1ZTPTTF(1)LAPACK routine (version 3.2) ZTPTTF(1)
2
6 ZTPTTF - copies a triangular matrix A from standard packed format (TP)
7 to rectangular full packed format (TF)
8
10 SUBROUTINE ZTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
11 CHARACTER TRANSR, UPLO
13 INTEGER INFO, N
15 COMPLEX*16 AP( 0: * ), ARF( 0: * )
17
19 ZTPTTF copies a triangular matrix A from standard packed format (TP) to
20 rectangular full packed format (TF).
21
23 TRANSR (input) CHARACTER
24 = 'N': ARF in Normal format is wanted;
25 = 'C': ARF in Conjugate-transpose format is wanted.
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 AP (input) COMPLEX*16 array, dimension ( N*(N+1)/2 ),
35 On entry, the upper or lower triangular matrix A, packed colum‐
36 nwise in a linear array. The j-th column of A is stored in the
37 array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j)
38 for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for
39 j<=i<=n.
40 ARF (output) COMPLEX*16 array, dimension ( N*(N+1)/2 ),
42 On exit, the upper or lower triangular matrix A stored in RFP
43 format. For a further discussion see Notes below.
44 INFO (output) INTEGER
46 = 0: successful exit
47 < 0: if INFO = -i, the i-th argument had an illegal value
48
50 We first consider Standard Packed Format when N is even.
51 We give an example where N = 6.
52 AP is Upper AP is Lower
53 00 01 02 03 04 05 00
54 11 12 13 14 15 10 11
55 22 23 24 25 20 21 22
56 33 34 35 30 31 32 33
57 44 45 40 41 42 43 44
58 55 50 51 52 53 54 55
59 Let TRANSR = 'N'. RFP holds AP as follows:
60 For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
61 three columns of AP upper. The lower triangle A(4:6,0:2) consists of
62 conjugate-transpose of the first three columns of AP upper. For UPLO =
63 'L' the lower trapezoid A(1:6,0:2) consists of the first three columns
64 of AP lower. The upper triangle A(0:2,0:2) consists of conjugate-trans‐
65 pose of the last three columns of AP lower. To denote conjugate we
66 place -- above the element. This covers the case N even and TRANSR =
67 'N'.
68 RFP A RFP A
69 -- -- --
70 03 04 05 33 43 53
71 -- --
72 13 14 15 00 44 54
73 --
74 23 24 25 10 11 55
75 33 34 35 20 21 22
76 --
77 00 44 45 30 31 32
78 -- --
79 01 11 55 40 41 42
80 -- -- --
81 02 12 22 50 51 52
82 Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
83 transpose of RFP A above. One therefore gets:
84 RFP A RFP A
85 -- -- -- -- -- -- -- -- -- --
86 03 13 23 33 00 01 02 33 00 10 20 30 40 50
87 -- -- -- -- -- -- -- -- -- --
88 04 14 24 34 44 11 12 43 44 11 21 31 41 51
89 -- -- -- -- -- -- -- -- -- --
90 05 15 25 35 45 55 22 53 54 55 22 32 42 52
91 We next consider Standard Packed Format when N is odd.
92 We give an example where N = 5.
93 AP is Upper AP is Lower
94 00 01 02 03 04 00
95 11 12 13 14 10 11
96 22 23 24 20 21 22
97 33 34 30 31 32 33
98 44 40 41 42 43 44
99 Let TRANSR = 'N'. RFP holds AP as follows:
100 For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
101 three columns of AP upper. The lower triangle A(3:4,0:1) consists of
102 conjugate-transpose of the first two columns of AP upper. For UPLO =
103 'L' the lower trapezoid A(0:4,0:2) consists of the first three columns
104 of AP lower. The upper triangle A(0:1,1:2) consists of conjugate-trans‐
105 pose of the last two columns of AP lower. To denote conjugate we
106 place -- above the element. This covers the case N odd and TRANSR =
107 'N'.
108 RFP A RFP A
109 -- --
110 02 03 04 00 33 43
111 --
112 12 13 14 10 11 44
113 22 23 24 20 21 22
114 --
115 00 33 34 30 31 32
116 -- --
117 01 11 44 40 41 42
118 Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
119 transpose of RFP A above. One therefore gets:
120 RFP A RFP A
121 -- -- -- -- -- -- -- -- --
122 02 12 22 00 01 00 10 20 30 40 50
123 -- -- -- -- -- -- -- -- --
124 03 13 23 33 11 33 11 21 31 41 51
125 -- -- -- -- -- -- -- -- --
126 04 14 24 34 44 43 44 22 32 42 52
127 LAPACK routine (version 3.2) November 2008 ZTPTTF(1)