1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
|
Unit Routines Description
-----------------------------------------------------------------------
utypes SetErrCode Sets error code
* DefaultVal Sets error code and default function value
* MathErr Returns the error code
* SetAutoInit Sets the auto-initialization of arrays
* DimVector Allocates a real vector
* DimIntVector Allocates an integer vector
* DimCompVector Allocates a complex vector
* DimBoolVector Allocates a boolean vector
* DimStrVector Allocates a string vector
* DimMatrix Allocates a real matrix
* DimIntMatrix Allocates an integer matrix
* DimCompMatrix Allocates a complex matrix
* DimBoolMatrix Allocates a boolean matrix
* DimStrMatrix Allocates a string matrix
* DelVector Deallocates a real vector
* DelIntVector Deallocates an integer vector
* DelCompVector Deallocates a complex vector
* DelBoolVector Deallocates a boolean vector
* DelStrVector Deallocates a string vector
* DelMatrix Deallocates a real matrix
* DelIntMatrix Deallocates an integer matrix
* DelCompMatrix Deallocates a complex matrix
* DelBoolMatrix Deallocates a boolean matrix
* DelStrMatrix Deallocates a string matrix
uminmax FMin Minimum of 2 reals
* FMax Maximum of 2 reals
* IMin Minimum of 2 integers
* IMax Maximum of 2 integers
* Sgn Sign, Sgn(0) = 1
* Sgn0 Sign, Sgn(0) = 0
* DSgn DSgn(A, B) = Sgn(B) * |A|
* FSwap Exchanges 2 reals
* ISwap Exchanges 2 integers
uround RoundN Rounds a number to N decimal places
* Ceil Ceiling function
* Floor Floor function
umath Expo Exponential (with bound checking)
* Exp2 Exponential, base 2
* Exp10 Exponential, base 10
* Log Natural log (with bound checking)
* Log2 Log, base 2
* Log10 Log, base 10
* LogA Log, base A
* IntPower Power (integer exponent)
* Power Power (real exponent)
utrigo Pythag Sqrt(X^2 + Y^2)
* FixAngle Set argument in -Pi..Pi
* Tan Tangent
* ArcSin Arc sinus
* ArcCos Arc cosinus
* ArcTan2 Angle (Ox, OM) with M(X,Y)
uhyper Sinh Hyperbolic sine
* Cosh Hyperbolic cosine
* Tanh Hyperbolic tangent
* ArcSinh Inverse hyperbolic sine
* ArcCosh Inverse hyperbolic cosine
* ArcTanh Inverse hyperbolic tangent
* SinhCosh Sinh and Cosh
upolev PolEvl Polynomial evaluation (coeff. of x^n <> 1)
* P1Evl Polynomial evaluation (coeff. of x^n = 1)
ugamma Gamma Gamma function
* LnGamma Logarithm of Gamma function
* SgnGamma Sign of Gamma function
* Stirling Stirling's formula for Gamma
* StirLog Stirling's formula for LnGamma
udigamma DiGamma DiGamma function
* TriGamma TriGamma function
uigamma IGamma Incomplete Gamma function
* JGamma Complement of incomplete Gamma function
* Erf Error function
* Erfc Complement of error function
ubeta Beta Beta function
uibeta IBeta Incomplete Beta function
ulambert LambertW Lambert's W-function
ufact Fact Factorial
ubinom Binomial Binomial coefficient
* PBinom Probability of binomial distribution
upoidist PPoisson Probability of Poisson distribution
uexpdist DExpo Density of exponential distribution
* FExpo Cumulative prob. of exponential dist.
unormal DNorm Density of standard normal distribution
ugamdist DBeta Density of Beta distribution
* DGamma Density of Gamma distribution
* DKhi2 Density of Khi-2 distribution
* DStudent Density of Student's distribution
* DSnedecor Density of Fisher-Snedecor distribution
uibtdist FBeta Cumulative prob. of Beta distribution
* FBinom Cumulative prob. of Binomial distribution
* FStudent Cumulative prob. of Student's distribution
* PStudent Prob(|t| > X) for Student's distribution
* FSnedecor Cumulative prob. of Fisher-Snedecor distribution
* PSnedecor Prob(F > X) for Fisher-Snedecor distribution
uigmdist FGamma Cumulative prob. of Gamma distribution
* FPoisson Cumulative prob. of Poisson distribution
* FNorm Cumulative prob. of standard normal distribution
* PNorm Prob(|U| > X) for standard normal distribution
* FKhi2 Cumulative prob. of Khi-2 distribution
* PKhi2 Prob(Khi2 > X) for Khi-2 distribution
uinvnorm InvNorm Inverse of normal distribution
uinvgam InvGamma Inverse of incomplete Gamma function
* InvKhi2 Inverse of khi-2 distribution
uinvbeta InvBeta Inverse of incomplete Beta function
* InvStudent Inverse of Student's t-distribution
* InvSnedecor Inverse of Snedecor's F-distribution
ucompvec CompVec Comparison of two vectors
ugausjor GaussJordan Linear equation system (Gauss-Jordan method)
ulineq LinEq Linear equation system (Gauss-Jordan method)
ucholesk Cholesky Cholesky factorization
ulu LU_Decomp LU decomposition
* LU_Solve Solves a system of equations after LU decomposition
uqr QR_Decomp QR decomposition
* QR_Solve Solves a system of equations after QR decomposition
usvd SV_Decomp Singular value decomposition
* SV_Solve Solves a system of equations after SV decomposition
* SV_SetZero Sets the lowest singular values to zero
* SV_Approx Approximates a matrix from its SV decomposition
ubalance Balance Balances a matrix and tries to isolate eigenvalues
ubalbak BalBak Back transformation of eigenvectors
uelmhes ElmHes Reduction of a square matrix to upper Hessenberg form
ueltran Eltran Save transformations used by ElmHes
uhqr Hqr Eigenvalues of a real upper Hessenberg matrix by the QR method
uhqr2 Hqr2 Eigenvalues and eigenvectors of a real upper Hessenberg matrix
ueigval EigenVals Eigenvalues of a general square matrix
ueigvec EigenVect Eigenvalues and eigenvectors of a general square matrix
ujacobi Jacobi Eigenvalues and eigenvectors of a symmetric matrix
uminbrak MinBrack Brackets a minimum of a function
ugoldsrc GoldSearch Minimization of a function of 1 variable (Golden Search method)
ulinmin LinMin Minimization of a function of several variables along a line
unewton Newton Minimization of a function of several var. (Newton's method)
* SaveNewton Save Newton iterations in a file
umarq Marquardt Minimization of a function of several var. (Marquardt's method)
* SaveMarquardt Save Marquardt iterations in a file
ubfgs BFGS Minimization of a function of several var. (BFGS method)
* SaveBFGS Save BFGS iterations in a file
usimplex Simplex Minimization of a function of several var. (simplex method)
* SaveSimplex Save simplex iterations in a file
ulinminq LinMinEq Minimization of a sum of squared functions along a line
ubisect RootBrack Brackets solution of equation
* Bisect Nonlinear equation (bisection method)
unewteq NewtEq Nonlinear equation (Newton-Raphson method)
usecant Secant Nonlinear equation (secant method)
unewteqs NewtEqs Nonlinear equation system (Newton-Raphson method)
ubroyden Broyden Nonlinear equation system (Broyden's method)
upolynom Poly Evaluates a polynomial
* RFrac Evaluates a rational fraction
urtpol1 RootPol1 Root of linear equation
urtpol2 RootPol2 Roots of quadratic equation
urtpol3 RootPol3 Roots of cubic equation
urtpol4 RootPol4 Roots of quartic equation
urootpol RootPol Roots of polynomial from companion matrix
upolutil SetRealRoots Set the imaginary part of a root to zero
* SortRoots Sorts the roots of a polynomial
utrapint TrapInt Integration by trapezoidal rule
ugausleg GausLeg Gauss-Legendre integration
* GausLeg0 Gauss-Legendre integration (lower bound=0)
* Convol Convolution product
urkf RKF45 Integration of a system of differential equations
ufft FFT Fast Fourier Transform
* IFFT Inverse Fast Fourier Transform
* FFT_Integer Fast Fourier Transform for integer data
* FFT_Integer_Cleanup Clear memory after a call to FFT_Integer
* CalcFrequency Direct computation of Fourier Transform
urandom SetRNG Select random number generator
* InitGen Initialize random number generator
* IRanGen 32-bit random integer in [-2^31 .. 2^31 - 1]
* IRanGen31 31-bit random integer in [0 .. 2^31 - 1]
* RanGen1 32-bit random real in [0,1]
* RanGen2 32-bit random real in [0,1)
* RanGen3 32-bit random real in (0,1)
* RanGen53 53-bit random real in [0,1)
uranmwc InitMWC Initialize Multiply-With-Carry generator
* IRanMWC 32-bit random integer from MWC generator
uranmt InitMT Initialize Mersenne Twister generator with a seed
* InitMTbyArray Initialize MT generator with an array
* IRanMT 32-bit random integer from MT generator
uranuvag InitUVAG Initialize UVAG generator with a seed
* InitUVAGbyString Initialize UVAG generator with a string
* IRanUVAG 32-bit random integer from UVAG generator
urangaus RanGaussStd Random number from standard normal distribution
* RanGauss Random number from normal distribution
uranmult RanMult Random vector from multinormal distrib. (correlated)
* RanMultIndep Random vector from multinormal distrib. (uncorrelated)
umcmc InitMHParams Initialize Metropolis-Hastings parameters
* GetMHParams Returns Metropolis-Hastings parameters
* Hastings Simulation of a p.d.f. by Metropolis-Hastings
usimann InitSAParams Initialize Simulated Annealing parameters
* SA_CreateLogFile Initialize log file for Simulated Annealing
* SimAnn Minimization of a function of several var. by Simulated Annealing
ugenalg InitGAParams Initialize Genetic Algorithm parameters
* GA_CreateLogFile Initialize log file for Genetic Algorithm
* GenAlg Minimization of a function of several var. by Genetic Algorithm
umeansd Mean Sample mean
* StDev Standard deviation estimated from sample
* StDevP Standard deviation of population
ucorrel Correl Correlation coefficient
umedian Median Sample median
uskew Skewness Sample skewness
* Kurtosis Sample kurtosis
uqsort QSort Quick sort (ascending order)
* DQSort Quick sort (descending order)
uinterv Interval Determines an interval for a set of values
ustudind StudIndep Student t-test for independent samples
ustdpair StudPaired Student t-test for paired samples
uanova1 AnOVa1 One-way analysis of variance
uanova2 AnOVa2 Two-way analysis of variance
usnedeco Snedecor Comparison of two variances
ubartlet Bartlett Comparison of several variances
ukhi2 Khi2_Conform Khi-2 test for conformity
* Khi2_Indep Khi-2 test for independence
uwoolf Woolf_Conform Woolf's test for conformity
* Woolf_Indep Woolf's test for independence
unonpar Mann_Whitney Mann-Whitney test
* Wilcoxon Wilcoxon test
* Kruskal_Wallis Kruskal-Wallis test
udistrib DimStatClassVector Allocates an array of statistical classes
* DelStatClassVector Deallocates an array of statistical classes
* Distrib Distributes an array into statistical classes
ulinfit LinFit Linear regression
* WLinFit Weighted linear regression
upolfit PolFit Polynomial regression
* WPolFit Weighted polynomial regression
umulfit MulFit Multiple regression (Gauss-Jordan method)
* WMulFit Weighted multiple regression (Gauss-Jordan method)
usvdfit SVDFit Multiple regression (SVD method)
* WSVDFit Weighted multiple regression (SVD method)
unlfit SetOptAlgo Selects optimization algorithm for nonlinear regression
* SetMaxParam Sets the maximal number of regression parameters
* SetParamBounds Sets the bounds on a regression parameter
* SetMCFile Set file for saving MCMC simulations
* NLFit Nonlinear regression
* WNLFit Weighted nonlinear regression
* SimFit Simulation of unweighted nonlinear regression by MCMC
* WSimFit Simulation of weighted nonlinear regression by MCMC
uregtest RegTest Test of unweighted regression
* WRegTest Test of weighted regression
upca VecMean Computes mean vector }
* VecSD Computes vector of standard deviations }
* MatVarCov Computes variance-covariance matrix }
* MatCorrel Computes correlation matrix }
* PCA Principal component analysis of correlation matrix }
* ScaleVar Scales a set of variables }
* PrinFac Computes principal factors }
ustrings LTrim Remove leading blanks
* RTrim Remove trailing blanks
* Trim Remove leading and trailing blanks
* StrChar Generate string by repeating a character
* RFill Complete string with trailing blanks
* LFill Complete string with leading blanks
* CFill Center string
* Replace Replace a character
* Extract Extract field from string
* Parse Parse string into several fields
* SetFormat Set numeric format
* FloatStr Convert real number to string
* IntStr Convert integer to string
* CompStr Convert complex number to string
uplot InitGraphics Initializes the graphic
* SetWindow Sets the graphic window
* AutoScale Automatic scale determination
* SetOxScale Sets the scale on the Ox axis
* SetOyScale Sets the scale on the Oy axis
* SetGraphTitle Sets the graph title
* SetOxTitle Sets the title for the Ox axis
* SetOyTitle Sets the title for the Oy axis
* SetTitleFont Sets the font for the main graph title
* SetOxFont Sets the font for the Ox axis
* SetOyFont Sets the font for the Oy axis
* SetLgdFont Sets the font for the legends
* PlotOxAxis Plots the Ox axis
* PlotOyAxis Plots the Oy axis
* WriteGraphTitle Writes title of graph
* PlotGrid Plots a grid on the graph
* SetClipping Limits the graphic to the current viewport
* SetMaxCurv Sets maximum number of curves
* SetPointParam Sets point parameters
* SetLineParam Sets line parameters
* SetCurvLegend Sets curve legend
* SetCurvStep Sets curve step
* PlotPoint Plots a point
* PlotCurve Plots a curve
* PlotCurveWithErrorBars Plots a curve with error bars
* PlotFunc Plots a function
* WriteLegend Writes the legends for the plotted curves
* ConRec Contour plot
* Xpixel Converts user abscissa X to screen coordinate
* Ypixel Converts user ordinate Y to screen coordinate
* Xuser Converts screen coordinate X to user abscissa
* Yuser Converts screen coordinate Y to user ordinate
* LeaveGraphics Quits the graphic mode
|