ls-demo.lisp

   1
   2 (load "init.lisp")
   3
   4 ;;; checking exports.
   5 ;;; This is generally not how I expect it to be used.
   6
   7 (in-package :cl-user)
   8 (lisp-stat:binomial-quant 0.95 3 0.4) ;;; 3
   9 (lisp-stat:binomial-quant 0 3 0.4) ;;; 0
  10 (lisp-stat:normal-rand 20) ;;; DOESN'T RETURN
  11
  12
  13 ;;; This is how I expect it to be used, either with work in ls-user,
  14 ;;; or a cloned package similar to ls-user.
  15
  16 (in-package :ls-user)
  17
  18 ;; Probability
  19
  20 (binomial-quant 0.95 3 0.4) ; 3
  21 (binomial-quant 0 3 0.4) ; 0
  22 (normal-rand 20)
  23
  24 ;; Matrix algebra.
  25
  26
  27 (chol-decomp  #2A((2 3 4) (1 2 4) (2 4 5)))
  28 ;; (#2A((1.7888543819998317 0.0 0.0)
  29 ;;      (1.6770509831248424 0.11180339887498929 0.0)
  30 ;;      (2.23606797749979 2.23606797749979 3.332000937312528e-8))
  31 ;;  5.000000000000003)
  32
  33 (lu-decomp  #2A((2 3 4) (1 2 4) (2 4 5)))
  34 ;; (#2A((2.0 3.0 4.0) (1.0 1.0 1.0) (0.5 0.5 1.5)) #(0 2 2) -1.0 NIL)
  35
  36 (lu-solve
  37  (lu-decomp #2A((2 3 4) (1 2 4) (2 4 5)))
  38  #(2 3 4))
  39 ;; #(-2.333333333333333 1.3333333333333335 0.6666666666666666)
  40
  41 (inverse #2A((2 3 4) (1 2 4) (2 4 5)))
  42 ;; #2A((2.0 -0.33333333333333326 -1.3333333333333335)
  43 ;;     (-1.0 -0.6666666666666666 1.3333333333333333)
  44 ;;     (0.0 0.6666666666666666 -0.3333333333333333))
  45
  46 (sv-decomp  #2A((2 3 4) (1 2 4) (2 4 5)))
  47 ;; (#2A((-0.5536537653489974 0.34181191712789266 -0.7593629708013371)
  48 ;;      (-0.4653437312661058 -0.8832095891230851 -0.05827549615722014)
  49 ;;      (-0.6905959164998124 0.3211003503429828 0.6480523475178517))
  50 ;;  #(9.699290438141343 0.8971681569301373 0.3447525123483081)
  51 ;;  #2A((-0.30454218417339873 0.49334669582252344 -0.8147779426198863)
  52 ;;      (-0.5520024849987308 0.6057035911404464 0.5730762743603965)
  53 ;;      (-0.7762392122368734 -0.6242853493399995 -0.08786630745236332))
  54 ;;  T)
  55
  56 (qr-decomp  #2A((2 3 4) (1 2 4) (2 4 5)))
  57 ;; (#2A((-0.6666666666666665 0.7453559924999298 5.551115123125783e-17)
  58 ;;      (-0.3333333333333333 -0.2981423969999719 -0.894427190999916)
  59 ;;      (-0.6666666666666666 -0.5962847939999439 0.44721359549995787))
  60 ;;  #2A((-3.0 -5.333333333333334 -7.333333333333332)
  61 ;;      (0.0 -0.7453559924999292 -1.1925695879998877)
  62 ;;      (0.0 0.0 -1.3416407864998738)))
  63
  64 (rcondest #2A((2 3 4) (1 2 4) (2 4 5)))
  65 ;; 6.8157451e7
  66
  67 (eigen #2A((2 3 4) (1 2 4) (2 4 5)))
  68 ;; (#(10.656854249492381 -0.6568542494923802 -0.9999999999999996)
  69 ;;  (#(0.4999999999999998 0.4999999999999997 0.7071067811865475)
  70 ;;   #(-0.49999999999999856 -0.5000000000000011 0.7071067811865474)
  71 ;;   #(0.7071067811865483 -0.7071067811865466 -1.2560739669470215e-15))
  72 ;;  NIL)
  73
  74 (spline #(1.0 1.2 1.3 1.8 2.1 2.5)
  75         #(1.2 2.0 2.1 2.0 1.1 2.8) :xvals 6)
  76 ;; ((1.0 1.3 1.6 1.9 2.2 2.5)
  77 ;;  (1.2 2.1 2.2750696543866313 1.6465231041904045 1.2186576148879609 2.8))
  78
  79 ;;; using KERNEL-SMOOTH-FRONT, not KERNEL-SMOOTH-CPORT
  80 (kernel-smooth #(1.0 1.2 1.3 1.8 2.1 2.5)
  81                #(1.2 2.0 2.1 2.0 1.1 2.8) :xvals 5)
  82 ;; ((1.0 1.375 1.75 2.125 2.5)
  83 ;;  (1.6603277642110226 1.9471748095239771 1.7938127405752287
  84 ;;   1.5871511322219498 2.518194783156392))
  85
  86 (kernel-dens #(1.0 1.2 2.5 2.1 1.8 1.2) :xvals 5)
  87 ;; ((1.0 1.375 1.75 2.125 2.5)
  88 ;;  (0.7224150453621405 0.5820045548233707 0.38216411702854214
  89 ;;   0.4829822708587095 0.3485939156929503))
  90
  91 (fft #(1.0 1.2 2.5 2.1 1.8))
  92 ;; #(#C(1.0 0.0) #C(1.2 0.0) #C(2.5 0.0) #C(2.1 0.0) #C(1.8 0.0))
  93
  94 (lowess #(1.0 1.2 2.5 2.1 1.8 1.2)  #(1.2 2.0 2.1 2.0 1.1 2.8))
  95 ;; (#(1.0 1.2 1.2 1.8 2.1 2.5))
  96
  97
  98
  99 ;;; Log-gamma function
 100
 101 (log-gamma 3.4) ;;1.0923280596789584
 102
 103 ;;; Probability functions
 104
 105 ;;; looking at these a bit more, perhaps a more CLOSy style is needed, i.e.
 106 ;;; (quantile :list-or-cons loc :type type (one of 'empirical 'normal 'cauchy, etc...))
 107 ;;; similar for the cdf, density, and rand.
 108 ;;; Probably worth figuring out how to add a new distribution
 109 ;;; efficiently, i.e. by keeping some kind of list.
 110
 111 ;;; Normal distribution
 112
 113 (normal-quant 0.95) ;;1.6448536279366268
 114 (normal-cdf 1.3) ;;0.9031995154143897
 115 (normal-dens 1.3) ;;0.17136859204780736
 116 (normal-rand 2) ;;(-0.40502015f0 -0.8091404f0)
 117
 118 (bivnorm-cdf 0.2 0.4 0.6) ;;0.4736873734160288
 119
 120 ;;; Cauchy distribution
 121
 122 (cauchy-quant 0.95) ;;6.313751514675031
 123 (cauchy-cdf 1.3) ;;0.7912855998398473
 124 (cauchy-dens 1.3) ;;0.1183308127104695
 125 (cauchy-rand 2) ;;(-1.06224644160405 -0.4524695943939537)
 126
 127 ;;; Gamma distribution
 128
 129 (gamma-quant 0.95 4.3) ;;8.178692439291645
 130 (gamma-cdf 1.3 4.3) ;;0.028895150986674906
 131 (gamma-dens 1.3 4.3) ;;0.0731517686447374
 132 (gamma-rand 2 4.3) ;;(2.454918912880936 4.081365384357454)
 133
 134 ;;; Chi-square distribution
 135
 136 (chisq-quant 0.95 3) ;;7.814727903379012
 137 (chisq-cdf 1 5) ;;0.03743422675631789
 138 (chisq-dens 1 5) ;;0.08065690818083521
 139 (chisq-rand 2 4) ;;(1.968535826180572 2.9988646156942997)
 140
 141 ;;; Beta distribution
 142
 143 (beta-quant 0.95 3 2) ;;0.9023885371149876
 144 (beta-cdf 0.4 2 2.4) ;;0.4247997418541529
 145 (beta-dens 0.4 2 2.4) ;;1.5964741858913518
 146 (beta-rand 2 2 2.4) ;;(0.8014897077282279 0.6516371997922659)
 147
 148 ;;; t distribution
 149
 150 (t-quant 0.95 3) ;;2.35336343484194
 151 (t-cdf 1 2.3) ;;0.794733624298342
 152 (t-dens 1 2.3) ;;0.1978163816318102
 153 (t-rand 2 2.3) ;;(-0.34303672776089306 -1.142505872436518)
 154
 155 ;;; F distribution
 156
 157 (f-quant 0.95 3 5) ;;5.409451318117459
 158 (f-cdf 1 3.2 5.4) ;;0.5347130905510765
 159 (f-dens 1 3.2 5.4) ;;0.37551128864591415
 160 (f-rand 2 3 2) ;;(0.7939093442091963 0.07442694152491144)
 161
 162 ;;; Poisson distribution
 163
 164 (poisson-quant 0.95 3.2) ;;6
 165 (poisson-cdf 1 3.2) ;;0.17120125672252395
 166 (poisson-pmf 1 3.2) ;;0.13043905274097067
 167 (poisson-rand 5 3.2) ;;(2 1 2 0 3)
 168
 169 ;;; Binomial distribution
 170
 171 (binomial-quant 0.95 3 0.4) ;;; DOESN'T RETURN
 172 (binomial-quant 0 3 0.4) ;;; -2147483648
 173 (binomial-cdf 1 3 0.4) ;;0.6479999999965776
 174 (binomial-pmf 1 3 0.4) ;;0.4320000000226171
 175 (binomial-rand 5 3 0.4) ;;(2 2 0 1 2)
 176
 177