1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
|
subroutine balbak(nm,n,low,igh,scale,m,z)
c
integer i,j,k,m,n,ii,nm,igh,low
double precision scale(n),z(nm,m)
double precision s
c! purpose
c
c this subroutine forms the eigenvectors of a real general
c matrix by back transforming those of the corresponding
c balanced matrix determined by balanc.
c
c! calling sequence
c
c subroutine balbak(nm,n,low,igh,scale,m,z)
c
c on input:
c
c nm must be set to the row dimension of two-dimensional
c array parameters as declared in the calling program
c dimension statement;
c
c n is the order of the matrix;
c
c low and igh are integers determined by balanc;
c
c scale contains information determining the permutations
c and scaling factors used by balanc;
c
c m is the number of columns of z to be back transformed;
c
c z contains the real and imaginary parts of the eigen-
c vectors to be back transformed in its first m columns.
c
c on output:
c
c z contains the real and imaginary parts of the
c transformed eigenvectors in its first m columns.
c
c! originator
c
c this subroutine is a translation of the algol procedure balbak,
c num. math. 13, 293-304(1969) by parlett and reinsch.
c handbook for auto. comp., vol.ii-linear algebra, 315-326(1971).
c!
c questions and comments should be directed to b. s. garbow,
c applied mathematics division, argonne national laboratory
c
c ------------------------------------------------------------------
c
if (m .eq. 0) go to 200
if (igh .eq. low) go to 120
c
do 110 i = low, igh
s = scale(i)
c :::::::::: left hand eigenvectors are back transformed
c if the foregoing statement is replaced by
c s=1.0d+0/scale(i). ::::::::::
do 100 j = 1, m
100 z(i,j) = z(i,j) * s
c
110 continue
c ::::::::: for i=low-1 step -1 until 1,
c igh+1 step 1 until n do -- ::::::::::
120 do 140 ii = 1, n
i = ii
if (i .ge. low .and. i .le. igh) go to 140
if (i .lt. low) i = low - ii
k = scale(i)
if (k .eq. i) go to 140
c
do 130 j = 1, m
s = z(i,j)
z(i,j) = z(k,j)
z(k,j) = s
130 continue
c
140 continue
c
200 return
end
|
