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DTPTTF(1LAPACK routine (version 3.2)				     DTPTTF(1)

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

SYNOPSIS
       SUBROUTINE DTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )

	   CHARACTER	  TRANSR, UPLO

	   INTEGER	  INFO, N

	   DOUBLE	  PRECISION AP( 0: * ), ARF( 0: * )

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

ARGUMENTS
       TRANSR	(input) CHARACTER
		= 'N':	ARF in Normal format is wanted;
		= 'T':	ARF in Conjugate-transpose format is wanted.

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

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

       AP      (input) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),
	       On entry, the upper or lower triangular matrix A, packed colum‐
	       nwise 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     (output) 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    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

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 first 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

 LAPACK routine (version 3.2)	 November 2008			     DTPTTF(1)
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