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