test_analytic_template.F90 15.4 KB
Newer Older
Pavel Kus's avatar
Pavel Kus committed
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
! (c) Copyright Pavel Kus, 2017, MPCDF
!
!    This file is part of ELPA.
!
!    The ELPA library was originally created by the ELPA consortium,
!    consisting of the following organizations:
!
!    - Max Planck Computing and Data Facility (MPCDF), formerly known as
!      Rechenzentrum Garching der Max-Planck-Gesellschaft (RZG),
!    - Bergische Universität Wuppertal, Lehrstuhl für angewandte
!      Informatik,
!    - Technische Universität München, Lehrstuhl für Informatik mit
!      Schwerpunkt Wissenschaftliches Rechnen ,
!    - Fritz-Haber-Institut, Berlin, Abt. Theorie,
!    - Max-Plack-Institut für Mathematik in den Naturwissenschaften,
!      Leipzig, Abt. Komplexe Strukutren in Biologie und Kognition,
!      and
!    - IBM Deutschland GmbH
!
!
!    More information can be found here:
!    http://elpa.mpcdf.mpg.de/
!
!    ELPA is free software: you can redistribute it and/or modify
!    it under the terms of the version 3 of the license of the
!    GNU Lesser General Public License as published by the Free
!    Software Foundation.
!
!    ELPA is distributed in the hope that it will be useful,
!    but WITHOUT ANY WARRANTY; without even the implied warranty of
!    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
!    GNU Lesser General Public License for more details.
!
!    You should have received a copy of the GNU Lesser General Public License
!    along with ELPA.  If not, see <http://www.gnu.org/licenses/>
!
!    ELPA reflects a substantial effort on the part of the original
!    ELPA consortium, and we ask you to respect the spirit of the
!    license that we chose: i.e., please contribute any changes you
!    may have back to the original ELPA library distribution, and keep
!    any derivatives of ELPA under the same license that we chose for
!    the original distribution, the GNU Lesser General Public License.

  subroutine prepare_matrix_analytic_&
    &MATH_DATATYPE&
    &_&
    &PRECISION&
    &(na, a, nblk, myid, np_rows, np_cols, my_prow, my_pcol)
    implicit none
    integer(kind=ik), intent(in)    :: na, nblk, myid, np_rows, np_cols, my_prow, my_pcol
    MATH_DATATYPE(kind=REAL_DATATYPE), intent(inout)   :: a(:,:)

    integer(kind=ik) :: globI, globJ, locI, locJ, levels(num_primes)

    ! for debug only, do it systematicaly somehow ... unit tests
Pavel Kus's avatar
Pavel Kus committed
56
57
58
59
60
    call check_module_sanity_&
            &MATH_DATATYPE&
            &_&
            &PRECISION&
            &(myid)
Pavel Kus's avatar
Pavel Kus committed
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

    if(.not. decompose(na, levels)) then
      if(myid == 0) then
        print *, "Analytic test can be run only with matrix sizes of the form 2^n * 3^m * 5^o"
        stop 1
      end if
    end if

    do globI = 1, na
      do globJ = 1, na
        if(map_global_array_index_to_local_index(globI, globJ, locI, locJ, &
                 nblk, np_rows, np_cols, my_prow, my_pcol)) then
           a(locI, locJ) = analytic_matrix_&
              &MATH_DATATYPE&
              &_&
              &PRECISION&
              &(na, globI, globJ)
        end if
      end do
    end do

  end subroutine

  function check_correctness_analytic_&
    &MATH_DATATYPE&
    &_&
    &PRECISION&
88
    &(na, nev, ev, z, nblk, myid, np_rows, np_cols, my_prow, my_pcol, check_all_evals) result(status)
Pavel Kus's avatar
Pavel Kus committed
89
90
91
92
93
94
    implicit none
#include "../../src/general/precision_kinds.F90"
    integer(kind=ik), intent(in)    :: na, nev, nblk, myid, np_rows, np_cols, my_prow, my_pcol
    integer(kind=ik)                :: status, mpierr
    MATH_DATATYPE(kind=rck), intent(inout)   :: z(:,:)
    real(kind=rk), intent(inout)   :: ev(:)
95
    logical, intent(in)            :: check_all_evals
Pavel Kus's avatar
Pavel Kus committed
96
97

    integer(kind=ik) :: globI, globJ, locI, locJ, levels(num_primes)
Pavel Kus's avatar
Pavel Kus committed
98
    real(kind=rk)   :: diff, max_z_diff, max_ev_diff, glob_max_z_diff, max_curr_z_diff 
Pavel Kus's avatar
Pavel Kus committed
99
100
101
102
103
104
105
106
107
108
109
110
111
#ifdef DOUBLE_PRECISION
    real(kind=rk), parameter   :: tol_eigenvalues = 5e-14_rk8
    real(kind=rk), parameter   :: tol_eigenvectors = 6e-11_rk8
#endif
#ifdef SINGLE_PRECISION
    ! tolerance needs to be very high due to qr tests
    ! it should be distinguished somehow!
    real(kind=rk), parameter   :: tol_eigenvalues = 7e-6_rk4
    real(kind=rk), parameter   :: tol_eigenvectors = 4e-3_rk4
#endif
    real(kind=rk)             :: computed_ev, expected_ev
    MATH_DATATYPE(kind=rck)   :: computed_z,  expected_z

Pavel Kus's avatar
Pavel Kus committed
112
    MATH_DATATYPE(kind=rck)   :: max_value_for_normalization, computed_z_on_max_position, normalization_quotient
113
    integer(kind=ik)          :: max_value_idx, rank_with_max, rank_with_max_reduced, num_checked_evals
Pavel Kus's avatar
Pavel Kus committed
114
115


Pavel Kus's avatar
Pavel Kus committed
116
117
118
119
120
    if(.not. decompose(na, levels)) then
      print *, "can not decomopse matrix size"
      stop 1
    end if

121
122
123
124
125
    if(check_all_evals) then
        num_checked_evals = na
    else
        num_checked_evals = nev
    endif
Pavel Kus's avatar
Pavel Kus committed
126
127
128
    !call print_matrix(myid, na, z, "z")
    max_z_diff = 0.0_rk
    max_ev_diff = 0.0_rk
129
    do globJ = 1, num_checked_evals
Pavel Kus's avatar
Pavel Kus committed
130
131
132
133
134
135
136
137
138
      computed_ev = ev(globJ)
      expected_ev = analytic_eigenvalues_real_&
              &PRECISION&
              &(na, globJ)
      diff = abs(computed_ev - expected_ev)
      max_ev_diff = max(diff, max_ev_diff)
    end do

    do globJ = 1, nev
Pavel Kus's avatar
Pavel Kus committed
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
      max_curr_z_diff = 0.0_rk

      ! eigenvectors are unique up to multiplication by scalar (complex in complex case)
      ! to be able to compare them with analytic, we have to normalize them somehow
      ! we will find a value in analytic eigenvector with highest absolut value and enforce
      ! such multiple of computed eigenvector, that the value on corresponding position is the same
      max_value_for_normalization = 0.0_rk
      max_value_idx = -1
      do globI = 1, na
        expected_z = analytic_eigenvectors_&
              &MATH_DATATYPE&
              &_&
              &PRECISION&
              &(na, globI, globJ)
        if(abs(expected_z) > abs(max_value_for_normalization)) then
          max_value_for_normalization = expected_z
          max_value_idx = globI
        end if
      end do

      assert(max_value_idx >= 0)
      if(map_global_array_index_to_local_index(max_value_idx, globJ, locI, locJ, &
               nblk, np_rows, np_cols, my_prow, my_pcol)) then
        rank_with_max = myid
        computed_z_on_max_position = z(locI, locJ)
      else
        rank_with_max = -1
      end if

#ifdef WITH_MPI
      call MPI_Allreduce(rank_with_max, rank_with_max_reduced, 1, MPI_INT, MPI_MAX, MPI_COMM_WORLD, mpierr)
      call MPI_Bcast(computed_z_on_max_position, 1, MPI_MATH_DATATYPE_PRECISION, rank_with_max_reduced, MPI_COMM_WORLD, mpierr)
#endif
      !write(*,*) computed_z_on_max_position, max_value_for_normalization
      normalization_quotient = max_value_for_normalization / computed_z_on_max_position
Pavel Kus's avatar
Pavel Kus committed
174
175
176
177
178
179
180
181
182
      do globI = 1, na
        if(map_global_array_index_to_local_index(globI, globJ, locI, locJ, &
                 nblk, np_rows, np_cols, my_prow, my_pcol)) then
           computed_z = z(locI, locJ)
           expected_z = analytic_eigenvectors_&
              &MATH_DATATYPE&
              &_&
              &PRECISION&
              &(na, globI, globJ)
Pavel Kus's avatar
Pavel Kus committed
183
           max_curr_z_diff = max(abs(normalization_quotient * computed_z - expected_z), max_curr_z_diff)
Pavel Kus's avatar
Pavel Kus committed
184
185
186
        end if
      end do
      ! we have max difference of one of the eigenvectors, update global
Pavel Kus's avatar
Pavel Kus committed
187
      max_z_diff = max(max_z_diff, max_curr_z_diff)
Pavel Kus's avatar
Pavel Kus committed
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
    end do

#ifdef WITH_MPI
    call mpi_allreduce(max_z_diff, glob_max_z_diff, 1, MPI_REAL_PRECISION, MPI_MAX, MPI_COMM_WORLD, mpierr)
#else
    glob_max_z_diff = max_z_diff
#endif
    if(myid == 0) print *, 'Maximum error in eigenvalues      :', max_ev_diff
    if(myid == 0) print *, 'Maximum error in eigenvectors     :', glob_max_z_diff
    status = 0
    if (nev .gt. 2) then
      if (max_ev_diff .gt. tol_eigenvalues .or. max_ev_diff .eq. 0.0_rk) status = 1
      if (glob_max_z_diff .gt. tol_eigenvectors .or. glob_max_z_diff .eq. 0.0_rk) status = 1
    else
      if (max_ev_diff .gt. tol_eigenvalues) status = 1
      if (glob_max_z_diff .gt. tol_eigenvectors) status = 1
    endif
  end function


  function analytic_matrix_&
    &MATH_DATATYPE&
    &_&
    &PRECISION&
    &(na, i, j) result(element)
    implicit none
    integer(kind=ik), intent(in) :: na, i, j
    MATH_DATATYPE(kind=REAL_DATATYPE)     :: element

    element = analytic_&
    &MATH_DATATYPE&
    &_&
    &PRECISION&
    &(na, i, j, ANALYTIC_MATRIX)

  end function

  function analytic_eigenvectors_&
    &MATH_DATATYPE&
    &_&
    &PRECISION&
    &(na, i, j) result(element)
    implicit none
    integer(kind=ik), intent(in) :: na, i, j
    MATH_DATATYPE(kind=REAL_DATATYPE)               :: element

    element = analytic_&
    &MATH_DATATYPE&
    &_&
    &PRECISION&
    &(na, i, j, ANALYTIC_EIGENVECTORS)

  end function

  function analytic_eigenvalues_&
    &MATH_DATATYPE&
    &_&
    &PRECISION&
    &(na, i) result(element)
    implicit none
    integer(kind=ik), intent(in) :: na, i
    real(kind=REAL_DATATYPE)              :: element

    element = analytic_real_&
    &PRECISION&
    &(na, i, i, ANALYTIC_EIGENVALUES)

  end function

  function analytic_&
    &MATH_DATATYPE&
    &_&
    &PRECISION&
    &(na, i, j, what) result(element)
    implicit none
#include "../../src/general/precision_kinds.F90"
    integer(kind=ik), intent(in)   :: na, i, j, what
    MATH_DATATYPE(kind=rck)        :: element, mat2x2(2,2), mat(5,5)
    real(kind=rk)                  :: a, am, amp
    integer(kind=ik)               :: levels(num_primes)
    integer(kind=ik)               :: ii, jj, m, prime_id, prime, total_level, level

    real(kind=rk), parameter      :: s = 0.5_rk
    real(kind=rk), parameter      :: c = 0.86602540378443864679_rk
    real(kind=rk), parameter      :: sq2 = 1.4142135623730950488_rk

    real(kind=rk), parameter      :: largest_ev = 2.0_rk

    assert(i <= na)
    assert(j <= na)
    assert(i >= 0)
    assert(j >= 0)
    assert(decompose(na, levels))
    ! go to zero-based indexing
    ii = i - 1
    jj = j - 1
    if (na .gt. 2) then
      a = exp(log(largest_ev)/(na-1))
    else
      a = exp(log(largest_ev)/(1))
    endif

    element = 1.0_rck
#ifdef COMPLEXCASE
    element = (1.0_rk, 0.0_rk)
#endif
    total_level = 0
    am = a
    do prime_id = 1,num_primes
      prime = primes(prime_id)
      do  level = 1, levels(prime_id)
        amp = am**(prime-1)
        total_level = total_level + 1
        if(what == ANALYTIC_MATRIX) then
#ifdef REALCASE
Pavel Kus's avatar
Pavel Kus committed
303
304
305
          mat2x2 = reshape((/ c*c + amp * s*s, (amp - 1.0_rk) * s*c,  &
                           (amp - 1.0_rk) * s*c, s*s + amp * c*c  /), &
                                      (/2, 2/), order=(/2,1/))
Pavel Kus's avatar
Pavel Kus committed
306
307
308
309
#endif
#ifdef COMPLEXCASE
          mat2x2 = reshape((/ 0.5_rck * (amp + 1.0_rck) * (1.0_rk, 0.0_rk),   sq2/4.0_rk * (amp - 1.0_rk) * (1.0_rk, 1.0_rk),   &
                              sq2/4.0_rk * (amp - 1.0_rk) * (1.0_rk, -1.0_rk),  0.5_rck * (amp + 1.0_rck) * (1.0_rk, 0.0_rk) /), &
Pavel Kus's avatar
Pavel Kus committed
310
                                      (/2, 2/), order=(/2,1/))
Pavel Kus's avatar
Pavel Kus committed
311
312
313
314
315
#endif
        else if(what == ANALYTIC_EIGENVECTORS) then
#ifdef REALCASE
          mat2x2 = reshape((/ c, s,  &
                           -s,  c  /), &
Pavel Kus's avatar
Pavel Kus committed
316
                                (/2, 2/), order=(/2,1/))
Pavel Kus's avatar
Pavel Kus committed
317
318
319
320
#endif
#ifdef COMPLEXCASE
          mat2x2 = reshape((/ -sq2/2.0_rck * (1.0_rk, 0.0_rk),       -sq2/2.0_rck * (1.0_rk, 0.0_rk),  &
                              0.5_rk * (1.0_rk, -1.0_rk),  0.5_rk * (-1.0_rk, 1.0_rk)  /), &
Pavel Kus's avatar
Pavel Kus committed
321
                                (/2, 2/), order=(/2,1/))
Pavel Kus's avatar
Pavel Kus committed
322
323
324
325
#endif
        else if(what == ANALYTIC_EIGENVALUES) then
          mat2x2 = reshape((/ 1.0_rck, 0.0_rck,  &
                           0.0_rck, amp  /), &
Pavel Kus's avatar
Pavel Kus committed
326
                                 (/2, 2/), order=(/2,1/))
Pavel Kus's avatar
Pavel Kus committed
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
        else
          assert(.false.)
        end if

        mat = 0.0_rck
        if(prime == 2) then
          mat(1:2, 1:2) = mat2x2
        else if(prime == 3) then
          mat((/1,3/),(/1,3/)) = mat2x2
          if(what == ANALYTIC_EIGENVECTORS) then
            mat(2,2) = 1.0_rck
          else
            mat(2,2) = am
          end if
        else if(prime == 5) then
          mat((/1,5/),(/1,5/)) = mat2x2
          if(what == ANALYTIC_EIGENVECTORS) then
            mat(2,2) = 1.0_rck
            mat(3,3) = 1.0_rck
            mat(4,4) = 1.0_rck
          else
            mat(2,2) = am
            mat(3,3) = am**2
            mat(4,4) = am**3
          end if
        else
          assert(.false.)
        end if

  !      write(*,*) "calc value, elem: ", element, ", mat: ", mod(ii,2), mod(jj,2),  mat(mod(ii,2), mod(jj,2)), "am ", am
  !      write(*,*) " matrix mat", mat
        element = element * mat(mod(ii,prime) + 1, mod(jj,prime) + 1)
        ii = ii / prime
        jj = jj / prime

        am = am**prime
      end do
    end do
    !write(*,*) "returning value ", element
  end function
Pavel Kus's avatar
Pavel Kus committed
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478


  subroutine print_matrix_&
    &MATH_DATATYPE&
    &_&
    &PRECISION&
    &(myid, na, mat, mat_name)
    implicit none
#include "../../src/general/precision_kinds.F90"
    integer(kind=ik), intent(in)    :: myid, na
    character(len=*), intent(in)    :: mat_name
    MATH_DATATYPE(kind=rck)         :: mat(na, na)
    integer(kind=ik)                :: i,j
    character(len=20)               :: na_str

    if(myid .ne. 0) &
      return
    write(*,*) "Matrix: "//trim(mat_name)
    write(na_str, *) na
    do i = 1, na
#ifdef REALCASE
      write(*, '('//trim(na_str)//'f8.3)') mat(i, :)
#endif
#ifdef COMPLEXCASE
      write(*,'('//trim(na_str)//'(A,f8.3,A,f8.3,A))') ('(', real(mat(i,j)), ',', aimag(mat(i,j)), ')', j=1,na)
#endif
    end do
    write(*,*)
  end subroutine


  subroutine check_matrices_&
    &MATH_DATATYPE&
    &_&
    &PRECISION&
    &(myid, na)
    implicit none
#include "../../src/general/precision_kinds.F90"
    integer(kind=ik), intent(in)    :: myid, na
    MATH_DATATYPE(kind=rck)                  :: A(na, na), S(na, na), L(na, na), res(na, na)
    integer(kind=ik)                :: i, j, decomposition(num_primes)

    assert(decompose(na, decomposition))

    do i = 1, na
      do j = 1, na
        A(i,j) = analytic_matrix_&
              &MATH_DATATYPE&
              &_&
              &PRECISION&
              &(na, i, j)
        S(i,j) = analytic_eigenvectors_&
              &MATH_DATATYPE&
              &_&
              &PRECISION&
              &(na, i, j)
        L(i,j) = analytic_&
              &MATH_DATATYPE&
              &_&
              &PRECISION&
              &(na, i, j, ANALYTIC_EIGENVALUES)
      end do
    end do

    res = matmul(A,S) - matmul(S,L)
#ifdef DOUBLE_PRECISION
    assert(maxval(abs(res)) < 1e-8)
#elif SINGLE_PRECISION
    assert(maxval(abs(res)) < 1e-4)
#else
    assert(.false.)
#endif
    if(.false.) then
    !if(na == 2 .or. na == 5) then
      call print_matrix(myid, na, A, "A")
      call print_matrix(myid, na, S, "S")
      call print_matrix(myid, na, L, "L")

      call print_matrix(myid, na, matmul(A,S), "AS")
      call print_matrix(myid, na, matmul(S,L), "SL")

      call print_matrix(myid, na, res , "res")
    end if

  end subroutine

  subroutine check_module_sanity_&
    &MATH_DATATYPE&
    &_&
    &PRECISION&
    &(myid)
    implicit none
    integer(kind=ik), intent(in)   :: myid
    integer(kind=ik)               :: decomposition(num_primes), i
    integer(kind=ik), parameter    :: check_sizes(7) = (/2, 3, 5, 6, 10, 25, 150/)
    if(myid == 0) print *, "Checking test_analytic module sanity.... "
    assert(decompose(1500, decomposition))
    assert(all(decomposition == (/2,1,3/)))
    assert(decompose(6,decomposition))
    assert(all(decomposition == (/1,1,0/)))

    do i =1, size(check_sizes)
      call check_matrices_&
          &MATH_DATATYPE&
          &_&
          &PRECISION&
          &(myid, check_sizes(i))
    end do

    if(myid == 0) print *, "Checking test_analytic module sanity.... DONE"

  end subroutine