dtrttf (3) - Linux Manuals

NAME

dtrttf.f -

SYNOPSIS

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine dtrttf (characterTRANSR, characterUPLO, integerN, double precision, dimension( 0: lda-1, 0: * )A, integerLDA, double precision, dimension( 0: * )ARF, integerINFO)

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

Purpose:

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

 

Parameters:

TRANSR

          TRANSR is CHARACTER*1
          = 'N':  ARF in Normal form is wanted;
          = 'T':  ARF in Transpose form is wanted.

UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

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

A

          A is DOUBLE PRECISION array, dimension (LDA,N).
          On entry, 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 matrix A. LDA >= max(1,N).

ARF

          ARF is DOUBLE PRECISION array, dimension (NT).
          NT=N*(N+1)/2. On exit, the triangular matrix A in RFP format.

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 195 of file dtrttf.f.

Author

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