1ZTFTTR(1)LAPACK routine (version 3.2) ZTFTTR(1)
2
6 ZTFTTR - copies a triangular matrix A from rectangular full packed for‐
7 mat (TF) to standard full format (TR)
8
10 SUBROUTINE ZTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
11 CHARACTER TRANSR, UPLO
13 INTEGER INFO, N, LDA
15 COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * )
17
19 ZTFTTR 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 = 'C': ARF is in Conjugate-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 matrix A. N >= 0.
33 ARF (input) COMPLEX*16 array, dimension ( N*(N+1)/2 ),
35 On entry, the upper or lower triangular matrix A stored in RFP
36 format. For a further discussion see Notes below.
37 A (output) COMPLEX*16 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 Standard Packed 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 conjugate-transpose of the first three columns of AP upper. For UPLO =
68 'L' the lower trapezoid A(1:6,0:2) consists of the first three columns
69 of AP lower. The upper triangle A(0:2,0:2) consists of conjugate-trans‐
70 pose of the last three columns of AP lower. To denote conjugate we
71 place -- above the element. This covers the case N even and TRANSR =
72 'N'.
73 RFP A RFP A
74 -- -- --
75 03 04 05 33 43 53
76 -- --
77 13 14 15 00 44 54
78 --
79 23 24 25 10 11 55
80 33 34 35 20 21 22
81 --
82 00 44 45 30 31 32
83 -- --
84 01 11 55 40 41 42
85 -- -- --
86 02 12 22 50 51 52
87 Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
88 transpose of RFP A above. One therefore gets:
89 RFP A RFP A
90 -- -- -- -- -- -- -- -- -- --
91 03 13 23 33 00 01 02 33 00 10 20 30 40 50
92 -- -- -- -- -- -- -- -- -- --
93 04 14 24 34 44 11 12 43 44 11 21 31 41 51
94 -- -- -- -- -- -- -- -- -- --
95 05 15 25 35 45 55 22 53 54 55 22 32 42 52
96 We next consider Standard Packed Format when N is odd.
97 We give an example where N = 5.
98 AP is Upper AP is Lower
99 00 01 02 03 04 00
100 11 12 13 14 10 11
101 22 23 24 20 21 22
102 33 34 30 31 32 33
103 44 40 41 42 43 44
104 Let TRANSR = 'N'. RFP holds AP as follows:
105 For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
106 three columns of AP upper. The lower triangle A(3:4,0:1) consists of
107 conjugate-transpose of the first two columns of AP upper. For UPLO =
108 'L' the lower trapezoid A(0:4,0:2) consists of the first three columns
109 of AP lower. The upper triangle A(0:1,1:2) consists of conjugate-trans‐
110 pose of the last two columns of AP lower. To denote conjugate we
111 place -- above the element. This covers the case N odd and TRANSR =
112 'N'.
113 RFP A RFP A
114 -- --
115 02 03 04 00 33 43
116 --
117 12 13 14 10 11 44
118 22 23 24 20 21 22
119 --
120 00 33 34 30 31 32
121 -- --
122 01 11 44 40 41 42
123 Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
124 transpose of RFP A above. One therefore gets:
125 RFP A RFP A
126 -- -- -- -- -- -- -- -- --
127 02 12 22 00 01 00 10 20 30 40 50
128 -- -- -- -- -- -- -- -- --
129 03 13 23 33 11 33 11 21 31 41 51
130 -- -- -- -- -- -- -- -- --
131 04 14 24 34 44 43 44 22 32 42 52
132 LAPACK routine (version 3.2) November 2008 ZTFTTR(1)