/
eig.F
276 lines (275 loc) · 4.84 KB
/
eig.F
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
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
c&EIG
c&EIG
subroutine eig(args,nargs,vname)
c*******************************************************************
c
c Subroutine to handle the command
c
c val=EIG(a,n,maxit,ier[,vec])
c
c*******************************************************************
c
#include 'tslabc'
character args(nargs)*15,vname
integer*2 ickl,icki,ickdg
c
c
if(ickl(args(1),npa,na).eq.1) go to 99
if(icki(args(2),2,n,5,56).eq.1) go to 99
ns=n*n
if(n.lt.1.or.n*n.gt.na) then
call error(args,2,2)
go to 99
endif
if(icki(args(3),3,maxit,1,1).eq.1) go to 99
if(maxit.gt.500) then
call error(args,3,2)
go to 99
endif
c
c
nbytes=4*n*n
call movxy(wk,array(nstart(npa)),nbytes)
call max(wk,ns,xmax,imax)
call min(wk,ns,xmin,imin)
xsc=xmax
if(abs(xmin).gt.abs(xmax)) xsc=xmin
if(xsc.eq.0.) then
write(*,102)
102 format(' Matrix all zeros')
imflag=1
go to 99
endif
do 3 i=1,ns
3 wk(i)=wk(i)/xsc
iptvec=0
if(nargs.eq.5) iptvec=1
ns=n*n
ns1=ns+1
ns2=ns1+n
ns3=ns2+2*n*n
ns4=ns3+2*n
call eig2(wk,wk(ns1),wk(ns2),wk(ns3),wk(ns4),n,iptvec,
1 maxit,ier)
if(ier.eq.1) then
write(*,2)
2 format(' Nonconvergence in EIG')
imflag=1
endif
call ckaddi(args(4),ier,iref)
if(iref.eq.1.or.ier.ne.0) go to 99
lab='Eigenvalues'
do 4 i=1,n
4 wk(ns+i)=wk(ns+i)*xsc
call ckadda(vname,n,lab,ns+1,iref)
if(iref.eq.1.or.iptvec.eq.0) go to 99
lab='Eigenvectors'
call ckadda(args(5),ns,lab,1,iref)
c
c
99 continue
return
end
c&EIG2
subroutine eig2(a,vals,wk1,wk2,wk3,n,iptvec,maxit,ier)
c*******************************************************************
c
c
c
c
c******************************************************************
c
dimension a(n,n),vals(n)
double precision wk1(n,n),wk2(n),wk3(n)
double precision h,scale,f,g,hh,dd,r,s,c,p,b
c
c
c Tridiagonalize:
c
if(n.lt.1) then
ier=2
go to 99
endif
if(n.eq.1) then
vals(1)=a(1,1)
ier=0
go to 99
endif
do 5 i=1,n
do 5 j=1,n
5 wk1(i,j)=a(i,j)
do 18 i=n,2,-1
l=i-1
h=0.d0
scale=0.d0
if(l.gt.1) then
do 11 k=1,l
scale=scale+dabs(wk1(i,k))
11 continue
if(scale.eq.0.d0) then
wk2(i)=wk1(i,l)
else
do 12 k=1,l
wk1(i,k)=wk1(i,k)/scale
h=h+wk1(i,k)**2
12 continue
f=wk1(i,l)
g=-dsign(dsqrt(h),f)
wk2(i)=scale*g
h=h-f*g
wk1(i,l)=f-g
f=0.d0
do 15 j=1,l
if(iptvec.eq.1) wk1(j,i)=wk1(i,j)/h
g=0.d0
do 13 k=1,j
g=g+wk1(j,k)*wk1(i,k)
13 continue
if(l.gt.j) then
do 14 k=j+1,l
g=g+wk1(k,j)*wk1(i,k)
14 continue
endif
wk2(j)=g/h
f=f+wk2(j)*wk1(i,j)
15 continue
hh=f/(h+h)
do 17 j=1,l
f=wk1(i,j)
g=wk2(j)-hh*f
wk2(j)=g
do 16 k=1,j
wk1(j,k)=wk1(j,k)-f*wk2(k)-g*wk1(i,k)
16 continue
17 continue
endif
else
wk2(i)=wk1(i,l)
endif
wk3(i)=h
18 continue
if(iptvec.eq.1) wk3(1)=0.d0
wk2(1)=0.d0
do 23 i=1,n
if(iptvec.eq.1) then
l=i-1
if(wk3(i).ne.0.d0) then
do 21 j=1,l
g=0.d0
do 19 k=1,l
g=g+wk1(i,k)*wk1(k,j)
19 continue
do 20 k=1,l
wk1(k,j)=wk1(k,j)-g*wk1(k,i)
20 continue
21 continue
endif
endif
wk3(i)=wk1(i,i)
if(iptvec.eq.1) then
wk1(i,i)=1.d0
if(l.ge.1) then
do 22 j=1,l
wk1(i,j)=0.d0
wk1(j,i)=0.d0
22 continue
endif
endif
23 continue
c
c
c
do 31 i=2,n
31 wk2(i-1)=wk2(i)
wk2(n)=0.d0
do 35 l=1,n
iter=0
1 do 32 m=l,n-1
dd=dabs(wk3(m))+dabs(wk3(m+1))
if(dabs(wk2(m))+dd.eq.dd) go to 2
32 continue
m=n
2 if(m.ne.l) then
if(iter.eq.maxit) then
ier=1
go to 99
endif
iter=iter+1
g=(wk3(l+1)-wk3(l))/(2.*wk2(l))
r=dsqrt(g**2+1.d0)
g=wk3(m)-wk3(l)+wk2(l)/(g+dsign(r,g))
s=1.d0
c=1.d0
p=0.d0
do 34 i=m-1,l,-1
f=s*wk2(i)
b=c*wk2(i)
if(dabs(f).ge.dabs(g)) then
c=g/f
r=dsqrt(c**2+1.d0)
wk2(i+1)=f*r
s=1.d0/r
c=c*s
else
s=f/g
r=dsqrt(s**2+1.d0)
wk2(i+1)=g*r
c=1.d0/r
s=s*c
endif
g=wk3(i+1)-p
r=(wk3(i)-g)*s+2.d0*c*b
p=s*r
wk3(i+1)=g+p
g=c*r-b
if(iptvec.eq.1) then
do 33 k=1,n
f=wk1(k,i+1)
wk1(k,i+1)=s*wk1(k,i)+c*f
wk1(k,i)=c*wk1(k,i)-s*f
33 continue
endif
34 continue
wk3(l)=wk3(l)-p
wk2(l)=g
wk2(m)=0.d0
go to 1
endif
35 continue
c
c
c
do 40 i=1,n
do 40 j=1,n
40 a(i,j)=wk1(i,j)
do 45 i=1,n
45 vals(i)=wk3(i)
c
c sort:
c
do 53 i=1,n-1
k=i
cp=vals(i)
do 51 j=i+1,n
if(vals(j).ge.cp) then
k=j
cp=vals(j)
endif
51 continue
if(k.ne.i) then
vals(k)=vals(i)
vals(i)=cp
if(iptvec.eq.1) then
do 52 j=1,n
cp=a(j,i)
a(j,i)=a(j,k)
a(j,k)=cp
52 continue
endif
endif
53 continue
ier=0
c
c
99 return
end