dtfttr.f man page
dtfttr.f 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). Purpose: TRANSR UPLO N ARF A LDA INFO Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. December 2016 Further Details: Definition at line 198 of file dtfttr.f. Generated automatically by Doxygen for LAPACK from the source code. The man page dtfttr(3) is an alias of dtfttr.f(3).Synopsis
Functions/Subroutines
DTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). Function/Subroutine Documentation
subroutine dtfttr (character TRANSR, character UPLO, integer N, double precision, dimension( 0: * ) ARF, double precision, dimension( 0: lda-1, 0: * ) A, integer LDA, integer INFO)
DTFTTR copies a triangular matrix A from rectangular full packed
format (TF) to standard full format (TR).
TRANSR is CHARACTER*1
= 'N': ARF is in Normal format;
= 'T': ARF is in Transpose format.
UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
N is INTEGER
The order of the matrices ARF and A. N >= 0.
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 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 is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
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
Author
Referenced By