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