Actual source code: chwirut2f.F90
1: ! Program usage: mpiexec -n 1 chwirut1f [-help] [all TAO options]
2: !
3: ! Description: This example demonstrates use of the TAO package to solve a
4: ! nonlinear least-squares problem on a single processor. We minimize the
5: ! Chwirut function:
6: ! sum_{i=0}^{n/2-1} ( alpha*(x_{2i+1}-x_{2i}^2)^2 + (1-x_{2i})^2)
7: !
8: ! The C version of this code is chwirut1.c
9: !
10: module chwirut2fmodule
11: use petscmpi ! or mpi or mpi_f08
12: use petsctao
13: #include <petsc/finclude/petsctao.h>
14: PetscReal t(0:213)
15: PetscReal y(0:213)
16: PetscInt m,n
17: PetscMPIInt nn
18: PetscMPIInt rank
19: PetscMPIInt size
20: PetscMPIInt idle_tag, die_tag
21: PetscMPIInt zero,one
22: parameter (m=214)
23: parameter (n=3)
24: parameter (nn=n)
25: parameter (idle_tag=2000)
26: parameter (die_tag=3000)
27: parameter (zero=0,one=1)
28: end module chwirut2fmodule
30: program main
31: use chwirut2fmodule
33: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
34: ! Variable declarations
35: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
36: !
37: ! See additional variable declarations in the file chwirut2f.h
39: PetscErrorCode ierr ! used to check for functions returning nonzeros
40: Vec x ! solution vector
41: Vec f ! vector of functions
42: Tao ta ! Tao context
44: ! Note: Any user-defined Fortran routines (such as FormGradient)
45: ! MUST be declared as external.
47: external FormFunction
49: ! Initialize TAO and PETSc
50: PetscCallA(PetscInitialize(ierr))
51: PetscCallMPIA(MPI_Comm_size(PETSC_COMM_WORLD,size,ierr))
52: PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr))
54: ! Initialize problem parameters
55: call InitializeData()
57: if (rank .eq. 0) then
58: ! Allocate vectors for the solution and gradient
59: PetscCallA(VecCreateSeq(PETSC_COMM_SELF,n,x,ierr))
60: PetscCallA(VecCreateSeq(PETSC_COMM_SELF,m,f,ierr))
62: ! The TAO code begins here
64: ! Create TAO solver
65: PetscCallA(TaoCreate(PETSC_COMM_SELF,ta,ierr))
66: PetscCallA(TaoSetType(ta,TAOPOUNDERS,ierr))
68: ! Set routines for function, gradient, and hessian evaluation
69: PetscCallA(TaoSetResidualRoutine(ta,f,FormFunction,0,ierr))
71: ! Optional: Set initial guess
72: call FormStartingPoint(x)
73: PetscCallA(TaoSetSolution(ta, x, ierr))
75: ! Check for TAO command line options
76: PetscCallA(TaoSetFromOptions(ta,ierr))
77: ! SOLVE THE APPLICATION
78: PetscCallA(TaoSolve(ta,ierr))
80: ! Free TAO data structures
81: PetscCallA(TaoDestroy(ta,ierr))
83: ! Free PETSc data structures
84: PetscCallA(VecDestroy(x,ierr))
85: PetscCallA(VecDestroy(f,ierr))
86: PetscCallA(StopWorkers(ierr))
88: else
89: PetscCallA(TaskWorker(ierr))
90: endif
92: PetscCallA(PetscFinalize(ierr))
93: end
95: ! --------------------------------------------------------------------
96: ! FormFunction - Evaluates the function f(X) and gradient G(X)
97: !
98: ! Input Parameters:
99: ! tao - the Tao context
100: ! X - input vector
101: ! dummy - not used
102: !
103: ! Output Parameters:
104: ! f - function vector
106: subroutine FormFunction(ta, x, f, dummy, ierr)
107: use chwirut2fmodule
109: Tao ta
110: Vec x,f
111: PetscErrorCode ierr
113: PetscInt i,checkedin
114: PetscInt finished_tasks
115: PetscMPIInt next_task
116: PetscMPIInt status(MPI_STATUS_SIZE),tag,source
117: PetscInt dummy
119: PetscReal, pointer :: f_v(:),x_v(:)
120: PetscReal fval(1)
122: ierr = 0
124: ! Get pointers to vector data
125: PetscCall(VecGetArrayRead(x,x_v,ierr))
126: PetscCall(VecGetArray(f,f_v,ierr))
128: ! Compute F(X)
129: if (size .eq. 1) then
130: ! Single processor
131: do i=1,m
132: PetscCall(RunSimulation(x_v,i,f_v(i),ierr))
133: enddo
134: else
135: ! Multiprocessor main
136: next_task = zero
137: finished_tasks = 0
138: checkedin = 0
140: do while (finished_tasks .lt. m .or. checkedin .lt. size-1)
141: PetscCallMPI(MPI_Recv(fval,one,MPIU_SCALAR,MPI_ANY_SOURCE,MPI_ANY_TAG,PETSC_COMM_WORLD,status,ierr))
142: tag = status(MPI_TAG)
143: source = status(MPI_SOURCE)
144: if (tag .eq. IDLE_TAG) then
145: checkedin = checkedin + 1
146: else
147: f_v(tag+1) = fval(1)
148: finished_tasks = finished_tasks + 1
149: endif
150: if (next_task .lt. m) then
151: ! Send task to worker
152: PetscCallMPI(MPI_Send(x_v,nn,MPIU_SCALAR,source,next_task,PETSC_COMM_WORLD,ierr))
153: next_task = next_task + one
154: else
155: ! Send idle message to worker
156: PetscCallMPI(MPI_Send(x_v,nn,MPIU_SCALAR,source,IDLE_TAG,PETSC_COMM_WORLD,ierr))
157: end if
158: enddo
159: endif
161: ! Restore vectors
162: PetscCall(VecRestoreArrayRead(x,x_v,ierr))
163: PetscCall(VecRestoreArray(F,f_v,ierr))
164: end
166: subroutine FormStartingPoint(x)
167: use chwirut2fmodule
169: Vec x
170: PetscReal, pointer :: x_v(:)
171: PetscErrorCode ierr
173: PetscCall(VecGetArray(x,x_v,ierr))
174: x_v(1) = 0.15
175: x_v(2) = 0.008
176: x_v(3) = 0.01
177: PetscCall(VecRestoreArray(x,x_v,ierr))
178: end
180: subroutine InitializeData()
181: use chwirut2fmodule
183: PetscInt i
184: i=0
185: y(i) = 92.9000; t(i) = 0.5000; i=i+1
186: y(i) = 78.7000; t(i) = 0.6250; i=i+1
187: y(i) = 64.2000; t(i) = 0.7500; i=i+1
188: y(i) = 64.9000; t(i) = 0.8750; i=i+1
189: y(i) = 57.1000; t(i) = 1.0000; i=i+1
190: y(i) = 43.3000; t(i) = 1.2500; i=i+1
191: y(i) = 31.1000; t(i) = 1.7500; i=i+1
192: y(i) = 23.6000; t(i) = 2.2500; i=i+1
193: y(i) = 31.0500; t(i) = 1.7500; i=i+1
194: y(i) = 23.7750; t(i) = 2.2500; i=i+1
195: y(i) = 17.7375; t(i) = 2.7500; i=i+1
196: y(i) = 13.8000; t(i) = 3.2500; i=i+1
197: y(i) = 11.5875; t(i) = 3.7500; i=i+1
198: y(i) = 9.4125; t(i) = 4.2500; i=i+1
199: y(i) = 7.7250; t(i) = 4.7500; i=i+1
200: y(i) = 7.3500; t(i) = 5.2500; i=i+1
201: y(i) = 8.0250; t(i) = 5.7500; i=i+1
202: y(i) = 90.6000; t(i) = 0.5000; i=i+1
203: y(i) = 76.9000; t(i) = 0.6250; i=i+1
204: y(i) = 71.6000; t(i) = 0.7500; i=i+1
205: y(i) = 63.6000; t(i) = 0.8750; i=i+1
206: y(i) = 54.0000; t(i) = 1.0000; i=i+1
207: y(i) = 39.2000; t(i) = 1.2500; i=i+1
208: y(i) = 29.3000; t(i) = 1.7500; i=i+1
209: y(i) = 21.4000; t(i) = 2.2500; i=i+1
210: y(i) = 29.1750; t(i) = 1.7500; i=i+1
211: y(i) = 22.1250; t(i) = 2.2500; i=i+1
212: y(i) = 17.5125; t(i) = 2.7500; i=i+1
213: y(i) = 14.2500; t(i) = 3.2500; i=i+1
214: y(i) = 9.4500; t(i) = 3.7500; i=i+1
215: y(i) = 9.1500; t(i) = 4.2500; i=i+1
216: y(i) = 7.9125; t(i) = 4.7500; i=i+1
217: y(i) = 8.4750; t(i) = 5.2500; i=i+1
218: y(i) = 6.1125; t(i) = 5.7500; i=i+1
219: y(i) = 80.0000; t(i) = 0.5000; i=i+1
220: y(i) = 79.0000; t(i) = 0.6250; i=i+1
221: y(i) = 63.8000; t(i) = 0.7500; i=i+1
222: y(i) = 57.2000; t(i) = 0.8750; i=i+1
223: y(i) = 53.2000; t(i) = 1.0000; i=i+1
224: y(i) = 42.5000; t(i) = 1.2500; i=i+1
225: y(i) = 26.8000; t(i) = 1.7500; i=i+1
226: y(i) = 20.4000; t(i) = 2.2500; i=i+1
227: y(i) = 26.8500; t(i) = 1.7500; i=i+1
228: y(i) = 21.0000; t(i) = 2.2500; i=i+1
229: y(i) = 16.4625; t(i) = 2.7500; i=i+1
230: y(i) = 12.5250; t(i) = 3.2500; i=i+1
231: y(i) = 10.5375; t(i) = 3.7500; i=i+1
232: y(i) = 8.5875; t(i) = 4.2500; i=i+1
233: y(i) = 7.1250; t(i) = 4.7500; i=i+1
234: y(i) = 6.1125; t(i) = 5.2500; i=i+1
235: y(i) = 5.9625; t(i) = 5.7500; i=i+1
236: y(i) = 74.1000; t(i) = 0.5000; i=i+1
237: y(i) = 67.3000; t(i) = 0.6250; i=i+1
238: y(i) = 60.8000; t(i) = 0.7500; i=i+1
239: y(i) = 55.5000; t(i) = 0.8750; i=i+1
240: y(i) = 50.3000; t(i) = 1.0000; i=i+1
241: y(i) = 41.0000; t(i) = 1.2500; i=i+1
242: y(i) = 29.4000; t(i) = 1.7500; i=i+1
243: y(i) = 20.4000; t(i) = 2.2500; i=i+1
244: y(i) = 29.3625; t(i) = 1.7500; i=i+1
245: y(i) = 21.1500; t(i) = 2.2500; i=i+1
246: y(i) = 16.7625; t(i) = 2.7500; i=i+1
247: y(i) = 13.2000; t(i) = 3.2500; i=i+1
248: y(i) = 10.8750; t(i) = 3.7500; i=i+1
249: y(i) = 8.1750; t(i) = 4.2500; i=i+1
250: y(i) = 7.3500; t(i) = 4.7500; i=i+1
251: y(i) = 5.9625; t(i) = 5.2500; i=i+1
252: y(i) = 5.6250; t(i) = 5.7500; i=i+1
253: y(i) = 81.5000; t(i) = .5000; i=i+1
254: y(i) = 62.4000; t(i) = .7500; i=i+1
255: y(i) = 32.5000; t(i) = 1.5000; i=i+1
256: y(i) = 12.4100; t(i) = 3.0000; i=i+1
257: y(i) = 13.1200; t(i) = 3.0000; i=i+1
258: y(i) = 15.5600; t(i) = 3.0000; i=i+1
259: y(i) = 5.6300; t(i) = 6.0000; i=i+1
260: y(i) = 78.0000; t(i) = .5000; i=i+1
261: y(i) = 59.9000; t(i) = .7500; i=i+1
262: y(i) = 33.2000; t(i) = 1.5000; i=i+1
263: y(i) = 13.8400; t(i) = 3.0000; i=i+1
264: y(i) = 12.7500; t(i) = 3.0000; i=i+1
265: y(i) = 14.6200; t(i) = 3.0000; i=i+1
266: y(i) = 3.9400; t(i) = 6.0000; i=i+1
267: y(i) = 76.8000; t(i) = .5000; i=i+1
268: y(i) = 61.0000; t(i) = .7500; i=i+1
269: y(i) = 32.9000; t(i) = 1.5000; i=i+1
270: y(i) = 13.8700; t(i) = 3.0000; i=i+1
271: y(i) = 11.8100; t(i) = 3.0000; i=i+1
272: y(i) = 13.3100; t(i) = 3.0000; i=i+1
273: y(i) = 5.4400; t(i) = 6.0000; i=i+1
274: y(i) = 78.0000; t(i) = .5000; i=i+1
275: y(i) = 63.5000; t(i) = .7500; i=i+1
276: y(i) = 33.8000; t(i) = 1.5000; i=i+1
277: y(i) = 12.5600; t(i) = 3.0000; i=i+1
278: y(i) = 5.6300; t(i) = 6.0000; i=i+1
279: y(i) = 12.7500; t(i) = 3.0000; i=i+1
280: y(i) = 13.1200; t(i) = 3.0000; i=i+1
281: y(i) = 5.4400; t(i) = 6.0000; i=i+1
282: y(i) = 76.8000; t(i) = .5000; i=i+1
283: y(i) = 60.0000; t(i) = .7500; i=i+1
284: y(i) = 47.8000; t(i) = 1.0000; i=i+1
285: y(i) = 32.0000; t(i) = 1.5000; i=i+1
286: y(i) = 22.2000; t(i) = 2.0000; i=i+1
287: y(i) = 22.5700; t(i) = 2.0000; i=i+1
288: y(i) = 18.8200; t(i) = 2.5000; i=i+1
289: y(i) = 13.9500; t(i) = 3.0000; i=i+1
290: y(i) = 11.2500; t(i) = 4.0000; i=i+1
291: y(i) = 9.0000; t(i) = 5.0000; i=i+1
292: y(i) = 6.6700; t(i) = 6.0000; i=i+1
293: y(i) = 75.8000; t(i) = .5000; i=i+1
294: y(i) = 62.0000; t(i) = .7500; i=i+1
295: y(i) = 48.8000; t(i) = 1.0000; i=i+1
296: y(i) = 35.2000; t(i) = 1.5000; i=i+1
297: y(i) = 20.0000; t(i) = 2.0000; i=i+1
298: y(i) = 20.3200; t(i) = 2.0000; i=i+1
299: y(i) = 19.3100; t(i) = 2.5000; i=i+1
300: y(i) = 12.7500; t(i) = 3.0000; i=i+1
301: y(i) = 10.4200; t(i) = 4.0000; i=i+1
302: y(i) = 7.3100; t(i) = 5.0000; i=i+1
303: y(i) = 7.4200; t(i) = 6.0000; i=i+1
304: y(i) = 70.5000; t(i) = .5000; i=i+1
305: y(i) = 59.5000; t(i) = .7500; i=i+1
306: y(i) = 48.5000; t(i) = 1.0000; i=i+1
307: y(i) = 35.8000; t(i) = 1.5000; i=i+1
308: y(i) = 21.0000; t(i) = 2.0000; i=i+1
309: y(i) = 21.6700; t(i) = 2.0000; i=i+1
310: y(i) = 21.0000; t(i) = 2.5000; i=i+1
311: y(i) = 15.6400; t(i) = 3.0000; i=i+1
312: y(i) = 8.1700; t(i) = 4.0000; i=i+1
313: y(i) = 8.5500; t(i) = 5.0000; i=i+1
314: y(i) = 10.1200; t(i) = 6.0000; i=i+1
315: y(i) = 78.0000; t(i) = .5000; i=i+1
316: y(i) = 66.0000; t(i) = .6250; i=i+1
317: y(i) = 62.0000; t(i) = .7500; i=i+1
318: y(i) = 58.0000; t(i) = .8750; i=i+1
319: y(i) = 47.7000; t(i) = 1.0000; i=i+1
320: y(i) = 37.8000; t(i) = 1.2500; i=i+1
321: y(i) = 20.2000; t(i) = 2.2500; i=i+1
322: y(i) = 21.0700; t(i) = 2.2500; i=i+1
323: y(i) = 13.8700; t(i) = 2.7500; i=i+1
324: y(i) = 9.6700; t(i) = 3.2500; i=i+1
325: y(i) = 7.7600; t(i) = 3.7500; i=i+1
326: y(i) = 5.4400; t(i) = 4.2500; i=i+1
327: y(i) = 4.8700; t(i) = 4.7500; i=i+1
328: y(i) = 4.0100; t(i) = 5.2500; i=i+1
329: y(i) = 3.7500; t(i) = 5.7500; i=i+1
330: y(i) = 24.1900; t(i) = 3.0000; i=i+1
331: y(i) = 25.7600; t(i) = 3.0000; i=i+1
332: y(i) = 18.0700; t(i) = 3.0000; i=i+1
333: y(i) = 11.8100; t(i) = 3.0000; i=i+1
334: y(i) = 12.0700; t(i) = 3.0000; i=i+1
335: y(i) = 16.1200; t(i) = 3.0000; i=i+1
336: y(i) = 70.8000; t(i) = .5000; i=i+1
337: y(i) = 54.7000; t(i) = .7500; i=i+1
338: y(i) = 48.0000; t(i) = 1.0000; i=i+1
339: y(i) = 39.8000; t(i) = 1.5000; i=i+1
340: y(i) = 29.8000; t(i) = 2.0000; i=i+1
341: y(i) = 23.7000; t(i) = 2.5000; i=i+1
342: y(i) = 29.6200; t(i) = 2.0000; i=i+1
343: y(i) = 23.8100; t(i) = 2.5000; i=i+1
344: y(i) = 17.7000; t(i) = 3.0000; i=i+1
345: y(i) = 11.5500; t(i) = 4.0000; i=i+1
346: y(i) = 12.0700; t(i) = 5.0000; i=i+1
347: y(i) = 8.7400; t(i) = 6.0000; i=i+1
348: y(i) = 80.7000; t(i) = .5000; i=i+1
349: y(i) = 61.3000; t(i) = .7500; i=i+1
350: y(i) = 47.5000; t(i) = 1.0000; i=i+1
351: y(i) = 29.0000; t(i) = 1.5000; i=i+1
352: y(i) = 24.0000; t(i) = 2.0000; i=i+1
353: y(i) = 17.7000; t(i) = 2.5000; i=i+1
354: y(i) = 24.5600; t(i) = 2.0000; i=i+1
355: y(i) = 18.6700; t(i) = 2.5000; i=i+1
356: y(i) = 16.2400; t(i) = 3.0000; i=i+1
357: y(i) = 8.7400; t(i) = 4.0000; i=i+1
358: y(i) = 7.8700; t(i) = 5.0000; i=i+1
359: y(i) = 8.5100; t(i) = 6.0000; i=i+1
360: y(i) = 66.7000; t(i) = .5000; i=i+1
361: y(i) = 59.2000; t(i) = .7500; i=i+1
362: y(i) = 40.8000; t(i) = 1.0000; i=i+1
363: y(i) = 30.7000; t(i) = 1.5000; i=i+1
364: y(i) = 25.7000; t(i) = 2.0000; i=i+1
365: y(i) = 16.3000; t(i) = 2.5000; i=i+1
366: y(i) = 25.9900; t(i) = 2.0000; i=i+1
367: y(i) = 16.9500; t(i) = 2.5000; i=i+1
368: y(i) = 13.3500; t(i) = 3.0000; i=i+1
369: y(i) = 8.6200; t(i) = 4.0000; i=i+1
370: y(i) = 7.2000; t(i) = 5.0000; i=i+1
371: y(i) = 6.6400; t(i) = 6.0000; i=i+1
372: y(i) = 13.6900; t(i) = 3.0000; i=i+1
373: y(i) = 81.0000; t(i) = .5000; i=i+1
374: y(i) = 64.5000; t(i) = .7500; i=i+1
375: y(i) = 35.5000; t(i) = 1.5000; i=i+1
376: y(i) = 13.3100; t(i) = 3.0000; i=i+1
377: y(i) = 4.8700; t(i) = 6.0000; i=i+1
378: y(i) = 12.9400; t(i) = 3.0000; i=i+1
379: y(i) = 5.0600; t(i) = 6.0000; i=i+1
380: y(i) = 15.1900; t(i) = 3.0000; i=i+1
381: y(i) = 14.6200; t(i) = 3.0000; i=i+1
382: y(i) = 15.6400; t(i) = 3.0000; i=i+1
383: y(i) = 25.5000; t(i) = 1.7500; i=i+1
384: y(i) = 25.9500; t(i) = 1.7500; i=i+1
385: y(i) = 81.7000; t(i) = .5000; i=i+1
386: y(i) = 61.6000; t(i) = .7500; i=i+1
387: y(i) = 29.8000; t(i) = 1.7500; i=i+1
388: y(i) = 29.8100; t(i) = 1.7500; i=i+1
389: y(i) = 17.1700; t(i) = 2.7500; i=i+1
390: y(i) = 10.3900; t(i) = 3.7500; i=i+1
391: y(i) = 28.4000; t(i) = 1.7500; i=i+1
392: y(i) = 28.6900; t(i) = 1.7500; i=i+1
393: y(i) = 81.3000; t(i) = .5000; i=i+1
394: y(i) = 60.9000; t(i) = .7500; i=i+1
395: y(i) = 16.6500; t(i) = 2.7500; i=i+1
396: y(i) = 10.0500; t(i) = 3.7500; i=i+1
397: y(i) = 28.9000; t(i) = 1.7500; i=i+1
398: y(i) = 28.9500; t(i) = 1.7500; i=i+1
400: end
402: subroutine TaskWorker(ierr)
403: use chwirut2fmodule
405: PetscErrorCode ierr
406: PetscReal x(n),f(1)
407: PetscMPIInt tag
408: PetscInt index
409: PetscMPIInt status(MPI_STATUS_SIZE)
411: tag = IDLE_TAG
412: f = 0.0
413: ! Send check-in message to rank-0
414: PetscCallMPI(MPI_Send(f,one,MPIU_SCALAR,zero,IDLE_TAG,PETSC_COMM_WORLD,ierr))
415: do while (tag .ne. DIE_TAG)
416: PetscCallMPI(MPI_Recv(x,nn,MPIU_SCALAR,zero,MPI_ANY_TAG,PETSC_COMM_WORLD,status,ierr))
417: tag = status(MPI_TAG)
418: if (tag .eq. IDLE_TAG) then
419: PetscCallMPI(MPI_Send(f,one,MPIU_SCALAR,zero,IDLE_TAG,PETSC_COMM_WORLD,ierr))
420: else if (tag .ne. DIE_TAG) then
421: index = tag
422: ! Compute local part of residual
423: PetscCall(RunSimulation(x,index,f(1),ierr))
425: ! Return residual to rank-0
426: PetscCallMPI(MPI_Send(f,one,MPIU_SCALAR,zero,tag,PETSC_COMM_WORLD,ierr))
427: end if
428: enddo
429: ierr = 0
430: end
432: subroutine RunSimulation(x,i,f,ierr)
433: use chwirut2fmodule
435: PetscReal x(n),f
436: PetscInt i
437: PetscErrorCode ierr
438: f = y(i) - exp(-x(1)*t(i))/(x(2)+x(3)*t(i))
439: ierr = 0
440: end
442: subroutine StopWorkers(ierr)
443: use chwirut2fmodule
445: integer checkedin
446: PetscMPIInt status(MPI_STATUS_SIZE)
447: PetscMPIInt source
448: PetscReal f(1),x(n)
449: PetscErrorCode ierr
450: PetscInt i
452: checkedin=0
453: do while (checkedin .lt. size-1)
454: PetscCallMPI(MPI_Recv(f,one,MPIU_SCALAR,MPI_ANY_SOURCE,MPI_ANY_TAG,PETSC_COMM_WORLD,status,ierr))
455: checkedin=checkedin+1
456: source = status(MPI_SOURCE)
457: do i=1,n
458: x(i) = 0.0
459: enddo
460: PetscCallMPI(MPI_Send(x,nn,MPIU_SCALAR,source,DIE_TAG,PETSC_COMM_WORLD,ierr))
461: enddo
462: ierr = 0
463: end
465: !/*TEST
466: !
467: ! build:
468: ! requires: !complex
469: !
470: ! test:
471: ! nsize: 3
472: ! args: -tao_monitor_short -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-5
473: ! requires: !single
474: !
475: !
476: !TEST*/