Solve problems using PDF.

corywalker · Jan 19, 2018 · ce41686 · ce41686
1 parent 25c3224
commit ce41686
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Showing 7 changed files with 81 additions and 7 deletions.
diff --git a/expreduce/builtin.go b/expreduce/builtin.go
@@ -192,6 +192,7 @@ func GetAllDefinitions() (defs []NamedDefSet) {
 	defs = append(defs, NamedDefSet{"boolean", GetBooleanDefinitions()})
 	defs = append(defs, NamedDefSet{"simplify", GetSimplifyDefinitions()})
 	defs = append(defs, NamedDefSet{"numbertheory", GetNumberTheoryDefinitions()})
+	defs = append(defs, NamedDefSet{"stats", GetStatsDefinitions()})
 	defs = append(defs, NamedDefSet{"manip", GetManipDefinitions()})
 	defs = append(defs, NamedDefSet{"rubi", GetRubiDefinitions()})
 

diff --git a/expreduce/builtin_arithmetic.go b/expreduce/builtin_arithmetic.go
@@ -256,6 +256,10 @@ func getArithmeticDefinitions() (defs []Definition) {
 				return res.Parts[1]
 			}
 
+			// Not exactly right because of "1. + foo[1]", but close enough.
+			if _, rIsReal := realPart.(*Flt); rIsReal {
+				return exprToN(es, res)
+			}
 			return res
 		},
 	})
@@ -335,6 +339,10 @@ func getArithmeticDefinitions() (defs []Definition) {
 				}
 			}
 
+			// Not exactly right because of "1. + foo[1]", but close enough.
+			if _, rIsReal := realPart.(*Flt); rIsReal {
+				return exprToN(es, res)
+			}
 			return res
 		},
 	})

diff --git a/expreduce/builtin_stats.go b/expreduce/builtin_stats.go
@@ -0,0 +1,8 @@
+package expreduce
+
+func GetStatsDefinitions() (defs []Definition) {
+	defs = append(defs, Definition{Name: "NormalDistribution"})
+	defs = append(defs, Definition{Name: "LogNormalDistribution"})
+	defs = append(defs, Definition{Name: "PDF"})
+	return
+}
diff --git a/expreduce/resources.go b/expreduce/resources.go
diff --git a/expreduce/resources/arithmetic.m b/expreduce/resources/arithmetic.m
@@ -176,7 +176,10 @@
         ESameTest[a^(2-c), a^2/a^c],
         ESameTest[m^2, m*m],
         ESameTest[1, m/m],
-        ESameTest[1, m^2/m^2]
+        ESameTest[1, m^2/m^2],
+
+        (*Conversion of exact numeric functions to reals*)
+        ESameTest[True, MatchQ[Sqrt[2*Pi]*.1, _Real]],
     ]
 };
 

diff --git a/expreduce/resources/solve.m b/expreduce/resources/solve.m
@@ -51,8 +51,11 @@
             C[1]\[Element]Integers
           ]
         },
-      E, {pow -> ConditionalExpression[2 I Pi C[1] + Log[rhs], 
-             C[1] \[Element] Integers]},
+      E, If[MatchQ[rhs, _Real],
+            {pow -> Log[rhs]},
+            {pow -> ConditionalExpression[2 I Pi C[1] + Log[rhs], 
+              C[1] \[Element] Integers]},
+           ],
       _, Message[Solve::ifun, Solve];{pow -> Log[rhs]/Log[base]}
     ]]
 ];
@@ -239,6 +242,8 @@
         (* Solve combination of Sin and ArcSin *)
         ESameTest[{{x->-b+y}}, Solve[Sin[ArcSin[x+b]]==y,x]],
         ESameTest[{{x->ConditionalExpression[Pi-ArcSin[Sin[y]]+2 Pi C[1],((Re[y]==-(Pi/2)&&Im[y]>=0)||-(Pi/2)<Re[y]<Pi/2||(Re[y]==Pi/2&&Im[y]<=0))&&C[1]\[Element]Integers]},{x->ConditionalExpression[ArcSin[Sin[y]]+2 Pi C[1],((Re[y]==-(Pi/2)&&Im[y]>=0)||-(Pi/2)<Re[y]<Pi/2||(Re[y]==Pi/2&&Im[y]<=0))&&C[1]\[Element]Integers]}}//normSol, Solve[ArcSin[Sin[x]]==y,x]//normSol],
+        (* Solve a problem involving a PDF *)
+        EStringTest["{{x -> -1.66352}, {x -> 1.66352}}", "Solve[PDF[NormalDistribution[0, 1], x] == .1, x]"],
 
         (* POLYNOMIALS *)
         ESameTest[{{x->(-b-Sqrt[b^2-4 a c])/(2 a)},{x->(-b+Sqrt[b^2-4 a c])/(2 a)}}, Solve[a*x^2==-b*x-c,x]],

diff --git a/expreduce/resources/stats.m b/expreduce/resources/stats.m
@@ -0,0 +1,26 @@
+NormalDistribution::usage = "`NormalDistribution[mu, sigma]` is a normal distribution with a mean `mu` and standard deviation of `sigma`.";
+Attributes[NormalDistribution] = {ReadProtected, Protected};
+Tests`NormalDistribution = {
+    ESimpleExamples[
+        ESameTest[E^(-((x-\[Mu])^2/(2 \[Sigma]^2)))/(Sqrt[2 \[Pi]] \[Sigma]), PDF[NormalDistribution[\[Mu],\[Sigma]],x]]
+    ]
+};
+
+LogNormalDistribution::usage = "`LogNormalDistribution[mu, sigma]` is a lognormal distribution with a mean `mu` and standard deviation of `sigma`.";
+Attributes[LogNormalDistribution] = {ReadProtected, Protected};
+Tests`LogNormalDistribution = {
+    ESimpleExamples[
+        ESameTest[Piecewise[{{1/(E^((-\[Mu] + Log[x])^2/(2*\[Sigma]^2))*Sqrt[2*Pi]*x*\[Sigma]), x > 0}}, 0], PDF[LogNormalDistribution[\[Mu],\[Sigma]],x]]
+    ]
+};
+
+PDF::usage = "`PDF[dist, var]` calculates the PDF of `dist`.";
+PDF[NormalDistribution[mu_, sigma_], x_] := E^(-((-mu+x)^2/(2 sigma^2)))/(Sqrt[2 \[Pi]] sigma);
+PDF[LogNormalDistribution[mu_, sigma_], x_] := Piecewise[{{1/(E^((-mu + Log[x])^2/(2*sigma^2))*Sqrt[2*Pi]*sigma*x), x > 0}},  0]
+Attributes[PDF] = {ReadProtected, Protected};
+Tests`PDF = {
+    ESimpleExamples[
+        ESameTest[E^(-((x-\[Mu])^2/(2 \[Sigma]^2)))/(Sqrt[2 \[Pi]] \[Sigma]), PDF[NormalDistribution[\[Mu],\[Sigma]],x]],
+        ESameTest[Piecewise[{{1/(E^((-\[Mu] + Log[x])^2/(2*\[Sigma]^2))*Sqrt[2*Pi]*x*\[Sigma]), x > 0}}, 0], PDF[LogNormalDistribution[\[Mu],\[Sigma]],x]]
+    ]
+};