Plot 73

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### Inquiries: email 2to32minus1@gmail.com

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### Globals

fontScale = 1.2 # Global font size variable

lf = 1.2 # Enlarge font of plot labels

verbose = FALSE # Verbose printing

lw = 2 # Line width

xMargin = 1 # X-axis margin for plots

yMargin = 1 # Y-axis margin for plots

de = 0.01 # Small constant for estimating derivatives numerically

smlPts = 1 # Small data point/circle

medPts = 1.5 # Medium data point/circle

lrgPts = 2.0 # Large data point/circle

### Run this function to generate this plot

runFunc = function() {

dw = 1000

dh = 750

path = "D:/Code/R/LeastSquaresPlay/PlotsAndAssocCode/Plot73/"

savePngVerbose( paste(path, "Plot73.png", sep=""), plotLineFitErrorContours, w=dw, h=dw, un="px", plotErrorContour=FALSE )

}

### Least-squares line fit cost function contour plot

plotLineFitErrorContours = function( plotCrossHairs=TRUE, plotLineFit=TRUE, plotErrorContour=TRUE, takeSquareRoot=FALSE, nLevels=50 ) {

# Create fake data

set.seed( 3 )

trueB = 2

trueM = 3

coeff = c( trueB, trueM )

x = seq( 0, 10, length=100 )

y = evalPoly( x, coeff ) + rnorm( length(x), sd=2 )

# Fit line so we know where center of bowl is located (best y-intercept & slope)

lmFit = lm( y ~ x )

fitB = lmFit$coefficients[1]

fitM = lmFit$coefficients[2]

# Draw line fit plot

if ( plotLineFit ) {

plot( x, y, main=sprintf( "Fit Line Using lm()\nTrue Slope = %.2f True y-Intercept = %.2f", trueM, trueB ),

xlab="", ylab="", cex=lrgPts, lwd=lw+1, cex.main=1.3*fontScale )

abline( fitB, fitM, lwd=lw, col="blue" )

e = compPolyFitError( x, y, lmFit$coefficients )

addLegend( coeff, lmFit$coefficients, meanAbsErr=e$meanAbsError, meanSsdErr=e$meanSsdError )

addAxisLabels()

grid()

}

# Compute grid of cost function values for 'z' surface

nc = 200

nr = 200

intercepts = seq( trueB - 2, trueB + 2, length.out=nc )

slopes = seq( trueM - 0.5, trueM + 0.5, length.out=nr )

z = getLineErrorGrid( meanLineSsdErr, slopes, intercepts, x, y )

if ( plotErrorContour ) {

# Create contour plot

xLim = c( min(intercepts), max(intercepts) )

yLim = c( min(slopes), max(slopes) )

plotTitle = sprintf( "Least-Squares SSD Line Cost Function Contour Plot\nTrue Slope = %.2f True y-Intercept = %.2f (noise added)",

trueM, trueB)

if ( takeSquareRoot )

z = sqrt( z )

contour( intercepts, slopes, t(z), main=plotTitle,

cex.axis=1.3, # Axis numeric label font scale factor

cex.main=1.3*fontScale, # Plot title font size

nlevels=nLevels,

labcex=1.4, # Contour line numeric labels,

xlab="", ylab="" )

addAxisLabels( "y-Intercept", "Slope", cexVal=1.6 )

if ( plotCrossHairs ) {

pl = gpl()

lines( c(pl$xLim[1], pl$xLim[2]), c(trueM, trueM), col="blue", lwd=lw )

lines( c(trueB, trueB), c(pl$yLim[1], pl$yLim[2]), col="blue", lwd=lw )

lines( c(pl$xLim[1], pl$xLim[2]), c(fitM, fitM), col="red", lwd=lw )

lines( c(fitB, fitB), c(pl$yLim[1], pl$yLim[2]), col="red", lwd=lw )

legLine1 = "True Params (noise added)"

legLine2 = "Fitted Params"

legend( 0, 2.95, legend=c(legLine1,legLine2),col=c("blue","red"), lwd=lw, cex=fontScale )

}

### Line fit error function

meanLineSsdErr = function( x, y, slope, yInt ) {

return( (1/length(x)) * sum( ( yInt + slope*x - y )^2 ) )

}

### Compute line fit cost function value over grid of slopes and intercepts

### errorFunc = the specific cost function

### Note: returned matrix may need to be transposed for some functions such as contour()

getLineErrorGrid = function( errorFunc, slopes, intercepts, x, y ) {

nr = length( slopes )

nc = length( intercepts )

z = matrix( nrow=nr, ncol=nc )

for ( row in 1:nr ) { # loop over y-coordinates (slopes)

slope = slopes[row]

for ( col in 1:nc ) { # loop over x-coordinates (y-intercepts)

yInt = intercepts[col]

z[row, col] = errorFunc( x, y, slope=slope, yInt=yInt )

}

return( z )

}

### Compute f(x) for a polynomial and a vector of x-coordinates

evalPoly = function( x, coeff ) {

if ( length( coeff ) < 1 ) return( c(0) )

termSum = 0

for ( i in 1:length(coeff) ) {

termSum = termSum + coeff[i] * x^(i-1)

}

return( termSum )

}

# Compute errors, ABS and SSD, return tuple

compPolyFitError = function( x, y, coeff ) {

predY = evalPoly( x, coeff )

meanAbsError = (1/length(x)) * sum( abs(predY - y) )

meanSsdError = (1/length(x)) * sum( (predY - y)^2 )

return( list( meanAbsError=meanAbsError, meanSsdError=meanSsdError ) )

}

### Add a legend to a plot suitable for this deck's polynomials/purpose

addLegend = function( coeff, fitCoeff, meanAbsErr=NULL, meanSsdErr=NULL, fontSz=1.35*fontScale, pos="topleft", wrapLimit=5 ) {

legList = list()

# Generate and append legend text lines for 'true model'

truePolyStrList = prettyPoly( coeff, nSigFigs=3, wrapLimit=wrapLimit )

legList[1] = paste( "'True model': y ==", truePolyStrList[1], sep="" )

if ( length( truePolyStrList ) > 1 ) {

for ( i in 2:length( truePolyStrList ) ) {

legList[length(legList)+1] = paste( "' '", truePolyStrList[i], sep="" )

}

# Generate and append legend text lines for 'fitted model'

fitPolyStrList = prettyPoly( fitCoeff, nSigFigs=3, wrapLimit=wrapLimit )

legList[length(legList) + 1] = paste( "'Fitted model': y ==", fitPolyStrList[1], sep="" )

if ( length( fitPolyStrList ) > 1 ) {

for ( i in 2:length( fitPolyStrList ) ) {

legList[length(legList)+1] = paste( "' '", fitPolyStrList[i], sep="" )

}

if ( !is.null(meanAbsErr) ) {

legError = paste( "'Mean ABS Error': ", sprintf( "%.2f", meanAbsErr ), sep="" )

legList[ length( legList ) + 1 ] = legError

}

if ( !is.null(meanSsdErr) ) {

legError = paste( "'Mean SSD Error': ", sprintf( "%.2f", meanSsdErr ), sep="" )

legList[ length( legList ) + 1 ] = legError

}

legend( pos, bty="n",inset=c(0.005,0.01),

legend=parse(text=legList), col=c("transparent","transparent"),

cex=fontSz, pch=15, y.intersp=1.1 )

}

### Return string suitable for plot titles with actual exponents (not '^')

### Examples: [ "1.23", "1.23-2.21x", "1.23-2.21x+4.98x^2" ]

prettyPoly = function( coeff, nSigFigs=3, wrapLimit=3 ) {

rc = signif( coeff, nSigFigs )

numTerms = length( coeff )

terms = c()

for ( termNum in 1:numTerms ) {

if ( termNum == 1 ) {

s = paste( rc[termNum], sep="" )

} else {

s = paste( abs(rc[termNum]), sep="" )

}

if ( termNum > 1 )

s = paste( s, "*x", sep="" )

if ( termNum > 2 )

s = paste( s, "^", (termNum-1), sep="" )

terms[ length(terms) + 1 ] = s

}

wrapLines = list()

catStr = ""

for ( termNum in 1:numTerms ) {

if ( termNum > 1 && ( termNum - 1 ) %% wrapLimit == 0 ) {

wrapLines[length(wrapLines) + 1] = catStr

catStr = ""

}

if ( termNum == 1 ) {

catStr = paste( catStr, terms[termNum], sep="" )

} else {

if ( rc[termNum] < 0 ) {

catStr = paste( catStr, " - ", terms[termNum], sep="" )

} else {

catStr = paste( catStr, " + ", terms[termNum], sep="" )

}

if ( catStr != "" )

wrapLines[length(wrapLines) + 1] = catStr

return( wrapLines )

}

### Get Plot Limits : gpl()$xLim[1] --> left x-coord

gpl = function() {

u = par( "usr" )

return( list( xLim=u[1:2], yLim=u[3:4] ) )

}

### Convience method to add x/y axis labels

addAxisLabels = function( xLabel="x", yLabel="y", cexVal=1.3 ) {

mtext( text=xLabel, side=1, line=2.5, cex=cexVal )

mtext( text=yLabel, side=2, line=2.5, cex=cexVal )

}

### Save to PNG file, specify width and height

savePngVerbose = function( path, plotFunc, w=512, h=512, un="px", doCopyright=TRUE, ... ) {

png( filename = path, type="cairo", units=un, width=w, height=h, pointsize=12, res=96 )

plotFunc( ... )

if ( doCopyright )

addCopyright()

dev.off()

}

### Add copyright notice to plot via text()

addCopyright = function() {

mtext( "Email: 2to32minus1@gmail.com", side=4, line=1, adj=0, cex=1.1 )

}

runFunc()

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