minor changes to chapter 1 demos for speed and updates to julia0.2

Author: vtjnash

demos/book/1/bellcurve.jl

@@ -9,8 +9,8 @@
 t=1000000
 dx=.2
 v=randn(t)
-grid=[-4:dx:4]
-count=hist(v,grid)/(t*dx)
+grid=-4:dx:4
+count=hist(v,grid)[2]/(t*dx)
 
 ## Theory
 x=grid
@@ -19,8 +19,13 @@ y=exp(-x.^2/2)/sqrt(2*pi)
 ## Plot
 using Winston
 p = FramedPlot()
-h = Histogram(count, dx)
-h.x0 = grid[1]
+h = Histogram(count, step(grid))
+h.x0 = first(grid)
 add(p, h)
 add(p, Curve(x, y, "color", "blue", "linewidth", 2)) 
-file(p, "bellcurve.png")
+if isinteractive()
+    Winston.display(p)
+else
+    file(p, "bellcurve.png")
+end
+

demos/book/1/largeeig.jl

@@ -7,31 +7,40 @@
 
 include("tracywidom.jl")
 
-## Parameters
-n=100        # matrix size
-t=5000       # trials
-v=[]         # eigenvalue samples
-dx=.2        # binsize
-grid=[-5:dx:2]
-## Experiment
-for i=1:t
-    a=randn(n,n)+im*randn(n,n) # random nxn complex matrix
-    s=(a+a')/2                 # Hermitian matrix
-    v=[v; max(eig(s)[1])]         # Largest Eigenvalue
-end
-v=n^(1/6)*(v-2*sqrt(n))        # normalized eigenvalues
+function largeeig_experiment(
+    ## Parameters
+    n=100,       # matrix size
+    t=5000,      # trials
+    dx=.2,       # binsize
+)
+    ## Experiment
+    v=Float64[] # eigenvalue samples
+    for i=1:t
+        a=randn(n,n)+im*randn(n,n) # random nxn complex matrix
+        s=(a+a')/2                 # Hermitian matrix
+        push!(v,max(eig(s)[1]))    # Largest Eigenvalue
+    end
+    v=n^(1/6)*(v-2*sqrt(n))        # normalized eigenvalues
 
-count=hist(v,grid)/(t*dx)
+    grid=-5:dx:2
+    count=hist(v,grid)[2]/(t*dx)
+    (grid, count)
+end
+(grid, count) = largeeig_experiment()
 
 ## Theory
 (t, f) = tracywidom(5., -8.)
 
 ## Plot
 using Winston
 p = FramedPlot()
-h = Histogram(count, dx)
-h.x0 = grid[1]
+h = Histogram(count, step(grid))
+h.x0 = first(grid)
 add(p, h)
-add(p, Curve(t+5, f, "linewidth", 2, "color", "blue")) 
-file(p, "largeeig.png")
+add(p, Curve(t, f, "linewidth", 2, "color", "blue"))
+if isinteractive()
+    Winston.display(p)
+else
+    file(p, "largeeig.png")
+end
 

demos/book/1/semicircle.jl

@@ -4,28 +4,39 @@
 #Experiment:  Sample random symmetric Gaussian matrices
 #Plot:        Histogram of the eigenvalues
 #Theory:      Semicircle as n->infinity
-## Parameters
-n=1000       # matrix size
-t=10         # trials
-v=[]         # eigenvalue samples
-dx=.2        # binsize
-grid=[-2.4:dx:2.4]
-## Experiment
-for i = 1:t
-    a=randn(n,n)      # n by n matrix of random Gaussians
-    s=(a+a')/sqrt(2*n)# symmetrize and normalize matrix
-    v=[v;eig(s)[1]]   # eigenvalues
+
+function semicircle_experiment(
+    ## Parameters
+    n=1000,      # matrix size
+    t=10,        # trials
+    dx=.2,       # binsize
+)
+    ## Experiment
+    v=Float64[] # eigenvalue samples
+    for i = 1:t
+        a=randn(n,n)      # n by n matrix of random Gaussians
+        s=(a+a')/sqrt(2*n)# symmetrize and normalize matrix
+        append!(v,eig(s)[1])# eigenvalues
+    end
+    grid=-2.4:dx:2.4
+    count=hist(v,grid)[2]/(n*t*dx)
+    (grid, count)
 end
-count=hist(grid)/(n*t*dx)
+grid,count = semicircle_experiment()
+
 ## Theory
 x=[-2:dx:2]
 y=sqrt(4-x.^2)/(2*pi)
 
 ## Plot
 using Winston
 p = FramedPlot()
-h = Histogram(count, dx)
-h.x0 = grid[1]
+h = Histogram(count, step(grid))
+h.x0 = first(grid)
 add(p, h)
-add(p, Curve(x+2.4+dx/2, y, "color", "blue", "linewidth", 2)) 
-file(p, "semicircle.png")
+add(p, Curve(x, y, "color", "blue", "linewidth", 2)) 
+if isinteractive()
+    Winston.display(p)
+else
+    file(p, "semicircle.png")
+end

demos/book/1/tracywidom.jl

@@ -28,5 +28,9 @@ end
 using Winston
 p = FramedPlot()
 add(p, Curve(t, f2, "linewidth", 2))
-file(p, "tracywidom.png")
+if isinteractive()
+    Winston.display(p)
+else
+    file(p, "tracywidom.png")
+end