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List of Figures<br />

Figure 11-8. Scatter Plot of a Gaussian Sample and Contour Ellipses . . . . . . . . . . . . . . . . . 439<br />

Figure 11-9. Scatter Plot and Marginal Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441<br />

Figure 11-10. The ISMC Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453<br />

Figure 11-11. Comparison Between Low Discrepancy and Pseudorandom Point Sets . . . . 456<br />

Figure 11-12. Latin Hypercube Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458<br />

Figure 11-13. Output Files Organization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464<br />

Figure 11-14. Illustration of Kurtosis and Skewness with μ=0 and σ=1. . . . . . . . . . . . . . . . 496<br />

Figure 11-15. Global/Local Hierarchy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506<br />

Figure 11-16. Histogram Annotations 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511<br />

Figure 11-17. CDF Plot (with Confidence Bounds) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512<br />

Figure 11-18. CDF Plot Right-Tail Part of the Empirical CDF. . . . . . . . . . . . . . . . . . . . . . . 513<br />

Figure 11-19. Principle of the SETTLING Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517<br />

Figure 11-20. Scatter Plots of Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522<br />

Figure 11-21. Monte Carlo Analysis Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527<br />

Figure 11-22. LIMIT Distribution with L=-1 and U=+1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 549<br />

Figure 11-23. Four Random Samples from NOR/UNI Distributions . . . . . . . . . . . . . . . . . . 551<br />

Figure 11-24. Four Random Samples when AUNIF(0,1,MULT) is Specified . . . . . . . . . . . 552<br />

Figure 11-25. Four Random Samples when AGAUSS (0,1,1,MULT) is Specified . . . . . . . 553<br />

Figure 12-1. Percentage of Cases in Eight Portions of the Gaussian Distribution . . . . . . . . 566<br />

Figure 12-2. Common Statistics for UNIF(x,h). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567<br />

Figure 12-3. Factor Levels for a Circuit Parameter x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568<br />

Figure 12-4. Cuboidal Representation of Two 3-factors Designs . . . . . . . . . . . . . . . . . . . . . 575<br />

Figure 13-1. Simulator as a Black Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594<br />

Figure 13-2. Discretization of Design Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595<br />

Figure 13-3. Illustration of Optimality Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625<br />

Figure 13-4. Illustration of Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625<br />

Figure 13-5. Non-Valid and Valid Zeros. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627<br />

Figure 13-6. Different Types of Minima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629<br />

Figure 13-7. Examples of Non-Smooth Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631<br />

Figure 13-8. Discretization of Design Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633<br />

Figure 13-9. Inner and Outer Sweep Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635<br />

Figure 13-10. Scaling Transformation For Design Objectives Output . . . . . . . . . . . . . . . . . 644<br />

Figure 13-11. Scaling Transformation for Variables Output. . . . . . . . . . . . . . . . . . . . . . . . . 645<br />

Figure 13-12. Optimization Phase Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646<br />

Figure 13-13. Statistics and Diagnostics Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647<br />

Figure 13-14. Status of Variables Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648<br />

Figure 13-15. Status of Objectives Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649<br />

Figure 13-16. Analysis Of Last Simulation Output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650<br />

Figure 13-17. Optimization Results with Respect to the Outer Loop Output . . . . . . . . . . . . 651<br />

Figure 13-18. Illustration of Constraint Violations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660<br />

Figure 13-19. Illustration of Slack. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662<br />

Figure 13-20. Plotted Values of the Merit Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671<br />

Figure 13-21. Filter Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672<br />

Figure 13-22. Optimized Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674<br />

Figure 13-23. Illustration of I-V characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675<br />

24 Eldo® User's Manual, 15.3

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