ctfttr.f(3)

NAME
ctfttr.f -

SYNOPSIS

  Functions/Subroutines

subroutine ctfttr (TRANSR, UPLO, N, ARF, A, LDA, INFO)
CTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR).

Function/Subroutine Documentation

  subroutine ctfttr (characterTRANSR, characterUPLO, integerN, complex, dimension( 0: * )ARF, complex, dimension( 0: lda-1, 0: * )A, integerLDA, integerINFO)

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

Purpose:

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

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.

    A

              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

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max(1,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:
    September 2012

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 217 of file ctfttr.f.

Author

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