dtpttf.f(3)

NAME
dtpttf.f -

SYNOPSIS

  Functions/Subroutines

subroutine dtpttf (TRANSR, UPLO, N, AP, ARF, INFO)
DTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).

Function/Subroutine Documentation

  subroutine dtpttf (characterTRANSR, characterUPLO, integerN, double precision, dimension( 0: * )AP, double precision, dimension( 0: * )ARF, integerINFO)

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

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:
    September 2012

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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