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dtfttr.f(3) LAPACK dtfttr.f(3)

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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