subroutine ctrttf (TRANSR, UPLO, N, A, LDA, ARF, INFO)
CTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
CTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
Purpose:
CTRTTF copies a triangular matrix A from standard full format (TR) to rectangular full packed format (TF) .
Parameters:
TRANSR is CHARACTER*1 = 'N': ARF in Normal mode is wanted; = 'C': ARF in Conjugate Transpose mode is wanted;
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.
A
A is COMPLEX 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 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
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
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 218 of file ctrttf.f.
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