ZTPTTF - Online Linux Manual Page

Section : 1
Updated : November 2008
Source : LAPACK routine (version 3.2)
Note : LAPACK routine (version 3.2)
NAMEZTPTTF - copies a triangular matrix A from standard packed format (TP) to rectangular full packed format (TF)
SYNOPSISSUBROUTINE ZTPTTF(  TRANSR, UPLO, N, AP, ARF, INFO )  CHARACTER TRANSR, UPLO  INTEGER INFO, N  COMPLEX*16 AP( 0: * ), ARF( 0: * )
PURPOSEZTPTTF copies a triangular matrix A from standard packed format (TP) to rectangular full packed format (TF).
ARGUMENTSTRANSR (input) CHARACTER  = 'N': ARF in Normal format is wanted;
= 'C': 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) COMPLEX*16 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 (output) 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 (output) INTEGER  = 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
FURTHER DETAILSWe 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
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