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wavelet analysis & data compression 287for ( i=1; i = 0) for (nd=n ; nd >= nend ; nd /= 2) daube4 ( f , nd , sign ) ;else for ( nd=4; nd =0 for DWT, @param sign : < 0 for inverse TF ∗/double tr [] = new double [n + 1]; / / Temporary variableint i , j , mp, mp1 ;if (n < 4) return ;mp = n/2; mp1 = mp + 1; / / Midpoint Midpoint +1 of arrayif ( sign >= 0) { / / DWTj = 1;for ( i = 1; j
288 chapter 113. Reproduce the scale–time diagram shown on the right in Figure 11.10. Thisdiagram shows the output at different scales and serves to interpret the maincomponents of the signal and the time in which they appear. The time line atthe bottom of the figure corresponds to a signal of length 1 over which 256samples were recorded. The low-band (smooth) components are shown onthe left, and the high-band components on the right.a. The bottommost figure results when nend = 256.b. The figure in the second row up results from nend = 128, and we havethe output from two filterings. The output contains 256 coefficients butdivides time into four intervals and shows the frequency components ofthe original signal in more detail.c. Continue with the subdivisions for nend =64, 32, 16, 8, and 4.4. For each of these choices except the topmost, divide the time by 2 and separatethe intervals by vertical lines.5. The topmost spectrum is your final output. Can you see any relation betweenit and the chirp signal?6. Change the sign of sign and check that the inverse DWT reproduces theoriginal signal.7. Use the code to visualize the time dependence of the Daubechies motherfunction at different scales.a. Start by performing an inverse transformation on the eight-componentsignal [0,0,0,0,1,0,0,0]. This should yield a function with a width of about5 units.b. Next perform an inverse transformation on a unit vector with N =32butwith all components except the fifth equal to zero. The width should nowbe about 25 units, a larger scale but still covering the same time interval.c. Continue this procedure until you obtain wavelets of 800 units.d. Finally, with N = 1024, select a portion of the mother wavelet with data inthe horizontal interval [590,800]. This should show self-similarity similarto that at the bottom of Figure 11.11.−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 288
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−101COPYRIGHT 2008, PRINCET O N U
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Copyright © 2008 by Princeton Univ
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viiicontents2.3 Experimental Error
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xcontents6.3 Experimentation 1356.4
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xiicontents9.7.1 Friction: Model an
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xvicontents14.15.2Exercise 2: Cache
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xxcontentsC.3 DX Tools Summary 576C
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xxivprefacewhich includes understan
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2 chapter 1PhysicsCPFigure 1.1 A re
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4 chapter 1Scientific LibrariesPerf
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6 chapter 1C DWe have tried to make
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8 chapter 1possibly when installing
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10 chapter 11.4.1 Structured Progra
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12 chapter 17. Revise Area.java so
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14 chapter 1argv). Because main met
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18 chapter 1Memory and storage size
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20 chapter 1TABLE 1.4The IEEE 754 S
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22 chapter 1gives 24-bit precision
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24 chapter 1TABLE 1.6Representation
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26 chapter 1The computer fetches th
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28 chapter 1Your problem is to use
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2Errors & Uncertainties in Computat
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32 chapter 2purposes, let us consid
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34 chapter 2can be avoided by combi
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36 chapter 2means that a program ru
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38 chapter 2To be more specific, le
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42 chapter 2To see if these assumpt
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44 chapter 2computation. Accordingl
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46 chapter 3is regular practice to
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48 chapter 3to plot for x and y, we
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50 chapter 3Sample PtPlot Data file
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52 chapter 3TABLE 3.1Text Files Gra
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54 chapter 3Figure 3.4 Left: A plot
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56 chapter 3TABLE 3.2Grace Menu and
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58 chapter 33.4.1 Gnuplot Input Dat
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60 chapter 3gnuplot> set output "pl
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62 chapter 3gnuplot> set terminal e
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66 chapter 33.6 Texturing and 3-D I
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68 chapter 4R R 2RL L 2LC C 2CFigur
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70 chapter 44.3 Resistance Becomes
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78 chapter 42. Compile and execute
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80 chapter 41 / Z0.51400R0400R80021
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84 chapter 42. Define a daughter cl
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86 chapter 4new features without
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88 chapter 4qFigure 4.7 Left: The t
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90 chapter 4with properties differi
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94 chapter 4data types called objec
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96 chapter 46. Change the mass of t
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98 chapter 4Check that all the plot
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100 chapter 43. You should see now
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102 chapter 44.9.11 Complex Object
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104 chapter 4✞/ / KomplexTest : t
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108 chapter 4✝protected double y(
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110 chapter 5Mathematically, the li
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112 chapter 5The linear congruent m
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114 chapter 5TABLE 5.1A Table of a
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116 chapter 55.3 Unit II. Monte Car
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118 chapter 5300y0-10-20R2001000 20
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120 chapter 54100,000log[N(t)]10,00
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122 chapter 5✞/ / Decay . java :
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124 chapter 6f(x)a x i x i+1 x i+2
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126 chapter 6f(x)f(x)parabola 1para
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128 chapter 6evaluate the function
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130 chapter 6⇒ N =( ) 2/91 1(ɛ m
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132 chapter 63. [−∞→∞], sca
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134 chapter 6}public static double
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136 chapter 6the integral of f(x)=1
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138 chapter 6f(x)< f(x) >xFigure 6.
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140 chapter 61. Conduct 16 trials a
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142 chapter 6acceptrejectFigure 6.6
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144 chapter 6The crux of this techn
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7Differentiation & SearchingIn this
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148 chapter 7the forward-difference
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150 chapter 7algorithm (7.7) is O(h
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154 chapter 7we know a zero occurs.
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156 chapter 7Figure 7.3 Two example
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8Solving Systems of Equationswith M
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160 chapter 8the spheres, and the d
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162 chapter 8We now have a solvable
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164 chapter 8of (8.19) by A −1 :x
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168 chapter 8having different varia
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172 chapter 8✞/∗ JamaFit : JAMA
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174 chapter 8( ) α β3. Consider t
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176 chapter 8discarding some inform
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180 chapter 8Figure 8.3 Three fits
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190 chapter 88.7.4 Linear Quadratic
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9Differential Equation Applications
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196 chapter 9V(x)HarmonicAnharmonic
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230 chapter 99.17.1.1 EXPLORATION:
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342 chapter 13Figure 13.8 Number 8
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14High-Performance Computing Hardwa
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354 chapter 14A(1)A(2)A(3)CPUA(N)M(
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360 chapter 14TABLE 14.2Computation
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362 chapter 14The processors in a p
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364 chapter 14Figure 14.7 Two views
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366 chapter 14Speedup8Amdahl's Lawp
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368 chapter 1414.11 Parallelization
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374 chapter 14yet in order to obtai
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378 chapter 14You see (Listing 14.1
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388 chapter 14✞Dimension Vec( idi
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16Simulating Matter withMolecular D
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430 chapter 162 3 2 3 2 31 4 1 4 1
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17PDEs for Electrostatics & Heat Fl
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solitons & computational fluid dyna
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Appendix A: Glossaryabsolute value
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glossary 557control character — A
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glossary 559log in (on) — To sign
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glossary 561supercomputer — The c
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installing ptplot & java developer
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industrial-strength data visualizat
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Appendix D: An MPI TutorialIn this
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an mpi tutorial 595• Open a shell
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an mpi tutorial 597of all the compu
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an mpi tutorial 599TABLE D.1Some Co
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an mpi tutorial 601jobs to MPI. 2 A
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an mpi tutorial 603✞> cd $HOME Do
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an mpi tutorial 605✞/ / MPIhello
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an mpi tutorial 607Argument Namemsg
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an mpi tutorial 609D.3.4 Broadcast
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an mpi tutorial 611D.4 Parallel Tun
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an mpi tutorial 613✝}MPI_Recv ( &
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an mpi tutorial 615✞/ / Code list
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an mpi tutorial 617-1) does not sen
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an mpi tutorial 619D.6.1 Nonblockin
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an mpi tutorial 621D.9 List of MPI
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Appendix E: Calling LAPACK from CCa
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calling LAPACK from C 625E.2 Compil
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software on the CD 627JavaCodes Con
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software on the CD 629JavaCodes Con
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software on the CD 631Applets Direc
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software on the CD 633Fortran77code
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Appendix G: Compression via DWTwith
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compression via DWT with thresholdi
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compression via DWT with thresholdi
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BIBLIOGRAPHY[Abar 93] Abarbanel, H.
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ibliography 643[Erco] Ercolessi, F.
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ibliography 645[L&F 93] Landau, R.
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ibliography 647[P&W 91] Pinson, L.
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ibliography 649[VdeV 94] van de Vel
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IndexAbstract data structures,70Abs
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index 653drand, 114Driving force, 2
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index 655Libraries, see Subroutines
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index 657structured, 10for virtual
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