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ztfttp.f(3) LAPACK ztfttp.f(3)

ztfttp.f -


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

ZTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP).
Purpose:
 ZTFTTP copies a triangular matrix A from rectangular full packed
 format (TF) to standard packed format (TP).
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*16 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.
AP
          AP is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
          On exit, 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.
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 209 of file ztfttp.f.

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