, characterUPLO, integerN, double precision, dimension( 0: * )AP, double precision, dimension( 0: * )ARF,
       integerINFO)
       DTPTTF

       Purpose:

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

       Parameters:
	   TRANSR

		     TRANSR is CHARACTER*1
		     = 'N':  ARF in Normal format is wanted;
		     = 'T':  ARF in Conjugate-transpose format 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.

	   AP

		     AP is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),
		     On entry, 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.

	   ARF

		     ARF is DOUBLE PRECISION 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:
	   November 2011

       Further Details:

	     We first consider Rectangular Full Packed (RFP) 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
	     the 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
	     the transpose of the last three columns of AP lower.
	     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 = 'T'. RFP A in both UPLO cases is just the
	     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 then consider Rectangular Full Packed (RFP) 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
	     the 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
	     the transpose of the last two columns of AP lower.
	     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 = 'T'. RFP A in both UPLO cases is just the
	     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 187 of file dtpttf.f.

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