CTFTTR(3)      LAPACK routine of NEC Numeric Library Collection      CTFTTR(3)



NAME
       CTFTTR

SYNOPSIS
       SUBROUTINE CTFTTR (TRANSR, UPLO, N, ARF, A, LDA, INFO)



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




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

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

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

           ARF       (input)
                     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.

           A         (output)
                     A is COMPLEX array, dimension ( LDA, N )
                     On exit, 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       (input)
                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,N).

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






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



LAPACK routine                  31 October 2017                      CTFTTR(3)