| blob | 0d2fdd8ef86182bf72aca1f648c2e1f0c6fb32f2 |
1 \r
2 #property copyright "Copyleft © 2007, GammaRat Forex"\r
3 #property link "http://www.gammarat.com/Forex/"\r
4 \r
5 \r
6 \r
7 //#include <GRFMatrixMath.mqh>\r
8 #property indicator_chart_window\r
9 #property indicator_buffers 7\r
10 #property indicator_color1 Orange\r
11 #property indicator_color2 Orange\r
12 #property indicator_color3 Orange\r
13 #property indicator_color4 Red\r
14 #property indicator_color5 Red\r
15 #property indicator_color6 Red\r
16 #property indicator_color7 Red\r
17 #property indicator_style1 0\r
18 #property indicator_style2 0\r
19 #property indicator_style3 0\r
20 #property indicator_style4 2\r
21 #property indicator_style5 2\r
22 #property indicator_style6 0\r
23 #property indicator_style7 0\r
24 \r
25 \r
26 //---- input parameters\r
27 extern double Samples=15;\r
28 extern double DevLevel1 = 2;\r
29 extern double DevLevel2 = 0;\r
30 extern double Suppression_dB = 0;\r
31 extern double PredictBars1 = 0;\r
32 extern double PredictBars2 = 0;\r
33 extern bool PrintCurrentState = true;\r
34 extern bool AutoGainOn = true;\r
35 \r
36 \r
37 //---- buffers\r
38 double KalmanBuffer[];\r
39 double KalmanBufferPlus1[];\r
40 double KalmanBufferNeg1[];\r
41 double KalmanBufferPlus2[];\r
42 double KalmanBufferNeg2[];\r
43 double KalmanBufferPlus3[];\r
44 double KalmanBufferNeg3[];\r
45 double xkk[2][1],xkk1[2][1],xk1k1[2][1],yk[1][1],zk[1][1];\r
46 double Pkk[2][2],Pkk1[2][2],Pk1k1[2][2],Pkk_inv[2][2];\r
47 double Qkk[2][2],Hk[1][2],Hk_t[2][1],Sk[1][1],Sk_inv[1][1],Rk[1][1],Kk[2][1];\r
48 double Fk[2][2],Fk_t[2][2],GGT[2][2];\r
49 double Eye[2][2];\r
50 double temp22[2][2],temp21[2][1],temp12[1][2],temp11[1][1];\r
51 double xp[1][1],xpt[1][1],xpt_t[1][1];\r
52 double Phi1[1][2],Phi2[1][2];\r
53 double xdel[1][1],xdel_t[1][1];\r
54 double LookAhead=0;\r
55 static bool initiated=false;\r
56 static double c0_above=0, c0_below = 0;\r
57 static double c1_above=0, c1_below = 0;\r
58 static int last_time=-1;\r
59 static int first_time = -1;\r
60 static int tick_count=0;\r
61 static int counted_bars = -1;\r
62 static double TestGain;\r
63 static bool PrintOn=false;\r
64 //+------------------------------------------------------------------+\r
65 //| Custom indicator initialization function |\r
66 //+------------------------------------------------------------------+\r
67 int init()\r
68 {\r
69 string shortname;\r
70 shortname = "KalmanAGAS "+DoubleToStr(Samples,1)+ " ";\r
71 //---- indicators\r
72 if(LookAhead <0)LookAhead=0;\r
73 SetIndexStyle(0,DRAW_LINE);\r
74 \r
75 SetIndexBuffer(0,KalmanBuffer);\r
76 SetIndexShift(0,LookAhead);\r
77 SetIndexDrawBegin(0,LookAhead);\r
78 SetIndexLabel(0,shortname);\r
79 if(MathAbs(DevLevel1) > 0) {\r
80 SetIndexStyle(1,DRAW_LINE);\r
81 SetIndexBuffer(1,KalmanBufferPlus1);\r
82 SetIndexShift(1,0);\r
83 SetIndexDrawBegin(1,1);\r
84 SetIndexLabel(1,shortname + DoubleToStr(DevLevel1,1) + " Dev");\r
85 SetIndexStyle(2,DRAW_LINE);\r
86 SetIndexBuffer(2,KalmanBufferNeg1);\r
87 SetIndexShift(2,0);\r
88 SetIndexDrawBegin(2,1);\r
89 SetIndexLabel(2,shortname + DoubleToStr(-DevLevel1,1) + " Dev");\r
90 }\r
91 if(MathAbs(DevLevel2) > 0){\r
92 SetIndexStyle(3,DRAW_LINE);\r
93 SetIndexBuffer(3,KalmanBufferPlus2);\r
94 SetIndexShift(3,0);\r
95 SetIndexDrawBegin(3,1);\r
96 SetIndexLabel(3,shortname + DoubleToStr(DevLevel2,1) + " Dev");\r
97 SetIndexStyle(4,DRAW_LINE);\r
98 SetIndexBuffer(4,KalmanBufferNeg2);\r
99 SetIndexShift(4,0);\r
100 SetIndexDrawBegin(4,1);\r
101 SetIndexLabel(4,shortname + DoubleToStr(-DevLevel2,1) + " Dev");\r
102 \r
103 SetIndexStyle(5,DRAW_LINE);\r
104 SetIndexBuffer(5,KalmanBufferPlus3);\r
105 SetIndexShift(5,0);\r
106 SetIndexDrawBegin(5,1);\r
107 SetIndexLabel(5,shortname + " Highs " + DoubleToStr(DevLevel2,1) + " Dev");\r
108 SetIndexStyle(6,DRAW_LINE);\r
109 SetIndexBuffer(6,KalmanBufferNeg3);\r
110 SetIndexShift(6,0);\r
111 SetIndexDrawBegin(6,1);\r
112 SetIndexLabel(6,shortname + " Lows " + DoubleToStr(-DevLevel2,1) + " Dev");\r
113 }\r
114 //----\r
115 return(0);\r
116 }\r
117 //| Point and figure |\r
118 //+------------------------------------------------------------------+\r
119 int start()\r
120 {\r
121 int i;\r
122 double TestGain_saved;\r
123 i=0;\r
124 if(counted_bars == -1 && AutoGainOn){\r
125 if(Bars<Samples*2)Samples =Bars/4;\r
126 \r
127 //ramp up the gain\r
128 //first time through\r
129 TestGain=-1;\r
130 TestGain_saved = Suppression_dB;\r
131 while(true){\r
132 PrintOn=false;\r
133 initiated = 0;\r
134 counted_bars = 0;\r
135 last_time=-1;\r
136 compute();\r
137 //Print("TestGain ",TestGain," trial ", i);\r
138 Suppression_dB=TestGain;\r
139 if(MathAbs(TestGain-TestGain_saved) < 0.5)break;\r
140 TestGain_saved=TestGain;\r
141 i++;\r
142 if(i>20)break; \r
143 }\r
144 return;\r
145 }\r
146 PrintOn=true;\r
147 counted_bars=IndicatorCounted();\r
148 if( counted_bars<0) counted_bars=0; \r
149 compute();\r
150 return(0);\r
151 }\r
152 int compute(){\r
153 int i,j;\r
154 \r
155 double g,g1;\r
156 double c0;\r
157 \r
158 static double acc_sigma2;\r
159 static double z_sigma2;\r
160 static double normalization_time;\r
161 static double working_samples;\r
162 double z,diff; \r
163 double ts[3][1];\r
164 static double dev_level1,dev_level2; \r
165 double temp11a[1][1],temp21a[2][1];\r
166 double temp22a[2][2]; \r
167 static double ZGain = 0;\r
168 static double AGain=1;\r
169 static double tgain=1;\r
170 static double time_last;\r
171 static double zk_saved[2][1];\r
172 int trial;\r
173 \r
174 //----\r
175 //give it some time to warm up\r
176 if(Bars<Samples*2) \r
177 return(0);\r
178 //rewrite the last bar\r
179 //if(counted_bars > Bars-2)return(0);\r
180 //Print(Time[0]);\r
181 \r
182 if(Time[1] <= last_time) return(0);\r
183 Sleep(500);\r
184 //tick_count--;\r
185 //if(tick_count>0)return(0);\r
186 //tick_count=3;\r
187 if(counted_bars<0) counted_bars=0;\r
188 \r
189 //if(counted_bars>0)counted_bars--;\r
190 \r
191 //if(counted_bars >2) counted_bars -= 2;\r
192 \r
193 if( !initiated){\r
194 \r
195 Phi1[0][0] = 1;\r
196 Phi1[0][1] = PredictBars1;\r
197 Phi2[0][0] = 1;\r
198 Phi2[0][1] = PredictBars2;\r
199 \r
200 dev_level1 = DevLevel1*MathSqrt(2);\r
201 dev_level2 = DevLevel2*MathSqrt(2);\r
202 ArrayCopy(KalmanBuffer,High);\r
203 xkk1[0][0] = get_avg(Bars-1);\r
204 xkk1[1][0] = 0;\r
205 //MatrixPrint(xkk);\r
206 MatrixEye(Pkk1);\r
207 Fk[0][0] = 1;\r
208 Fk[0][1]=1;\r
209 Fk[1][0]=0;\r
210 Fk[1][1] =1;\r
211 MatrixTranspose(Fk,Fk_t);\r
212 Qkk[0][0] = 1;\r
213 Qkk[0][1] = 0;\r
214 Qkk[1][0]=0;\r
215 Qkk[1][1] = 1;\r
216 GGT[0][0]=.25;\r
217 GGT[1][0]=.5;\r
218 GGT[0][1]=.5;\r
219 GGT[1][1]=1;\r
220 Hk[0][0] = 1;\r
221 Hk[0][1] = 0;\r
222 MatrixTranspose(Hk,Hk_t);\r
223 \r
224 Rk[0][0] = .1;\r
225 MatrixEye(Eye);\r
226 ZGain = 0;\r
227 z_sigma2 = MathPow(10,-ZGain);\r
228 acc_sigma2 = Point*MathPow(10,-Suppression_dB/20.);//*MathSqrt(0.0001/Point);\r
229 MatrixScalarMul(acc_sigma2,Pkk1);\r
230 working_samples = Samples;\r
231 acc_sigma2 *= acc_sigma2;\r
232 Rk[0][0] = z_sigma2;\r
233 initiated = true;\r
234 MatrixScalarMul(acc_sigma2,Pkk);\r
235 //Print(1./MathSqrt(acc_sigma2));\r
236 //Print(" ");\r
237 AGain=1;\r
238 zk_saved[0][0] = get_avg(Bars-1);\r
239 zk_saved[1][0] = 0;\r
240 //double A1[20][2],A1t[2][20],A11[2][2],A11_inv[2][2],X[2],B[20];\r
241 //for(i=0;i<20;i++){\r
242 ArrayCopy(xkk1,zk_saved);\r
243 \r
244 }\r
245 \r
246 for(i=Bars-counted_bars-1; i> 0;i--){ //ticks are handled elsewhere\r
247 \r
248 //Start the update procedure\r
249 \r
250 MatrixZero(yk);\r
251 zk[0][0] = get_avg(i);\r
252 zk[1][0]= zk[0][0]-zk_saved[0][0];\r
253 ArrayCopy(zk_saved,zk);\r
254 diff = (zk[0][0]*Point-xkk1[0][0]*Point);\r
255 if(diff>=0) {\r
256 diff = diff*diff;\r
257 c0_above = (c0_above*(working_samples-1)+MathPow(get_avg(i)*Point-KalmanBuffer[i],2))/working_samples;\r
258 c0_below = c0_below*(working_samples-1)/working_samples;\r
259 c1_above = (c1_above*(working_samples-1)+MathPow(High[i]-KalmanBuffer[i],2))/working_samples;\r
260 c1_below = c1_below*(working_samples-1)/working_samples;\r
261 }else{\r
262 diff = diff*diff;\r
263 c0_below = (c0_below*(working_samples-1)+MathPow(get_avg(i)*Point-KalmanBuffer[i],2))/working_samples;\r
264 c0_above = c0_above*(working_samples-1)/working_samples;\r
265 c1_below = (c1_below*(working_samples-1)+MathPow(Low[i]-KalmanBuffer[i],2))/working_samples;\r
266 c1_above = c1_above*(working_samples-1)/working_samples;\r
267 } \r
268 if(MathAbs(DevLevel1)>0){\r
269 KalmanBufferPlus1[i-1] = KalmanBuffer[i]+dev_level1*MathSqrt(c0_above);\r
270 KalmanBufferNeg1[i-1] = KalmanBuffer[i]-dev_level1*MathSqrt(c0_below);\r
271 }\r
272 if(MathAbs(DevLevel2)>0){ \r
273 KalmanBufferPlus2[i-1] = KalmanBuffer[i]+dev_level2*MathSqrt(c0_above);\r
274 KalmanBufferNeg2[i-1] = KalmanBuffer[i]-dev_level2*MathSqrt(c0_below);\r
275 KalmanBufferPlus3[i-1] = KalmanBuffer[i]+dev_level2*MathSqrt(c1_above);\r
276 KalmanBufferNeg3[i-1] = KalmanBuffer[i]-dev_level2*MathSqrt(c1_below);\r
277 } \r
278 //this is always left alone, for now\r
279 \r
280 \r
281 ArrayCopy(Qkk,GGT);\r
282 \r
283 // set the auto gain\r
284 if(AutoGainOn && MathSqrt((c0_above+c0_below)/2)> Point){ \r
285 if(c0_below >0 || c0_above>0)\r
286 tgain = MathAbs((c0_below)/(c0_below+c0_above));\r
287 else tgain = 0.5;\r
288 if(tgain< 0.2 || tgain > 0.8)\r
289 AGain = AGain*MathPow(10,0.001);\r
290 else if(tgain> 0.45 && tgain < 0.55)\r
291 AGain=AGain*MathPow(10,-0.001);\r
292 }else{\r
293 AGain = 1;\r
294 } \r
295 tgain = AGain*acc_sigma2;\r
296 TestGain=-20*MathLog(MathSqrt(tgain)/Point)/MathLog(10.);\r
297 MatrixScalarMul(tgain,Qkk);\r
298 MatrixMul(Hk,xkk1,temp11);\r
299 //MatrixPrint(xkk1);\r
300 MatrixAdd(zk,temp11,yk, -1); \r
301 MatrixMul(Hk,Pkk1,temp12);\r
302 MatrixMul(temp12,Hk_t,temp11);\r
303 MatrixAdd(temp11,Rk,Sk,1);\r
304 MatrixInvert(Sk,Sk_inv);\r
305 MatrixMul(Pkk1,Hk_t,temp21);\r
306 MatrixMul(temp21,Sk_inv,Kk);\r
307 MatrixMul(Kk,yk,temp21);\r
308 MatrixAdd(temp21,xkk1,xkk,1);\r
309 \r
310 MatrixMul(Kk,Hk,temp22);\r
311 MatrixAdd(Eye,temp22,temp22a,-1);\r
312 MatrixMul(temp22a,Pkk1,Pkk);\r
313 \r
314 //predict cycle\r
315 //make copies of the last iteration;\r
316 ArrayCopy(Pk1k1,Pkk);\r
317 ArrayCopy(xk1k1,xkk);\r
318 //g = MathSqrt(MathPow(xkk[0][0]-get_avg(i),2))/Pkk[0][0]*Point;\r
319 //g = xkk[1][0];\r
320 //predict the state\r
321 //Print("Doing Predict");\r
322 MatrixMul(Fk,xk1k1,xkk1);\r
323 //MatrixPrint(xkk1);\r
324 MatrixMul(Fk,Pk1k1,temp22);\r
325 MatrixMul(temp22,Fk_t,Pk1k1);\r
326 MatrixAdd(Pk1k1,Qkk,Pkk1,1);\r
327 //Print("Predict Ended");\r
328 KalmanBuffer[i-1] = (xkk1[0][0]*Point);\r
329 \r
330 if(i==1 && PrintOn){\r
331 if(PrintCurrentState){\r
332 Print("Suppression (dB):", -20*MathLog(MathSqrt(tgain)/Point)/MathLog(10.),"dB; Value:",xkk1[0][0]*Point\r
333 ,"; Speed (pips/bar):",xkk1[1][0],"; dp/p:"\r
334 , xkk1[1][0]/xkk1[0][0]*100.*240.*(24.*60.)/Period()\r
335 ,"; Line speed "\r
336 ,(KalmanBuffer[i-1]-KalmanBuffer[i])/KalmanBuffer[i]\r
337 *100.*240.*(24.*60.)/Period());\r
338 }\r
339 if(PredictBars1 > 0){\r
340 MatrixMul(Phi1,xkk,xpt);\r
341 xp[0][0] = xkk[0][0];\r
342 \r
343 MatrixTranspose(Phi1,temp21);\r
344 MatrixMul(Pkk,temp21,temp21a);\r
345 MatrixMul(Phi1,temp21a,temp11a);\r
346 MatrixInvert(temp11a,temp11);\r
347 MatrixAdd(xp,xpt,xdel,-1);\r
348 MatrixTranspose(xdel,xdel_t);\r
349 MatrixMul(temp11,xdel,temp11a);\r
350 MatrixMul(xdel_t,temp11a,temp11);\r
351 g1=MathSqrt(temp11[0][0]);\r
352 Print(Phi1[0][1], " bar bounds ",(xpt[0][0]-g1)*Point\r
353 ,",",(xpt[0][0]+g1)*Point);\r
354 Print(Phi1[0][1], " bar center, r(t) (in pips) ",(xpt[0][0])*Point\r
355 ,",",g1);\r
356 }\r
357 if(PredictBars2 > 0){\r
358 MatrixMul(Phi2,xkk,xpt);\r
359 xp[0][0] = xkk[0][0];\r
360 MatrixTranspose(Phi2,temp21);\r
361 MatrixMul(Pkk,temp21,temp21a);\r
362 MatrixMul(Phi2,temp21a,temp11a);\r
363 MatrixInvert(temp11a,temp11);\r
364 MatrixAdd(xp,xpt,xdel,-1);\r
365 MatrixTranspose(xdel,xdel_t);\r
366 MatrixMul(temp11,xdel,temp11a);\r
367 MatrixMul(xdel_t,temp11a,temp11);\r
368 g1=MathSqrt(temp11[0][0]);\r
369 Print(Phi2[0][1], " bar bounds ",(xpt[0][0]-g1)*Point\r
370 ,",",(xpt[0][0]+g1)*Point);\r
371 Print(Phi2[0][1], " bar center, r(t) (in pips) ",(xpt[0][0])*Point\r
372 ,",",g1);\r
373 } \r
374 }else g= -1;\r
375 \r
376 last_time=Time[i];\r
377 }\r
378 \r
379 //Print(Pkk1[0][0]/Point," ",Pkk1[1][0]/Point," ",Pkk1[1][1]/Point);\r
380 //Print("24 hours:", xpt[0][0]*Point," ,Gate ",g);\r
381 //Print ("Gate 2 ", MathSqrt(xdel[0][0]*xdel[0][0]*g)*Point," g1 ",g1);\r
382 \r
383 }\r
384 \r
385 double get_avg(int k){\r
386 return(MathPow((High[k]*Low[k]*Close[k]*Close[k]),1/4.)/Point);\r
387 } \r
388 //+++++++-----------------------------------------------------+\r
389 double determinant_fixed(double a[][], int k){\r
390 double z;\r
391 switch(k){\r
392 case 1: return(a[0][0]);\r
393 break;\r
394 case 2: return( a[0][0]*a[1][1]-a[1][0]*a[0][1]);\r
395 break;\r
396 case 3:\r
397 z = a[0][0]*a[1][1]*a[2][2] + a[0][1]*a[1][2]*a[2][0] + \r
398 a[0][2]*a[1][0]*a[2][1] -\r
399 (a[2][0]*a[1][1]*a[0][2] + a[1][0]*a[0][1]*a[2][2] + \r
400 a[0][0]*a[2][1]*a[1][2]);\r
401 return(z);\r
402 break;\r
403 default: \r
404 Print("array_range too large for determinant calculation");\r
405 return(0);\r
406 } \r
407 }\r
408 double determinant(double a[][]){\r
409 double z;\r
410 if(ArrayRange(a,0) != ArrayRange(a,1)){\r
411 Print("Non-square array entered into determinant");\r
412 return(0);\r
413 }\r
414 switch(ArrayRange(a,0)){\r
415 case 1: return(a[0][0]);\r
416 break;\r
417 case 2: return( a[0][0]*a[1][1]-a[1][0]*a[0][1]);\r
418 break;\r
419 case 3:\r
420 z = a[0][0]*a[1][1]*a[2][2] + a[0][1]*a[1][2]*a[2][0] + \r
421 a[0][2]*a[1][0]*a[2][1] -\r
422 (a[2][0]*a[1][1]*a[0][2] + a[1][0]*a[0][1]*a[2][2] + \r
423 a[0][0]*a[2][1]*a[1][2]);\r
424 return(z);\r
425 break;\r
426 default: \r
427 Print("array_range too large for determinant calculation");\r
428 return(0);\r
429 } \r
430 }\r
431 \r
432 int MatrixAdd(double a[][], double b[][],double & c[][],double w=1){\r
433 int i,j;\r
434 for(i=0;i<ArrayRange(c,0);i++){\r
435 for(j=0;j<ArrayRange(c,1);j++){\r
436 c[i][j] = a[i][j]+w*b[i][j];\r
437 }\r
438 }\r
439 return(0); \r
440 }\r
441 int MatrixMul(double a[][], double b[][],double & c[][]){\r
442 int i,j, k;\r
443 if(ArrayRange(a,1) != ArrayRange(b,0)){\r
444 Print("array Range Mismatch in Matrix Mul");\r
445 return(-1);\r
446 }\r
447 for(i=0;i<ArrayRange(a,0);i++){\r
448 for(j=0;j<ArrayRange(b,1);j++){\r
449 c[i][j] = 0;\r
450 for(k=0;k<ArrayRange(a,1);k++){\r
451 c[i][j] += (a[i][k]*b[k][j]);\r
452 } \r
453 }\r
454 }\r
455 return(0); \r
456 }\r
457 int MatrixScalarMul(double b,double & a[][]){\r
458 int i,j;\r
459 for(i =0;i<ArrayRange(a,0);i++){\r
460 for(j=0;j<ArrayRange(a,1);j++){\r
461 a[i][j] *= b;\r
462 }\r
463 }\r
464 } \r
465 int MatrixInvert(double a[][],double & b[][]){\r
466 double d;\r
467 double temp1[4][4],temp2[4][4];\r
468 int i,j,i1,j1,k;\r
469 \r
470 if(ArrayRange(a,0) != ArrayRange(a,1)){\r
471 Print("Matrix Inverse attempted on non square matrix. Not implemented yet");\r
472 return(-1);\r
473 }\r
474 if(ArrayRange(a,1) > 3){\r
475 Print("Bugger off, not implemented yet");\r
476 return(-1);\r
477 }\r
478 d = determinant(a);\r
479 if(MathAbs(d)<0.000001){\r
480 Print("unstable matrix");\r
481 d = 1;\r
482 }\r
483 k = ArrayRange(a,0);\r
484 if(k==0){\r
485 b[0][0]=1./a[0][0];\r
486 return(0);\r
487 }\r
488 d = determinant(a);\r
489 for(i1=0;i1<k;i1++){\r
490 for(j1=0;j1<k;j1++){\r
491 temp1[i1][j1] = a[i1][j1];\r
492 }\r
493 } \r
494 for(i=0;i<k;i++){\r
495 for(j=0;j<k;j++){\r
496 //copy the arry. There must be a better way!!\r
497 ArrayCopy(temp2,temp1);\r
498 for(j1=0;j1<k;j1++){\r
499 if(j1==j){\r
500 temp2[i][j1] = 1;\r
501 }else{\r
502 temp2[i][j1] = 0;\r
503 }\r
504 } \r
505 b[i][j]=determinant_fixed(temp2,k)/d;\r
506 }\r
507 }\r
508 } \r
509 int MatrixTranspose(double a[][],double & b[][]){\r
510 int i,j;\r
511 for(i=0;i<ArrayRange(a,0);i++){\r
512 for(j=0;j<ArrayRange(a,1);j++){\r
513 b[j][i] = a[i][j];\r
514 }\r
515 }\r
516 return(0);\r
517 }\r
518 int MatrixZero(double & a[][]){\r
519 int i,j; \r
520 for(i= 0;i<ArrayRange(a,0);i++){\r
521 for(j=0;j<ArrayRange(a,1);j++){\r
522 a[i][j]=0;\r
523 }\r
524 }\r
525 return(0);\r
526 } \r
527 int MatrixEye(double & a[][]){\r
528 int i,j; \r
529 for(i= 0;i<ArrayRange(a,0);i++){\r
530 for(j=0;j<ArrayRange(a,1);j++){\r
531 a[i][j]=0;\r
532 if(i==j)a[i][j]=1;\r
533 }\r
534 }\r
535 return(0);\r
536 } \r
537 int MatrixPrint(double a[][]){\r
538 int i,j; \r
539 for(i= 0;i<ArrayRange(a,0);i++){\r
540 for(j=0;j<ArrayRange(a,1);j++){\r
541 Print(i," ,",j," ,",a[i][j]);\r
542 }\r
543 }\r
544 return(0);\r
545 } \r
546 //+------------------------------------------------------------------+\r
547 \r