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NAME

       dtfttr.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dtfttr (TRANSR, UPLO, N, ARF, A, LDA, INFO)
           DTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the
           standard full format (TR).

Function/Subroutine Documentation

   subroutine dtfttr (characterTRANSR, characterUPLO, integerN, double precision, dimension( 0: *
       )ARF, double precision, dimension( 0: lda-1, 0: * )A, integerLDA, integerINFO)
       DTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the
       standard full format (TR).

       Purpose:

            DTFTTR 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;
                     = 'T':  ARF is in 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 matrices ARF and A. N >= 0.

           ARF

                     ARF is DOUBLE PRECISION array, dimension (N*(N+1)/2).
                     On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
                     matrix A in RFP format. See the "Notes" below for more
                     details.

           A

                     A is DOUBLE PRECISION 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 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 197 of file dtfttr.f.

Author

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