1DTFTTR(1)LAPACK routine (version 3.2) DTFTTR(1)
2
6 DTFTTR - copies a triangular matrix A from rectangular full packed for‐
7 mat (TF) to standard full format (TR)
8
10 SUBROUTINE DTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
11 CHARACTER TRANSR, UPLO
13 INTEGER INFO, N, LDA
15 DOUBLE PRECISION A( 0: LDA-1, 0: * ), ARF( 0: * )
17
19 DTFTTR copies a triangular matrix A from rectangular full packed format
20 (TF) to standard full format (TR).
21
23 TRANSR (input) CHARACTER
24 = 'N': ARF is in Normal format;
25 = 'T': ARF is in Transpose format.
26 UPLO (input) CHARACTER
28 = 'U': A is upper triangular;
29 = 'L': A is lower triangular.
30 N (input) INTEGER
32 The order of the matrices ARF and A. N >= 0.
33 ARF (input) DOUBLE PRECISION array, dimension (N*(N+1)/2).
35 On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
36 matrix A in RFP format. See the "Notes" below for more details.
37 A (output) DOUBLE PRECISION array, dimension (LDA,N)
39 On exit, the triangular matrix A. If UPLO = 'U', the leading
40 N-by-N upper triangular part of the array A contains the upper
41 triangular matrix, and the strictly lower triangular part of A
42 is not referenced. If UPLO = 'L', the leading N-by-N lower
43 triangular part of the array A contains the lower triangular
44 matrix, and the strictly upper triangular part of A is not ref‐
45 erenced.
46 LDA (input) INTEGER
48 The leading dimension of the array A. LDA >= max(1,N).
49 INFO (output) INTEGER
51 = 0: successful exit
52 < 0: if INFO = -i, the i-th argument had an illegal value
53
55 We first consider Rectangular Full Packed (RFP) Format when N is even.
56 We give an example where N = 6.
57 AP is Upper AP is Lower
58 00 01 02 03 04 05 00
59 11 12 13 14 15 10 11
60 22 23 24 25 20 21 22
61 33 34 35 30 31 32 33
62 44 45 40 41 42 43 44
63 55 50 51 52 53 54 55
64 Let TRANSR = 'N'. RFP holds AP as follows:
65 For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
66 three columns of AP upper. The lower triangle A(4:6,0:2) consists of
67 the transpose of the first three columns of AP upper.
68 For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
69 three columns of AP lower. The upper triangle A(0:2,0:2) consists of
70 the transpose of the last three columns of AP lower.
71 This covers the case N even and TRANSR = 'N'.
72 RFP A RFP A
73 03 04 05 33 43 53
74 13 14 15 00 44 54
75 23 24 25 10 11 55
76 33 34 35 20 21 22
77 00 44 45 30 31 32
78 01 11 55 40 41 42
79 02 12 22 50 51 52
80 Now let TRANSR = 'T'. RFP A in both UPLO cases is just the transpose of
81 RFP A above. One therefore gets:
82 RFP A RFP A
83 03 13 23 33 00 01 02 33 00 10 20 30 40 50
84 04 14 24 34 44 11 12 43 44 11 21 31 41 51
85 05 15 25 35 45 55 22 53 54 55 22 32 42 52
86 We first consider Rectangular Full Packed (RFP) Format when N is odd.
87 We give an example where N = 5.
88 AP is Upper AP is Lower
89 00 01 02 03 04 00
90 11 12 13 14 10 11
91 22 23 24 20 21 22
92 33 34 30 31 32 33
93 44 40 41 42 43 44
94 Let TRANSR = 'N'. RFP holds AP as follows:
95 For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
96 three columns of AP upper. The lower triangle A(3:4,0:1) consists of
97 the transpose of the first two columns of AP upper.
98 For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
99 three columns of AP lower. The upper triangle A(0:1,1:2) consists of
100 the transpose of the last two columns of AP lower.
101 This covers the case N odd and TRANSR = 'N'.
102 RFP A RFP A
103 02 03 04 00 33 43
104 12 13 14 10 11 44
105 22 23 24 20 21 22
106 00 33 34 30 31 32
107 01 11 44 40 41 42
108 Now let TRANSR = 'T'. RFP A in both UPLO cases is just the transpose of
109 RFP A above. One therefore gets:
110 RFP A RFP A
111 02 12 22 00 01 00 10 20 30 40 50
112 03 13 23 33 11 33 11 21 31 41 51
113 04 14 24 34 44 43 44 22 32 42 52
114 Reference
115 =========
116 LAPACK routine (version 3.2) November 2008 DTFTTR(1)