Mastering SciPy

Cover......Page 1
Copyright......Page 3
Credits......Page 4
About the Author......Page 5
About the Reviewers......Page 6
www.PacktPub.com......Page 7
Table of Contents......Page 8
Preface......Page 14
 Motivation......Page 20
  Constructing matrices in the ndarray class......Page 33
  Constructing matrices in the matrix class......Page 37
  Constructing sparse matrices......Page 38
  Linear operators......Page 45
 Basic matrix manipulation......Page 47
  Scalar multiplication, matrix addition, and matrix multiplication......Page 48
  Traces and determinants......Page 49
  Transposes and inverses......Page 50
  Norms and condition numbers......Page 52
 Matrix functions......Page 54
   Pivoted LU decomposition......Page 57
   Singular value decomposition......Page 58
  Matrix equations......Page 59
   Basic systems: banded matrices......Page 60
   Basic systems: generic square matrices......Page 63
   Least squares......Page 70
   Other matrix equation solvers......Page 72
  Spectral decomposition......Page 73
  Schur decomposition......Page 77
 Summary......Page 78
 Motivation......Page 80
  Implementation details......Page 86
   Nearest-neighbors interpolation......Page 88
   Lagrange interpolation......Page 89
   Hermite interpolation......Page 92
   Piecewise polynomial interpolation......Page 94
   Spline interpolation......Page 96
  Multivariate interpolation......Page 100
  Linear least squares approximation......Page 111
  Nonlinear least squares approximation......Page 114
 Summary......Page 122
 Motivation......Page 124
 Differentiation......Page 126
  Numerical differentiation......Page 127
  Symbolic differentiation......Page 128
 Integration......Page 129
  Symbolic integration......Page 130
   Functions without singularities on finite intervals......Page 132
   Functions with singularities on bounded domains......Page 138
   Integration on unbounded domains......Page 140
  Numerical multivariate integration......Page 141
 Summary......Page 142
 Motivation......Page 144
 Non-linear equations and systems......Page 148
  Iterative methods for univariate functions......Page 149
   Bracketing methods......Page 150
   Secant methods......Page 151
   Brent method......Page 153
  Systems of nonlinear equations......Page 154
   Simple iterative solvers......Page 158
   The Broyden method......Page 160
   Powell\'s hybrid solver......Page 161
   Large-scale solvers......Page 164
  Unconstrained optimization for univariate functions......Page 165
  Unconstrained optimization for multivariate functions......Page 169
   The stochastic methods......Page 173
   Deterministic algorithms that exclusively employ function evaluations......Page 174
   The Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method......Page 176
   The conjugate gradient method......Page 177
  Constrained optimization for multivariate functions......Page 180
 Summary......Page 182
Chapter 5: Initial Value Problems for Ordinary Differential Equations......Page 184
 Symbolic solution of differential equations......Page 185
 Analytic approximation methods......Page 187
 Discrete-variable methods......Page 189
  One-step methods......Page 191
  Two-step methods......Page 195
 Summary......Page 197
Chapter 6: Computational Geometry......Page 198
 Plane geometry......Page 199
  Static problems......Page 206
   Convex hulls......Page 207
   Voronoi diagrams......Page 211
   Triangulations......Page 214
   Shortest paths......Page 218
   Point location......Page 221
   Nearest neighbors......Page 224
   Range searching......Page 227
  Dynamic problems......Page 228
  Numerical computational geometry......Page 230
  Bézier curves......Page 231
 Summary......Page 235
Chapter 7: Descriptive Statistics......Page 236
 Motivation......Page 238
  Symbolic setting......Page 250
  Numerical setting......Page 253
 Data exploration......Page 256
   Bar plots and pie charts......Page 257
   Histograms......Page 263
   Time plots......Page 265
  Describing distributions with numbers and boxplots......Page 266
  Relationship between quantitative variables......Page 270
   Scatterplots and correlation......Page 271
   Regression......Page 275
  Analysis of the time series......Page 283
 Summary......Page 293
 Statistical inference......Page 294
   Bayesian approach......Page 296
   Likelihood approach......Page 299
   Frequentist approach......Page 301
 Data mining and machine learning......Page 302
  Classification......Page 303
   Support vector classification......Page 305
   Trees......Page 307
   Naive Bayes......Page 309
   Nearest neighbors......Page 310
  Dimensionality reduction......Page 311
   Principal component analysis......Page 313
   Isometric mappings......Page 314
   Spectral embedding......Page 315
   Locally linear embedding......Page 316
  Clustering......Page 317
   MeanShift......Page 318
   Gaussian mixture models......Page 323
   Kmeans......Page 325
 Summary......Page 328
Chapter 9: Mathematical Imaging......Page 330
  Binary......Page 332
  Gray-scale......Page 333
 Color......Page 335
  Alpha channels......Page 338
  Object measurements......Page 339
  Mathematical morphology......Page 340
  Smoothing filters......Page 342
  Multivariate calculus......Page 343
  Statistical filters......Page 345
  Fourier analysis......Page 346
  Wavelet decompositions......Page 348
 Image compression......Page 350
  Lossless compression......Page 351
  Lossy compression......Page 353
  Transformations of the domain......Page 355
   Swirl......Page 356
   Geometric transformations......Page 357
   Histogram equalization......Page 361
   Intensity clipping/resizing......Page 364
   Contrast enhancement......Page 365
  Image restoration......Page 367
   Noise reduction......Page 368
   Sharpening and blurring......Page 372
  Inpainting......Page 374
 Image analysis......Page 376
  Image structure......Page 377
   Line, circle, and ellipse detection......Page 384
   Blob detection......Page 386
   Corner detection......Page 387
   Beyond geometric entities......Page 389
 Summary......Page 393
Index......Page 394