Monte Carlo Simulation with Noisy Signals in .NET framework

Creation QR Code 2d barcode in .NET framework Monte Carlo Simulation with Noisy Signals
Monte Carlo Simulation with Noisy Signals
Recognizing QR Code In .NET Framework
Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in .NET framework applications.
A single simulation run produces the n time histories x(t) and also computes time histories of the statistics xAvg = xAvg(t) and xVar = xVar(t) with
Draw Quick Response Code In .NET Framework
Using Barcode creator for VS .NET Control to generate, create QR Code JIS X 0510 image in .NET applications.
DOT xSum = x * 1 | DOT xxSum = x * x xAvg = xSum/n | xxAvg = xxSum/n | xVar = xxAvg xAvg^2 (5-9)
Reading QR Code In VS .NET
Using Barcode recognizer for .NET Control to read, scan read, scan image in .NET framework applications.
Figure 5-2a exhibits several random walks, and Figure 5-2b shows scaled time histories of xAvg, and xVar(t) Note how xVar(t) approximates the theoretical value Var = t * DT * (a^2)/3 An extra DYNAMIC program segment (Section 4-10c) computes a probability density estimate of x(TMAX) as in Section 4-10c and compares it to the theoretical Gaussian probability density (Fig 5-2c) Figure 5-3 shows the complete random-walk program For a typical run with NN = 10,000 steps and n = 5000, we measured xAvg = 0008 and xVar = 1025, which approximates the theoretical results (27) Monte Carlo results were unchanged with rescrambled pseudorandom noise obtained by changing the value of n from 5000 to 5002 (Section 5-10) On a 24-GHz personal computer running Linux, vectorized simulation of 5000 replicated 10,000-step random walks took 46 s, and 73 s with runtime computation and display of xAvg(t) and xVar(t) Five thousand repeated 10,000-step random walks (without runtime statistics computation) took 84 s The post-run probability density estimation required 24 s in either case 5-7 The 1776 Cannonball with Air Turbulence Referring to Figure 4-2, we can add a random wind force W(t) to our cannonball simulation in Section 4-6 by changing the DYNAMIC program segment in Figure 4-3 as follows:
Print Barcode In Visual Studio .NET
Using Barcode generation for .NET Control to generate, create barcode image in VS .NET applications.
DYNAMIC --------------------------------------------------------------------------------------------v = sqrt(xdot^2 + ydot^2) d/dt W = - r * W + noise | -a simple low-pass filter d/dt x = xdot | d/dt y = ydot d/dt xdot = - R * v * xdot + W | -W is the horizontal wind force d/dt ydot = - R * v * ydot-g -step xI = xI + swtch(y) * (x - xI) | -hold the impact abscissa OUT noise = b * (ran()+ran()+ran()+ran()) | -- roughly Gaussian noise
Bar Code Decoder In .NET Framework
Using Barcode recognizer for VS .NET Control to read, scan read, scan image in .NET applications.
Random-process Simulation and Monte Carlo Studies with Noisy Signals
QR Code JIS X 0510 Encoder In Visual C#
Using Barcode creation for .NET Control to generate, create QR-Code image in .NET applications.
(a) scale = 1
Drawing QR Code In .NET Framework
Using Barcode generation for ASP.NET Control to generate, create QR Code JIS X 0510 image in ASP.NET applications.
+ xVar
Create QR In Visual Basic .NET
Using Barcode encoder for VS .NET Control to generate, create QR-Code image in .NET framework applications.
05 [1], [2], [3], [4] vs t
Make Bar Code In .NET
Using Barcode printer for VS .NET Control to generate, create bar code image in Visual Studio .NET applications.
0 xAvg
Data Matrix Creation In .NET Framework
Using Barcode maker for .NET framework Control to generate, create Data Matrix ECC200 image in Visual Studio .NET applications.
(b) scale = 1
Code-39 Printer In Visual Studio .NET
Using Barcode encoder for VS .NET Control to generate, create ANSI/AIM Code 39 image in VS .NET applications.
+ 2* error
Identcode Creation In .NET
Using Barcode maker for .NET Control to generate, create Identcode image in Visual Studio .NET applications.
05 1 Avg 20, Var,truVar vs t
DataMatrix Recognizer In VS .NET
Using Barcode scanner for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications.
(c) scale = 4
Scanning Code128 In VS .NET
Using Barcode reader for VS .NET Control to read, scan read, scan image in VS .NET applications.
10
Make Code 128 Code Set A In .NET Framework
Using Barcode creation for ASP.NET Control to generate, create Code 128C image in ASP.NET applications.
05
GS1 - 13 Generator In Java
Using Barcode printer for Java Control to generate, create GS1 - 13 image in Java applications.
00 xx,yy,F,error 2
Create USS-128 In Java
Using Barcode encoder for Java Control to generate, create EAN / UCC - 14 image in Java applications.
FIGURE 5-2 (a) 4 of n = 5000 random walks, (b) time-histories of the statistics xAvg and xVar, and (c) post-run probability-density estimate for x(TMAX) Figure 5-2b compares the time history of the sample variance xVar with the theoretical variance Var = t DT a2/3 Figure 5-2c compares the computed probability density estimate with the Gaussian probability density The original displays were in color
Creating Data Matrix ECC200 In C#.NET
Using Barcode generator for .NET framework Control to generate, create Data Matrix image in VS .NET applications.
Monte Carlo Simulation with Noisy Signals
Encode GS1-128 In Visual C#
Using Barcode creator for .NET Control to generate, create EAN / UCC - 13 image in .NET framework applications.
-- VECTORIZED MONTE CARLO STUDY OF A RANDOM WALK ---------------------------------------------------------------------------------------------------------------irule 2 | -Euler integration NN = 10001 | TMAX = 1 DT = TMAX/NN | -< COMINT = TMAX/(NN- 1) a = sqrt(3 * NN) | ---scaled noise amplitude VAR0 = TMAX^2 | scale = VAR0 -n = 5000 | STATE x[n] | ARRAY noise[n] for i = 1 to n | noise[i] = a * ran() | next | -initialize drun write "type go to continue" | STOP ----------------------------------------------------------------------------------------------------------------post-run probability-density estimation ARRAY f[n] irule 0 | -just sampled data scale = 4 | TMAX = scale | NN = 2500 a = 2 * scale | b= - scale | -for display sweep t = 0 | h = 015 | -h is the Parzen-window width alpha = 1/(2 * h * h) | beta = 1/(h * n * sqrt(2 * PI)) drun PARZEN ---------------------------------------------------------------------------------------------------------------DYNAMIC ---------------------------------------------------------------------------------------------------------------Vectr d/dt x = noise OUT Vector noise = a * ran() -----------------------------------compute statistics DOT xSum = x * 1 | DOT xxSum = x * x xAvg = xSum/n | xxAvg = xxSum/n | xVar = xxAvg - xAvg^2 Var = t * DT * (a^2)/3 | -theoretical variance of x -xAvgx20 = 20 * xAvg | -scaled display dispt xVar, Var, xAvgx20 ---------------------------------------------------------------------------------------------------------------label PARZEN -xx = a * t + b | -display sweep for Parzen Window Vector f = beta * exp(- alpha * (xx - x)^2) DOT F = f * 1 | F = 10 * F - scale -- display Gaussian density for comparison yy = 10*exp(- (xx^2)/(2 * VAR0))/sqrt(2 * VAR0 * PI) - scale errorx2 = 2*(F - yy) + 05*scale | -deviation from normal density dispxy xx, yy, F, errorx2 | -scaled and offset display FIGURE 5-3 DESIRE program for the vectorized random-walk simulation and runtime statistics computations An extra DYNAMIC program segment estimates the post-run probability density and compares it with the Gaussian probability density
Bar Code Recognizer In VS .NET
Using Barcode recognizer for .NET Control to read, scan read, scan image in .NET framework applications.