CTPTTF(1LAPACK routine (version 3.2)CTPTTF(1)NAME
CTPTTF - copies a triangular matrix A from standard packed format (TP)
to rectangular full packed format (TF)
SYNOPSIS
SUBROUTINE CTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
CHARACTER TRANSR, UPLO
INTEGER INFO, N
COMPLEX AP( 0: * ), ARF( 0: * )
PURPOSE
CTPTTF copies a triangular matrix A from standard packed format (TP) to
rectangular full packed format (TF).
ARGUMENTS
TRANSR (input) CHARACTER
= 'N': ARF in Normal format is wanted;
= 'C': ARF in Conjugate-transpose format is wanted.
UPLO (input) CHARACTER
= 'U': A is upper triangular;
= 'L': A is lower triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input) COMPLEX array, dimension ( N*(N+1)/2 ),
On entry, the upper or lower triangular matrix A, packed colum‐
nwise 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 (output) COMPLEX 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 (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
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-trans‐
pose 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-trans‐
pose 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
LAPACK routine (version 3.2) November 2008 CTPTTF(1)
