# NMath User's Guide

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Numerics

1-norm 179

A

absolute value 19, 45, 70, 181

abstract indexing 26

accessing underlying data 23, 24

ActiveSetLineSearchSQP 274

ActiveSetLineSearchSQP.Options 275

ActiveSetQPSolver 277

converting to data frames 14

creating from data frames 46

alpha levels 91

ALS 194

Alternating Least Squares (ALS) 194

analysis of variance (ANOVA) 137

Anderson-Darling test 159

annealing 253

annealing history 257

annealing schedules 253

custom 255

linear 254

annealing temperature 253

AnnealingHistory 258

AnnealingHistory.Step 258

AnnealingMinimizer 253, 256, 257

AnnealingScheduleBase 254

ANOVA 137

ANOVA regression parameters 148

AnovaRegressionFactorParam 150

AnovaRegressionInteractionParam 150

AnovaRegressionParameter 150

appending to a vector 38

applying functions 46, 71, 182, 10

argument of a complex number 19

arithmetic mean 56

arithmetic operators 176, 187, 193

arrays, converting to 24

ASP.NET web applications 8

Assemblies 2

asymptotic function 301

autocorrelation 61

B

balancing 232

banded matrices 162

bandwidth 168, 173

Bessel functions 153

beta distribution 69

beta function 154, 66

BiasType 58, 59, 60, 61

binary nonlinear programming 262, 271

binary serialization 47, 223

binomial coefficient 154, 65

binomial distribution 70

BinomialDistribution 67, 70

block-splitting 96

Boole's rule 126

boolean columns 4

BoundedMultiVariableFunctionFitter 305

BoundedOneVariableFunctionFitter 297

Box-Cox power transformations 89

Bracket 242, 243, 245

bracketing minima 241

Brent's Method 242

BrentMinimizer 242

Bunch-Kaufman factorization 197

C

calculus 121

categorical vectors 34

CDF 68

cell data 146, 147

cell means 148

CenterSpace.NMath.Stats namespace 2

central moments 60

central tendency 56

chi-square distribution 71

ChiSquareDistribution 67, 71

Cholesky

least squares 205

Cholesky factorization 197

choose function 65

city-block (Manhattan) distance 181

clamped cubic spline 138

clearing

matrices 58

vectors 37

cloning 34, 55, 172

CLRConfigFile 11

cluster analysis 180

ClusterAnalysis 180, 184, 202

clustering 196

ClusterSet 187, 191

coefficient of determination 285, 305, 215

column names 3, 4, 21

column sums 70

columns

accessing 7

creating 4

exporting to a string 12

exporting to a vector 12

exporting to an array 12

properties 7

removing data 6

reordering 8

combinatorial functions 65

Common Language Specification 1

complete orthogonal decomposition 114

complex argument 182

complex conjugate 182

complex numbers 15

absolute value function 19

accessing values 17

argument function 19

comparing 18, 39, 59

conjugate function 19

creating 15

creating from polar coordinates 16

creating from strings 16

modifying 17

norm function 19

trigonometric functions 20

component matrices 77

compressed row format 189

condition numbers 79, 202

confidence interval 220

conjugate of a complex number 19

consensus matrix 200

constrained least squares 280

ConstraintType 262

contingency table 109

convergence check period 197

convolution 13, 99, 106

cophenetic distance 188

copying matrices 55, 172

copying vectors 34

CORegressionCalculation 114

correlated random inputs 85

correlation 61

counts 53

covariance 60

covariance matrix 61

Cox and Snell pseudo R-squared statistic 135

Cp 219, 220

Cpk 219, 220

Cpm 219, 220

creating matrices 167

critical values 141, 144, 167

Cronbach's alpha 61

cross product 42

cross validation 210

cross-tabulation 40

cubic spline interpolation 138

cumulative distribution function 68

curve fitting 235, 287

CustomAnnealingSchedule 255

D

data block classes 23

data blocks 23

accessing 23, 24

properties 24

data frames

column properties 7

column types 4

creating 12

exporting to a matrix 44

exporting to a string 45

permuting rows and columns 33

properties 21

removing columns 16

removing rows 18

sorting 32

database integration 229

DataFrame 3–??

DataTables 229

data-view pattern 23

datetime columns 4

DBrentMinimizer 244

deciles 54

decimal types 51

decomposition servers 217, 218

decompositions 217

deployment 11

descriptive statistics 49

design variables 130

determinants 78, 202

DFBoolColumn 4

DFColumn 4

DFDateTimeColumn 4

DFGenericColumn 4

DFIntColumn 4

DFNumericColumn 4

DFStringColumn 4

differential equations 321

differentiating polynomials 136

digamma function 154

DIgital Smoothing POlynomial 142

discrete wavelet transform 111

DISPO 142

Distance 180

distance functions 180

Distance.Function 180

distribution classes 67

Dormand-Prince method 324

dot product 42

DoubleBandFact 197

DoubleBandMatrix 163

DoubleBisquareWeightingFunction 215

DoubleCholeskyLeastSq 206

DoubleComplex 15

DoubleComplexBandFact 197

DoubleComplexBandMatrix 163

DoubleComplexCholeskyLeastSq 206

DoubleComplexDataBlock 23

DoubleComplexEigDecomp 228

DoubleComplexEigDecompServer 228

DoubleComplexLeastSquares 84

DoubleComplexLowerTriMatrix 160

DoubleComplexLUFact 75

DoubleComplexMatrix 49

DoubleComplexQRDecomp 217

DoubleComplexQRDecompServer 218

DoubleComplexQRLeastSq 207

DoubleComplexSVDecomp 222

DoubleComplexSVDecompServer 222

DoubleComplexSVDLeastSq 207

DoubleComplexTriDiagFact 197

DoubleComplexTriDiagMatrix 164

DoubleComplexUpperTriMatrix 161

DoubleComplexVector 29

DoubleCOWeightedLeastSq 209

DoubleDataBlock 23

DoubleDWT 113

DoubleEigDecomp 228

DoubleEigDecompServer 228

DoubleFairWeightingFunction 216

DoubleFunctional 265

DoubleFunctionalDelegate 265

DoubleHermitianBandMatrix 166

DoubleHermitianEigDecomp 228

DoubleHermitianEigDecompServer 228

DoubleHermitianFact 197

DoubleHermitianMatrix 162

DoubleHermitianPDBandFact 197

DoubleHermitianPDFact 197

DoubleHermPDTriDiagFact 197

DoubleIterativelyReweightedLeastSq 212

DoubleLeastSquares 83

DoubleLeastSqWeightingFunction 215

DoubleLowerTriMatrix 160

DoubleLUFact 75

DoubleMatrix 49

DoubleMultiVariableFunction 288

DoubleNonnegativeLeastSquares 84, 86

DoubleParameterizedDelegate 298

DoubleParameterizedFunction 298

DoubleParameterizedFunctional 306

DoubleQRDecomp 217

DoubleQRDecompServer 218

DoubleQRLeastSq 207

DoubleRandomCauchyDistribution 92

DoubleRandomExponentialDistribution 93

DoubleRandomGaussianDistribution 93

DoubleRandomGumbelDistribution 93

DoubleRandomLaplaceDistribution 93

DoubleRandomLogNormalDistribution 93

DoubleRandomRayleighDistribution 93

DoubleRandomUniformDistribution 93

DoubleRandomWeibullDistribution 93

DoubleSVDecomp 222

DoubleSVDecompServer 222

DoubleSVDLeastSq 207

DoubleSymBandMatrix 165

DoubleSymEigDecomp 228

DoubleSymEigDecompServer 228

DoubleSymFact 197

DoubleSymmetricMatrix 162

DoubleSymPDBandFact 197

DoubleSymPDFact 197

DoubleSymPDTriDiagFact 197

DoubleTriDiagFact 197

DoubleTriDiagMatrix 164

DoubleUpperTriMatrix 161

DoubleVector 29

DoubleVectorParameterizedDelegate 306

DoubleWavelet 111

downhill simplex method 247

DownhillSimplexMinimizer 247

DualSimplexSolver 261, 263

DualSimplexSolverParams 263

dummy variable regression parameters in ANOVA 150

dummy variables 130

Durbin-Watson statistic 61

DWT 111

E

effective rank 85

effects encoding 149

eigenvalue classes 227

eigenvalue servers 227, 231

eigenvalue tolerance 232

eigenvalues 227, 228

eigenvectors 227

elliptic functions 154

elliptic integrals 154

encapsulating functions 121

enumeration 47, 73

equality operators 176, 187, 193

error tolerance 241

Euclidean distance 181

Euler gamma 154

Euler-Macheroni constant 154

evaluating functions 122, 238

evaluating polynomials 134

exception classes 233

exponential distribution 72

exponential function 301

exponential integral 154

ExponentialDistribution 67, 72

exponentially weighted moving average (EWMA) 142, 143

F

F distribution 73

F test 106

Factor 30, 34, 138, 164

Factor analysis 174

factor extraction 174

factor rotation 174

factor score 205

factor score coefficients 179

factor scores 179

factorial 155, 65

factorization 185, 194, 197

factorization classes 194, 197

factorizations 185, 194, 197

creating 195, 198

using 196, 200

factors 34

accessing 36

creating 34

grouping by 36

properties 36

Fast Fourier Transforms 99

FDistribution 67, 73

FFT 13, 99

FFTKernelException 233

filtering 141, 145

finding roots 313

FirstOrderInitialValueProblem 321

Fisher transformation 61

Fisher's Exact Test 110

FloatBandFact 197

FloatBandMatrix 163

FloatCholeskyLeastSq 206

FloatComplex 15

FloatComplexBandFact 197

FloatComplexBandMatrix 163

FloatComplexCholeskyLeastSq 206

FloatComplexDataBlock 23

FloatComplexEigDecomp 228

FloatComplexEigDecompServer 228

FloatComplexLeastSquares 84

FloatComplexLowerTriMatrix 160

FloatComplexLUFact 75

FloatComplexMatrix 49, 106

FloatComplexQRDecomp 217

FloatComplexQRDecompServer 218

FloatComplexQRLeastSq 207

FloatComplexSVDecomp 222

FloatComplexSVDecompServer 222

FloatComplexSVDLeastSq 207

FloatComplexTriDiagFact 197

FloatComplexTriDiagMatrix 164

FloatComplexUpperTriMatrix 161

FloatComplexVector 29

FloatDataBlock 23

FloatDWT 113

FloatEigDecomp 228

FloatEigDecompServer 228

FloatHermitianBandMatrix 166

FloatHermitianEigDecomp 228

FloatHermitianEigDecompServer 228

FloatHermitianFact 197

FloatHermitianMatrix 162

FloatHermitianPDBandFact 197

FloatHermitianPDFact 197

FloatHermPDTriDiagFact 197

FloatLeastSquares 83

FloatLowerTriMatrix 160

FloatLUFact 75

FloatMatrix 49

FloatNonnegativeLeastSquares 84, 86

FloatQRDecomp 217

FloatQRDecompServer 218

FloatQRLeastSq 207

FloatRandomExponentialDistribution 93

FloatRandomGaussianDistribution 93

FloatRandomGumbelDistribution 93

FloatRandomLaplaceDistribution 93

FloatRandomLogNormalDistribution 93

FloatRandomRayleighDistribution 93

FloatRandomUniformDistribution 93

FloatRandomWeibullDistribution 93

FloatSVDecomp 222

FloatSVDecompServer 222

FloatSVDLeastSq 207

FloatSymBandMatrix 165

FloatSymEigDecomp 228

FloatSymEigDecompServer 228

FloatSymFact 197

FloatSymmetricMatrix 162

FloatSymPDBandFact 197

FloatSymPDFact 197

FloatSymPDTriDiagFact 197

FloatTriDiagFact 197

FloatTriDiagMatrix 164

FloatUpperTriMatrix 161

FloatVector 29

FloatWavelet 111

Frobenius matrix norm 193

Frobenius norm 64

function encapsulation 121

function evaluation 122, 238

function interpolation 137

functions of one variable 121

FZero 314

fzero 314

G

G statistic 132

GAC 3

gamma distribution 73

gamma function 155, 65

gaussian distribution 80

Gauss-Kronrod integration 124, 128

GaussKronrodIntegrator 125, 129, 130, 317

gcAllowVeryLargeObjects 10

GDCLS 195

general sparse matrix 185, 189

general sparse matrix factorizations 194

generalized multivariable functions 305

generalized one variable functions 297

generating random numbers 89

generic columns 4

generic functions 46, 71, 182, 10

geometric distribution 75

geometric mean 57

GeometricDistribution 67, 75

global assembly cache 3

global minimum 253

golden section search 242

GoldenMinimizer 242

goodness of fit 285, 305, 131, 215

GoodnessOfFit 215

GoodnessOfFitParameter 215, 217

Gradient Descent - Constrained Least Squares (GDCLS) 195

grand mean 140, 144, 148

group means 140, 148

grouping by factors 30, 36

groupings 30, 36

H

half bandwidth 165, 166, 169, 173

harmonic mean 57

harmonic number 155

Hermitian banded matrices 166

Hermitian matrices 162

high-pass decimation filter 112

high-pass reconstruction filter 112

Histogram 117

histograms

creating 117

displaying 120

stem-leaf diagrams 120

hold out method 209

Hosmer Lemeshow statistic 132

hypergeometric functions 155

hypothesis tests 91

creating 92

properties 91, 93

HypothesisType 91

I

IBoundedNonlinearLeastSqMinimizer 287, 290, 291

IDFColumn 4

IDifferentiator 131

IDoubleLeastSqWeightingFunction 215

IIntegrator 125, 126, 317

ILogisticRegressionCalc 127

implicit conversion 172

matrices 55

vectors 34

IMultiVariableDMinimizer 247, 249

IMultiVariableMinimizer 247, 256

incomplete beta 66

incomplete beta function 155

incomplete gamma 65

incomplete gamma integral 155

independent streams 96

indexers 174, 187, 192

indexing objects 25

IndexOutOfRangeException 233

infinity-norm 63, 179

inner product 42

inner product of matrices 178

INonlinearLeastSqMinimizer 287, 291, 296

InputVariableCorrelator 85

integer columns 4

integer nonlinear programming 262, 271

integration 124

integration of polynomials 136

Intel Math Kernel Library 2

intercept parameter 83, 84, 113

intercept parameters 115

InteriorPointQPSolver 277, 278

internally studentized residuals 116

interpolation 137

interquartile range 59, 220

IntRandomBernoulliDistribution 93

IntRandomBinomialDistribution 93

IntRandomGeometricDistribution 93

IntRandomHypergeometricDistribution 93

IntRandomNegativeBinomialDistribution 93

IntRandomPoissonDistribution 93

IntRandomPoissonVaryingMeanDistribution 94

IntRandomUniformBitsDistribution 94

IntRandomUniformDistribution 94

InvalidArgumentException 233

InvalidBinBdryException 233

inverse 65, 78, 202

inverse CDF 68

inverse cumulative distribution function 68

inverse Fisher transformation 61

IOneVariableDMinimizer 241, 244

IOneVariableDRootFinder 313, 315

IOneVariableMinimizer 241, 242

IOneVariableRootFinder 313

IRandomNumberDistribution 87

IRandomVariableMoments 68

IRegressionCalculation 114

ISerializable interface 47, 223

Iterative Power Method 207

iteratively reweighted least squares 212

J

jackknife estimates 210

jackknifing 210

Johnson system of distributions 75

JohnsonDistribution 75

K

k-fold cross validation 210

KMeansClustering 189, 190

Kolmogorov-Smirnov test 159, 161

Kruskal-Wallis rank sum test 159, 163

KruskalWallisTest 159, 163

kurtosis 60, 68

L

large objects 9

leapfrog method 96

LeapfrogRandomStreams 96

least squares

Cholesky 205

QR decomposition 206

solving 208

SVD 206

least squares minimization 114

least squares solutions 83, 205

left singular vectors 222

Levenberg-Marquardt method 235, 287, 295

LevenbergMarquardtMinimizer 291, 295

libiomp.dll 6

likelihood function 135

linear bound constraints 293

linear constraints 261, 262

linear interpolation 138

linear programming 261

linear regressions 113

creating 113

modifying 118

predictions 117, 134

results 115

significance of parameters 123

significance of the overall model 125

linear spline interpolation 138

LinearAnnealingSchedule 254

LinearConstraint 267

LinearContraint 262

LinearProgrammingProblem 261

LinearRegression 113

LinearRegressionAnova 125

LinearRegressionParameter 123, 124, 150

local minima 253

log binomial 65

log factorial 65

log file 5

log gamma 65

logical functions 53, 62

logistic function 301

logistic regression 127

LogisticDistribution 67, 77, 78

LogisticRegression 127

LogisticRegressionFitAnalysis 131

log-normal distribution 78

LognormalDistribution 67, 78

lower bandwidth 162, 168, 173

lower triangular matrices 159

lower triangular matrix 75, 77

low-pass decimation filter 112

low-pass reconstruction filter 112

LP problems 261

LU factorization 75, 121, 141, 153, 197

M

manipulating functions 238

matrices

arithmetic operations 59, 176, 187, 193

clearing 58

converting to data frames 14

copying 55

creating from ADO.NET objects 54, 230

creating from data frames 44

creating from numeric values 50

creating from strings 52

equality testing 59, 176, 187, 193

functions 63, 178, 188, 193

implicit conversion 55

modifying values 57, 174, 187, 192

properties 56

resizing 58, 175

matrix

decompositions 217

factorization 185, 194, 197

functions 167

norms 179

properties 173

shape parameters 168

transposition 178, 188, 193

types 159

matrix classes 49

matrix indexers 49

matrix norm 63

matrix transposition 63

matrix views 56

MatrixFunctions 167

MatrixNotSquareException 233

maximum (Chebychev) distance 181

maximum iterations 241

mean 43, 68, 56, 68

mean deviation 59

mean of the ranges method 219

median 43, 68, 56

median deviation from mean 59

Mersenne Twister algorithm 88

Microsoft Solver Foundation 3

min/max functions 54

vectors 43, 68

minimization 241, 247

MinimizerBase 241, 247

MismatchedSizeException 233

missing values 8, 51

MixedIntegerLinearProgrammingProblem 261, 262

MixedIntegerNonlinearProgrammingProblem 268

MKL 2

mode 56

Modified Bessel functions 153

moving average 142

MovingWindowFilter 141

multiple linear regression 113

multiplicative update rule 195

MultiVariableFunction 237, 247, 249, 256

MultiVariableFunctionFitter 305

multivariate functions 237

multivariate techniques 171

N

Nagelkerke pseudo R-squared statistic 135

namespaces 2

NaN values 51

natural cubic spline 138

negative binomial distribution 79

NegativeBinomialDistribution 68, 79

Newton-Cotes formulas 126

NewtonRalphsonRootFinder 315

Newton-Raphson Method 315

NewtonRaphsonParameterCalc 127

NiederreiterQuasiRandomGenerator 98

NIPALS 208

NMath.dll 2

NMathConfiguration 4

NMathException 233

NMathFormatException 234

NMathKernelx64.dll 2

NMathKernelx86.dll 2

NMF 193

NMFClustering 196, 200, 201

Nonlinear Iterative PArtial Least Squares (NIPALS) 208

nonlinear least squares 287

Nonlinear Programming (NLP) 265, 268

NonlinearConstraint 267

NonlinearProgrammingProblem 268

nonnegative least squares 83, 84

nonnegative least squares solutions 86

nonnegative matrix factorization (NMF) 193, 196

Non-parametric tests 159

norm of a complex number 19

normal distribution 80

NormalDistribution 68, 80

norms 179

Not-A-Number values 51

numeric columns 4

numerical integration 124

numerical rank 209

O

objective function 261

odds ratio 135

one-norm 63

OneSampleAndersonDarlingTest 159

OneSampleKSTest 159

OneSampleTTest 98

OneSampleZTest 96

OneVariableFunction 121, 237

OneVariableFunctionFitter 297

one-way ANOVA 137

accessing the ANOVA table 139, 166

one-way RANOVA 141

accessing the RANOVA table 143

OneWayAnova 137

OneWayAnovaTable 139, 165

OneWayRanova 141

OneWayRanovaTable 143

operators 176, 187, 193

optimization 241, 247

order 168, 173

ordinary differential equations 321

outer product 42

P

parabolic interpolation 242

Partial Least Squares 205

Partial least squares Discriminant Analysis 211

parts per million defective 221

PDF 68

peak finding 141, 147

PeakFinderRuleBased 141, 149

PeakFinderSavitzkyGolay 141, 147

Pearson chi-square statistic 132

Pearson correlation 61

Pearson's chi-square test 108

PearsonsChiSquareTest 108

percent defective 221

percentiles 54

permutation matrices 217, 219

permutation matrix 75, 77

permuting columns 8

permuting data frames 33

phase 182

pivot indices 77

pivoting 217, 218

PLS-DA 211

pointers to underlying data 23, 24

poisson distribution 80

PoissonDistribution 68, 80

polar coordinates 16, 31

polylogarithm 155

Polynomial 133, 237

PolynomialLeastSquares 285, 286

polynomials 133

Position enumeration 26

positive definite matrices 195, 198

Powell's Method 248

PowellMinimizer 248

power distance 181

Pp 219, 220

Ppk 219, 220

predicted values 85

predictions 117, 134

predictor matrix 118

PrimalSimplexSolver 261, 263

PrimalSimplexSolverParam 263

principal component analysis 171

probability density function 68

probability distributions 67

ProbabilityDistribution 68

process capability 219, 220

process capability index 220

process performance 220

ProcessCapability 219

ProcessPerformance 220

product

features 1

overview 1

product of matrices 64

pseudo R-squared 135

pseudoinverse 66

Q

QR decomposition 217, 114

classes 217

least squares 206

servers 218

QRRegressionCalculation 114

quartiles 54

quasi-Newton method 249

quasirandom numbers 98

R

R2 285, 305, 215

RandGenBeta 87

RandGenBinomial 87

RandGenExponential 87

RandGenGamma 87

RandGenGeometric 87

RandGenJohnson 88

RandGenLogNormal 88

RandGenMTwist 88

RandGenNormal 88

RandGenPareto 88

RandGenPoisson 88

RandGenUniform 87

RandGenWeibull 88

random number generators 87, 99, 111

scalar 87

vectorized 92

random samples 30

random seeds 91

RandomNumberGenerator 87, 90

RandomNumbers 95

RandomNumberStream 87, 94

Range 25

ranges 25, 35

rank 209

ranks 54

ReducedVarianceInputCorrelator 85

regression calculators 114

regression matrix 118

regularization 195

reordering columns 8

reordering data frames 33

replicating a matrix 52

RepMat() functions 52

residual standard error 285, 305, 215

residual sum of squares 85

residual vector 205

residuals 85, 287

resizing

matrices 58

vectors 37

resizing matrices 175

reversing a vector 46

Ridders' Method 314

RiddersDifferentiator 131

RiddersRootFinder 314

Riemann zeta function 155

right singular vectors 222

RMS 58

Romberg integration 124

RombergIntegrator 125, 126, 317

root mean square 58

RootFinderBase 313

root-finding 313

rounding functions 41, 66

row keys 3, 18, 21

modifying 20

Rule-based peak finding 149

Runge-Kutta method 321

RungeKutta45OdeSolver 324

RungeKutta5OdeSolver 324

RungeKuttaSolver 321, 322

S

sampling 30

Savitzky-Golay 142

SavitzkyGolayFilter 141, 145

secant method 313

SecantRootFinder 313

seeds for random number generators 91

serialization 47, 223

ShapiroWilkTest 159

signal processing 141

SIMPLS 208

Simpson's rule 126

simulated annealing 253

sine function 301

singular value decomposition 217, 222, 114

classes 222

servers 222

singular values 222

singular vectors 222

SingularMatrixException 234

skewness 59, 68

Slice 25

slices 25, 35

smooth splines 139

SmoothCubicSpline 139

SOAP serialization 47, 224

SobolQuasiRandomGenerator 98

solutions of linear systems 75, 121, 141, 153, 185, 194, 197

solver parameters 263

solving for right-hand sides 77, 200

sorting functions 45, 70

SortingType 32, 55, 62

sparse vector 185

SparseMatrixBuilder 191

sparsity 195

Spearman's rank correlation coefficient 159

Spearman's rho 61, 159

special functions 2, 153, 65

spline interpolation 138

square root 45, 70

squared Euclidean distance 181

SSE 58

standard deviation 58

standardized residuals 116

statistical functions 49

data types 49

missing values 51

statistical process control 219

StatsFunctions 49–??

StatsSettings 9

stiff differential equations 321

stiff equations 327

Stochastic Hill Climbing algorithm 272

StochasticHillClimbingSolver 272

Straightforward IMplementation of PLS (SIMPLS) 208

string columns 4

structured sparse matrices 159

Student's t distribution 81

studentized residuals 116

subject means 144

Subset 25

subsets 25

accessing elements 26

arithmetic operations 27

creating 25

logical operations 27

properties 26

sum of squared errors 58

sum of squares 43, 68

sums 53

surface fitting 287, 305

SVD 222

convergence 208

least squares 206

SVDRegressionCalculation 114

symmetric banded matrices 165

symmetric matrices 161

T

t test 98, 100, 103

tabulated functions 137

TabulatedFunction 237

tabulation 40

Taguchi capability index 220

TDistribution 68, 81

tiling a matrix 52

time series 61

transcendental functions 44, 69, 181

transpose product 64, 179

transposing matrices 63, 178, 188, 193

trapezoidal rule 126

treatment means 144

triangular distribution 82

triangular matrices 159, 160

TriangularDistribution 68, 82

tridiagonal matrices 164

trigonometric functions 20, 44, 69, 181

trimmed mean 57

trimming data 57

Trust-Region method 235, 287, 290, 291

TrustRegionMinimizer 290, 291

TrustRegionParameterCalc 128

TwoSampleFTest 106

TwoSampleKSTest 159, 161

TwoSamplePairedTTest 100

TwoSampleUnpairedTTest 103

TwoSampleUnpairedUnequalTTest 103

TwoVariableIntegrator 317, 318

two-way ANOVA 145

accessing the ANOVA table 146

two-way RANOVA 156

TwoWayAnova 145

TwoWayAnovaTable 146

TwoWayAnovaTypeI 154

TwoWayAnovaTypeII 154

TwoWayAnovaTypeIII 154

TwoWayAnovaUnbalanced 154

TwoWayRanova 156

TwoWayRanovaTable 157

TwoWayRanovaTwo 156

TwoWayRanovaTwoTable 158

typographic conventions 12

U

Unbalanced two-way ANOVA 154

unbalanced two-way ANOVA 154

uniform distribution 83

UniformDistribution 68, 83

upper bandwidth 162, 168, 173

upper triangular matrices 160

upper triangular matrix 75, 77

V

variable bounds 261

variable metric method 249

VariableMetricMinimizer 249

VariableOrderOdeSolver 321, 327

variance 43, 68, 59, 68

variance inflation factor 116

varimax rotation 174

vector classes 29

vector indexers 29

vector views 35, 61

vectors

arithmetic operations 39

clearing 37

copying 34

creating from ADO.NET objects 33, 230

creating from numeric values 30

creating from strings 31

equality testing 39

functions 41

implicit conversion 34

modifying values 37

properties 36

resizing 37

Von Neumann ratio 61

W

wavelet 111

wavelet threshold calculation 115

wavelet thresholding 115

Wavelet.Wavelets 111

web applications 8

web projects 8

Weibull distribution 84

WeibullDistribution 68, 84

weighted least squares 209

weighted mean 57

weighting functions 211, 215

Wilcoxon signed-rank test 159, 168

WilcoxonSignedRankTest 159, 168

X

XML serialization 226

Z

Z Bench 221

Z bench 219, 221

z test 96

ZBench 221

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