-
Notifications
You must be signed in to change notification settings - Fork 3
/
Copy pathtest_la_solve.f90
371 lines (274 loc) · 12.7 KB
/
test_la_solve.f90
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
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
module test_linalg_solve
use linear_algebra
implicit none(type,external)
contains
!> Solve real linear system
subroutine test_solve(error)
logical,intent(out) :: error
call test_ssolve(error)
if (error) return
call test_ssolve_multiple(error)
if (error) return
call test_dsolve(error)
if (error) return
call test_dsolve_multiple(error)
if (error) return
call test_qsolve(error)
if (error) return
call test_qsolve_multiple(error)
if (error) return
call test_csolve(error)
if (error) return
call test_2x2_csolve(error)
if (error) return
call test_zsolve(error)
if (error) return
call test_2x2_zsolve(error)
if (error) return
call test_wsolve(error)
if (error) return
call test_2x2_wsolve(error)
if (error) return
end subroutine test_solve
!> Simple linear system
subroutine test_ssolve(error)
logical,intent(out) :: error
type(la_state) :: state
real(sp) :: A(3,3) = transpose(reshape([real(sp) :: 1,3,3, &
1,3,4, &
1,4,3], [3,3]))
real(sp) :: b(3) = [real(sp) :: 1,4,-1]
real(sp) :: res(3) = [real(sp) :: -2,-2,3]
real(sp) :: x(3)
x = solve(a,b,err=state)
error = state%error() .or. .not. all(abs(x - res) < abs(res*epsilon(0.0_sp)))
print *, 'res = ',res
print *, 'x = ',x
print *, 'err = ',abs(x - res)
print *, 'tst = ',res*epsilon(0.0_sp)
print *, 'state = ',state%print()
end subroutine test_ssolve
subroutine test_dsolve(error)
logical,intent(out) :: error
type(la_state) :: state
real(dp) :: A(3,3) = transpose(reshape([real(dp) :: 1,3,3, &
1,3,4, &
1,4,3], [3,3]))
real(dp) :: b(3) = [real(dp) :: 1,4,-1]
real(dp) :: res(3) = [real(dp) :: -2,-2,3]
real(dp) :: x(3)
x = solve(a,b,err=state)
error = state%error() .or. .not. all(abs(x - res) < abs(res*epsilon(0.0_dp)))
print *, 'res = ',res
print *, 'x = ',x
print *, 'err = ',abs(x - res)
print *, 'tst = ',res*epsilon(0.0_dp)
print *, 'state = ',state%print()
end subroutine test_dsolve
subroutine test_qsolve(error)
logical,intent(out) :: error
type(la_state) :: state
real(qp) :: A(3,3) = transpose(reshape([real(qp) :: 1,3,3, &
1,3,4, &
1,4,3], [3,3]))
real(qp) :: b(3) = [real(qp) :: 1,4,-1]
real(qp) :: res(3) = [real(qp) :: -2,-2,3]
real(qp) :: x(3)
x = solve(a,b,err=state)
error = state%error() .or. .not. all(abs(x - res) < abs(res*epsilon(0.0_qp)))
print *, 'res = ',res
print *, 'x = ',x
print *, 'err = ',abs(x - res)
print *, 'tst = ',res*epsilon(0.0_qp)
print *, 'state = ',state%print()
end subroutine test_qsolve
!> Simple linear system with multiple right hand sides
subroutine test_ssolve_multiple(error)
logical,intent(out) :: error
type(la_state) :: state
real(sp) :: A(3,3) = transpose(reshape([real(sp) :: 1,-1,2, &
0,1,1, &
1,-1,3], [3,3]))
real(sp) :: b(3,3) = transpose(reshape([real(sp) :: 0,1,2, &
1,-2,-1, &
2,3,-1], [3,3]))
real(sp) :: res(3,3) = transpose(reshape([real(sp) :: -5,-7,10, &
-1,-4,2, &
2,2,-3], [3,3]))
real(sp) :: x(3,3)
x = solve(a,b,err=state)
error = state%error() .or. .not. all(abs(x - res) < abs(res*epsilon(0.0_sp)))
print *, 'res = ',res
print *, 'x = ',x
print *, 'err = ',abs(x - res)
print *, 'tst = ',res*epsilon(0.0_sp)
print *, 'state = ',state%print()
end subroutine test_ssolve_multiple
subroutine test_dsolve_multiple(error)
logical,intent(out) :: error
type(la_state) :: state
real(dp) :: A(3,3) = transpose(reshape([real(dp) :: 1,-1,2, &
0,1,1, &
1,-1,3], [3,3]))
real(dp) :: b(3,3) = transpose(reshape([real(dp) :: 0,1,2, &
1,-2,-1, &
2,3,-1], [3,3]))
real(dp) :: res(3,3) = transpose(reshape([real(dp) :: -5,-7,10, &
-1,-4,2, &
2,2,-3], [3,3]))
real(dp) :: x(3,3)
x = solve(a,b,err=state)
error = state%error() .or. .not. all(abs(x - res) < abs(res*epsilon(0.0_dp)))
print *, 'res = ',res
print *, 'x = ',x
print *, 'err = ',abs(x - res)
print *, 'tst = ',res*epsilon(0.0_dp)
print *, 'state = ',state%print()
end subroutine test_dsolve_multiple
subroutine test_qsolve_multiple(error)
logical,intent(out) :: error
type(la_state) :: state
real(qp) :: A(3,3) = transpose(reshape([real(qp) :: 1,-1,2, &
0,1,1, &
1,-1,3], [3,3]))
real(qp) :: b(3,3) = transpose(reshape([real(qp) :: 0,1,2, &
1,-2,-1, &
2,3,-1], [3,3]))
real(qp) :: res(3,3) = transpose(reshape([real(qp) :: -5,-7,10, &
-1,-4,2, &
2,2,-3], [3,3]))
real(qp) :: x(3,3)
x = solve(a,b,err=state)
error = state%error() .or. .not. all(abs(x - res) < abs(res*epsilon(0.0_qp)))
print *, 'res = ',res
print *, 'x = ',x
print *, 'err = ',abs(x - res)
print *, 'tst = ',res*epsilon(0.0_qp)
print *, 'state = ',state%print()
end subroutine test_qsolve_multiple
!> Complex linear system
!> Militaru, Popa, "On the numerical solving of complex linear systems",
!> Int J Pure Appl Math 76(1), 113-122, 2012.
subroutine test_csolve(error)
logical,intent(out) :: error
type(la_state) :: state
complex(sp) :: A(5,5),b(5),res(5),x(5)
integer(ilp) :: i
! Fill in linear system
A = (0.0_sp,0.0_sp)
A(1:2,1) = [(19.73_sp,0.0_sp), (0.0_sp,-0.51_sp)]
A(1:3,2) = [(12.11_sp,-1.0_sp), (32.3_sp,7.0_sp), (0.0_sp,-0.51_sp)]
A(1:4,3) = [(0.0_sp,5.0_sp), (23.07_sp,0.0_sp), (70.0_sp,7.3_sp), (1.0_sp,1.1_sp)]
A(2:5,4) = [(0.0_sp,1.0_sp), (3.95_sp,0.0_sp), (50.17_sp,0.0_sp), (0.0_sp,-9.351_sp)]
A(3:5,5) = [(19.0_sp,31.83_sp), (45.51_sp,0.0_sp), (55.0_sp,0.0_sp)]
b = [(77.38_sp,8.82_sp), (157.48_sp,19.8_sp), (1175.62_sp,20.69_sp), (912.12_sp,-801.75_sp), (550.0_sp,-1060.4_sp)]
! Exact result
res = [(3.3_sp,-1.0_sp), (1.0_sp,0.17_sp), (5.5_sp,0.0_sp), (9.0_sp,0.0_sp), (10.0_sp,-17.75_sp)]
x = solve(a,b,err=state)
error = state%error() .or. .not. all(abs(x - res) < abs(res)*1.0e-3_sp)
do i = 1,5
print *, 'res = ',res(i),' x =',x(i),' b =',b(i)
end do
print *, 'state = ',state%print()
end subroutine test_csolve
subroutine test_zsolve(error)
logical,intent(out) :: error
type(la_state) :: state
complex(dp) :: A(5,5),b(5),res(5),x(5)
integer(ilp) :: i
! Fill in linear system
A = (0.0_dp,0.0_dp)
A(1:2,1) = [(19.73_dp,0.0_dp), (0.0_dp,-0.51_dp)]
A(1:3,2) = [(12.11_dp,-1.0_dp), (32.3_dp,7.0_dp), (0.0_dp,-0.51_dp)]
A(1:4,3) = [(0.0_dp,5.0_dp), (23.07_dp,0.0_dp), (70.0_dp,7.3_dp), (1.0_dp,1.1_dp)]
A(2:5,4) = [(0.0_dp,1.0_dp), (3.95_dp,0.0_dp), (50.17_dp,0.0_dp), (0.0_dp,-9.351_dp)]
A(3:5,5) = [(19.0_dp,31.83_dp), (45.51_dp,0.0_dp), (55.0_dp,0.0_dp)]
b = [(77.38_dp,8.82_dp), (157.48_dp,19.8_dp), (1175.62_dp,20.69_dp), (912.12_dp,-801.75_dp), (550.0_dp,-1060.4_dp)]
! Exact result
res = [(3.3_dp,-1.0_dp), (1.0_dp,0.17_dp), (5.5_dp,0.0_dp), (9.0_dp,0.0_dp), (10.0_dp,-17.75_dp)]
x = solve(a,b,err=state)
error = state%error() .or. .not. all(abs(x - res) < abs(res)*1.0e-3_dp)
do i = 1,5
print *, 'res = ',res(i),' x =',x(i),' b =',b(i)
end do
print *, 'state = ',state%print()
end subroutine test_zsolve
subroutine test_wsolve(error)
logical,intent(out) :: error
type(la_state) :: state
complex(qp) :: A(5,5),b(5),res(5),x(5)
integer(ilp) :: i
! Fill in linear system
A = (0.0_qp,0.0_qp)
A(1:2,1) = [(19.73_qp,0.0_qp), (0.0_qp,-0.51_qp)]
A(1:3,2) = [(12.11_qp,-1.0_qp), (32.3_qp,7.0_qp), (0.0_qp,-0.51_qp)]
A(1:4,3) = [(0.0_qp,5.0_qp), (23.07_qp,0.0_qp), (70.0_qp,7.3_qp), (1.0_qp,1.1_qp)]
A(2:5,4) = [(0.0_qp,1.0_qp), (3.95_qp,0.0_qp), (50.17_qp,0.0_qp), (0.0_qp,-9.351_qp)]
A(3:5,5) = [(19.0_qp,31.83_qp), (45.51_qp,0.0_qp), (55.0_qp,0.0_qp)]
b = [(77.38_qp,8.82_qp), (157.48_qp,19.8_qp), (1175.62_qp,20.69_qp), (912.12_qp,-801.75_qp), (550.0_qp,-1060.4_qp)]
! Exact result
res = [(3.3_qp,-1.0_qp), (1.0_qp,0.17_qp), (5.5_qp,0.0_qp), (9.0_qp,0.0_qp), (10.0_qp,-17.75_qp)]
x = solve(a,b,err=state)
error = state%error() .or. .not. all(abs(x - res) < abs(res)*1.0e-3_qp)
do i = 1,5
print *, 'res = ',res(i),' x =',x(i),' b =',b(i)
end do
print *, 'state = ',state%print()
end subroutine test_wsolve
!> 2x2 Complex linear system
!> https://math.stackexchange.com/questions/1996540/solving-linear-equation-systems-with-complex-coefficients-and-variables
subroutine test_2x2_csolve(error)
logical,intent(out) :: error
type(la_state) :: state
complex(sp) :: A(2,2),b(2),res(2),x(2)
integer(ilp) :: i
! Fill in linear system
A(1,:) = [(+1.0_sp,+1.0_sp), (-1.0_sp,0.0_sp)]
A(2,:) = [(+1.0_sp,-1.0_sp), (+1.0_sp,1.0_sp)]
b = [(0.0_sp,1.0_sp), (1.0_sp,0.0_sp)]
! Exact result
res = [(0.5_sp,0.5_sp), (0.0_sp,0.0_sp)]
x = solve(a,b,err=state)
error = state%error() .or. .not. all(abs(x - res) < max(tiny(0.0_sp),abs(res)*epsilon(0.0_sp)))
do i = 1,2
print *, 'res = ',res(i),' x =',x(i),' b =',b(i)
end do
print *, 'state = ',state%print()
end subroutine test_2x2_csolve
subroutine test_2x2_zsolve(error)
logical,intent(out) :: error
type(la_state) :: state
complex(dp) :: A(2,2),b(2),res(2),x(2)
integer(ilp) :: i
! Fill in linear system
A(1,:) = [(+1.0_dp,+1.0_dp), (-1.0_dp,0.0_dp)]
A(2,:) = [(+1.0_dp,-1.0_dp), (+1.0_dp,1.0_dp)]
b = [(0.0_dp,1.0_dp), (1.0_dp,0.0_dp)]
! Exact result
res = [(0.5_dp,0.5_dp), (0.0_dp,0.0_dp)]
x = solve(a,b,err=state)
error = state%error() .or. .not. all(abs(x - res) < max(tiny(0.0_dp),abs(res)*epsilon(0.0_dp)))
do i = 1,2
print *, 'res = ',res(i),' x =',x(i),' b =',b(i)
end do
print *, 'state = ',state%print()
end subroutine test_2x2_zsolve
subroutine test_2x2_wsolve(error)
logical,intent(out) :: error
type(la_state) :: state
complex(qp) :: A(2,2),b(2),res(2),x(2)
integer(ilp) :: i
! Fill in linear system
A(1,:) = [(+1.0_qp,+1.0_qp), (-1.0_qp,0.0_qp)]
A(2,:) = [(+1.0_qp,-1.0_qp), (+1.0_qp,1.0_qp)]
b = [(0.0_qp,1.0_qp), (1.0_qp,0.0_qp)]
! Exact result
res = [(0.5_qp,0.5_qp), (0.0_qp,0.0_qp)]
x = solve(a,b,err=state)
error = state%error() .or. .not. all(abs(x - res) < max(tiny(0.0_qp),abs(res)*epsilon(0.0_qp)))
do i = 1,2
print *, 'res = ',res(i),' x =',x(i),' b =',b(i)
end do
print *, 'state = ',state%print()
end subroutine test_2x2_wsolve
end module test_linalg_solve