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@@ -0,0 +1,491 @@
+library('cowplot')
+library('ggplot2')
+
+theme_set(theme_gray())
+
+
+isEq = function(a,b,error=1e-5){
+ abs(a - b) <= error
+}
+
+isLt = function(a,b,error=1e-5){
+ !isEq(a,b,error) & a < b
+}
+
+isGt = function(a,b,error=1e-5){
+ !isEq(a,b,error) & a > b
+}
+
+isLE = function(a,b,error=1e-5){
+ isEq(a,b,error) | a < b
+}
+
+isGE = function(a,b,error=1e-5){
+ isEq(a,b,error) | a > b
+}
+
+#Scale: Scales a number to a different scale
+Scale = function(value, toMin, toMax, fromMin=min(value), fromMax=max(value)){
+ (toMax - toMin) / (fromMax - fromMin) * (value - fromMin) + toMin
+}
+
+#Basic
+
+term.triangle = function(x, a, b, c){
+ if (isLt(x,a) | isGt(x,c))
+ 0.0
+ else if (isEq(x,b))
+ 1.0
+ else if (isLt(x,b))
+ (x - a) / (b - a)
+ else
+ result = (c - x) / (c - b)
+}
+
+term.trapezoid = function(x,a,b,c,d){
+ if (isLt(x, a) | isGt(x, d))
+ 0.0
+ else if (isLE(x, b))
+ min(1.0, (x - a) / (b - a))
+ else if (isLE(x, c))
+ 1.0
+ else if (isLE(x, d))
+ (d - x) / (d - c)
+}
+
+term.rectangle = function(x,a,b){
+ if (isLt(x, a) | isGt(x,b))
+ 0.0
+ else 1.0
+}
+
+term.discrete = function(x, a, b){
+ diff = b-a
+ if (isLt(x,a) | isGt(x,b))
+ 0.0
+ else if (isLt(x,.25 * diff))
+ Scale(x, 0, 1, a, a + diff*.25)
+ else if (isLt(x, .5*diff))
+ Scale(x,1,0.5, a + diff*.25, a + diff*.5)
+ else if (isLt(x, .75*diff))
+ Scale(x,0.5,1,a+diff*.5, a+diff*.75)
+ else if (isLt(x, diff))
+ Scale(x, 1, 0, a+diff*.75, a+diff)
+ else {0.0}
+# else if (isLt(x, a*.5)
+}
+
+
+term.bell = function(x, center, width, slope){
+ 1.0 / (1.0 + abs((x - center) / width)**(2 * slope));
+}
+
+#EXTENDED
+
+term.cosine = function(x, center, width){
+ if (isLt(x, center-width/2.0) || isGt(x, center+width/2.0)){
+ 0.0
+ }else{
+ 0.5 * (1.0 + cos(2.0 / width * pi * (x - center)))
+ }
+}
+
+term.gaussian = function(x, mean, sd){
+ exp((-(x - mean) * (x - mean)) / (2 * sd * sd));
+}
+
+term.gaussianProduct = function(x, meanA, sdA, meanB, sdB){
+ xLEa = isLE(x, meanA)
+ a = exp((-(x - meanA) * (x - meanA)) / (2 * sdA * sdA)) * xLEa + (1 - xLEa)
+ xGEb = isGE(x, meanB)
+ b = exp((-(x - meanB) * (x - meanB)) / (2 * sdB * sdB)) * xGEb + (1 - xGEb)
+ a * b
+}
+
+term.bell = function(x, center, width, slope){
+ 1.0 / (1.0 + abs((x - center) / width)** (2 * slope))
+}
+
+term.piShape = function(x, bottomLeft, topLeft, topRight, bottomRight){
+ a_b_ave = (bottomLeft + topLeft) / 2.0
+ b_minus_a = topLeft - bottomLeft
+ c_d_ave = (topRight + bottomRight) / 2.0
+ d_minus_c = bottomRight - topRight
+
+ if (isLE(x, bottomLeft)) 0.0
+
+ else if (isLE(x, a_b_ave))
+ 2.0 * ((x - bottomLeft) / b_minus_a) ** 2
+
+ else if (isLt(x, topLeft))
+ 1.0 - 2.0 * ((x - topLeft) / b_minus_a)** 2
+
+ else if (isLE(x, topRight))
+ 1.0
+
+ else if (isLE(x, c_d_ave))
+ 1 - 2 * ((x - topRight) / d_minus_c)**2
+
+ else if (isLt(x, bottomRight))
+ 2 * ((x - bottomRight) / d_minus_c)** 2
+
+ else 0.0
+}
+
+term.sigmoidDifference = function(x, left, rising, falling, right){
+ a = 1.0 / (1 + exp(-rising * (x - left)))
+ b = 1.0 / (1 + exp(-falling * (x - right)))
+ abs(a - b)
+}
+
+term.sigmoidProduct = function(x, left, rising, falling, right){
+ a = 1.0 / (1 + exp(-rising * (x - left)))
+ b = 1.0 / (1 + exp(-falling * (x - right)))
+ abs(a * b)
+}
+
+term.spike = function(x, center, width){
+ exp(-abs( 10 / width * (x-center)))
+}
+
+#EDGES
+
+term.binary = function(x, threshold, direction){
+ if (isGE(direction,0.0) && isGE(x, threshold)){
+ 1.0
+ }else if (isLt(direction, 0.0) && isLE(x, threshold)){
+ 1.0
+ }else{
+ 0.0
+ }
+}
+
+term.concave = function(x, inflection, end){
+ if (isLE(inflection, end)){ #Concave increasing
+ if (isLt(x, end)){
+ (end - inflection) / (2 * end - inflection - x)
+ }else{ 1.0 }
+ } else{ #Concave decreasing
+ if (isGt(x, end)){
+ (inflection - end) / (inflection -2 * end + x)
+ }else{ 1.0 }
+ }
+}
+
+
+term.ramp = function(x, start, end){
+ if (isEq(start, end)) 0.0
+
+ else if (isLt(start, end)) {
+ if (isLE(x, start)) 0.0
+ else if (isGE(x, end)) 1.0
+ else (x - start) / (end - start)
+ } else {
+ if (isGE(x, start)) 0.0
+ else if (isLE(x, end)) 1.0
+ else (start - x) / ( start - end)
+ }
+}
+
+term.sigmoid = function(x, inflection, slope){
+ 1.0 / (1.0 + exp(-slope * (x - inflection)))
+}
+
+term.sShape = function(x, start, end){
+ average = (start + end) / 2
+ difference = end - start
+
+ if (isLE(x, start)) 0.0
+
+ else if (isLE(x, average))
+ 2 * ((x - start) / difference) ** 2
+
+ else if (isLt(x, end))
+ 1.0 - 2.0 * ((x - end) / difference) ** 2
+ else 1.0
+}
+
+term.zShape = function(x, start, end){
+ average = (start + end) / 2
+ difference = end - start
+
+ if (isLE(x, start)) 1.0
+
+ else if (isLE(x, average))
+ 1.0 - 2.0 * ((x - start) / difference) ** 2
+
+ else if (isLt(x, end))
+ 2.0 * ((x - end) / difference)** 2
+
+ else 0.0
+}
+
+
+
+
+
+
+
+x = seq(0,1,length=500)
+average = (max(x) + min(x))/2
+diff = (max(x) - min(x))
+
+
+
+
+
+dir.create('figure',showWarnings=F)
+
+
+##################BASIC
+
+triangle.df = data.frame(x, y=sapply(x, term.triangle, min(x), average, max(x)))
+triangle.plot = ggplot(triangle.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/triangle.svg', triangle.plot, width=3, height=3)
+
+
+trapezoid.df = data.frame(x, y=sapply(x, term.trapezoid, min(x), min(x) + .25 * diff, min(x) + .75*diff, max(x)))
+trapezoid.plot = ggplot(trapezoid.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/trapezoid.svg', trapezoid.plot, width=3, height=3)
+
+
+rectangle.df = data.frame(x, y=sapply(x, term.rectangle, min(x) + .25*diff, min(x) + .75*diff))
+rectangle.plot = ggplot(rectangle.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/rectangle.svg', rectangle.plot, width=3, height=3)
+
+
+discrete.x = x[c(1, seq(10, 495, 10), 500)]
+discrete.df = data.frame(x=discrete.x, y=sapply(discrete.x, term.discrete, min(x), max(x)))
+discrete.plot = ggplot(discrete.df, aes(x,y, size=2, lineend='round')) + geom_point() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/discrete.svg', discrete.plot, width=3, height=3)
+
+
+
+#################EXTENDED
+
+cosine.df = data.frame(x, y=sapply(x, term.cosine, average, diff))
+cosine.plot = ggplot(cosine.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/cosine.svg', cosine.plot, width=3, height=3)
+
+
+gaussian.df = data.frame(x, y=sapply(x, term.gaussian, average, .2*diff))
+gaussian.plot = ggplot(gaussian.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/gaussian.svg', gaussian.plot, width=3, height=3)
+
+
+gaussianProduct.df = data.frame(x, y=sapply(x, term.gaussianProduct, average+.1, .2*diff, average-.1, .2*diff))
+gaussianProduct.plot = ggplot(gaussianProduct.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/gaussianProduct.svg', gaussianProduct.plot, width=3, height=3)
+
+
+bell.df = data.frame(x, y=sapply(x, term.bell, average, .25*diff, 3.0))
+bell.plot = ggplot(bell.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/bell.svg', bell.plot, width=3, height=3)
+
+
+piShape.df = data.frame(x, y=sapply(x, term.piShape, min(x), average, average, max(x)))
+piShape.plot = ggplot(piShape.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/piShape.svg', piShape.plot, width=3, height=3)
+
+
+sigmoidDifference.df = data.frame(x, y=sapply(x, term.sigmoidDifference, min(x) + .25*diff, 20/diff, 20/diff, min(x)+.75*diff))
+sigmoidDifference.plot = ggplot(sigmoidDifference.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/sigmoidDifference.svg', sigmoidDifference.plot, width=3, height=3)
+
+
+sigmoidProduct.df = data.frame(x, y=sapply(x, term.sigmoidProduct, min(x) + .25*diff, 10/diff, -10/diff, min(x)+.75*diff))
+sigmoidProduct.plot = ggplot(sigmoidProduct.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/sigmoidProduct.svg', sigmoidProduct.plot, width=3, height=3)
+
+
+spike.df = data.frame(x, y=sapply(x, term.spike, average, diff))
+spike.plot = ggplot(spike.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/spike.svg', spike.plot, width=3, height=3)
+
+
+
+###############EDGE
+
+#Binary
+binary.dfa = data.frame(x, y=sapply(x, term.binary, min(x) + .25*diff, -1))
+binary.dfb = data.frame(x, y=sapply(x, term.binary, min(x) + .75*diff, 1))
+binary.plot = ggplot(binary.dfa, aes(x,y, size=2, lineend='round')) +
+ geom_line(data=binary.dfb, aes(x,y, size=2, lineend='round')) +
+ geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/binary.svg', binary.plot, width=3, height=3)
+
+#Concave
+concave.dfa = data.frame(x, y=sapply(x, term.concave, average, max(x)-.2))
+concave.dfb = data.frame(x, y=sapply(x, term.concave, average, 1-(max(x)-.2)))
+concave.plot = ggplot(concave.dfa, aes(x,y, size=2, lineend='round')) +
+ geom_line(data=concave.dfb, aes(x,y, size=2, lineend='round')) +
+ geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/concave.svg', concave.plot, width=3, height=3)
+
+#RAMP
+ramp.dfa = data.frame(x, y=sapply(x, term.ramp, max(x)-.2, min(x)+.2))
+ramp.dfb = data.frame(x, y=sapply(x, term.ramp, min(x)+.2, max(x)-.2))
+ramp.plot = ggplot(ramp.dfa, aes(x,y, size=2, lineend='round')) +
+ geom_line(data=ramp.dfb, aes(x,y, size=2, lineend='round')) +
+ geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/ramp.svg', ramp.plot, width=3, height=3)
+
+
+sigmoid.dfa = data.frame(x, y=sapply(x, term.sigmoid, average, 20/diff))
+sigmoid.dfb = data.frame(x, y=sapply(x, term.sigmoid, average, -20/diff))
+sigmoid.plot = ggplot(sigmoid.dfa, aes(x,y, size=2, lineend='round')) +
+ geom_line(data=sigmoid.dfb, aes(x,y, size=2, lineend='round')) +
+ geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/sigmoid.svg', sigmoid.plot, width=3, height=3)
+
+
+sShape.df = data.frame(x, y=sapply(x, term.sShape, min(x), max(x)))
+sShape.plot = ggplot(sShape.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/sShape.svg', sShape.plot, width=3, height=3)
+
+
+zShape.df = data.frame(x, y=sapply(x, term.zShape, min(x), max(x)))
+zShape.plot = ggplot(zShape.df, aes(x,y, size=2, lineend='round')) + geom_line() + ylab(expression(mu(x))) + theme(legend.position='none')
+ggsave('figure/zShape.svg', zShape.plot, width=3, height=3)
+
+
+##############Terms
+
+ constant.plot =
+ ggplot(data=data.frame(x=0,y=0)) +
+ geom_point(aes(x=0,y=0), size=0) +
+ ylab(expression(f(x))) + xlab('x') +
+ coord_cartesian(ylim = c(-0.05, 1.05), xlim=c(-0.05,1.05)) +
+ annotate('text', x = .5, y = .5, label = "f(x)==k", parse = T,size=10)
+
+ linear.plot =
+ ggplot(data=data.frame(x=0,y=0)) +
+ geom_point(aes(x=0,y=0), size=0) +
+ ylab(expression(f(x))) + xlab('x') +
+ coord_cartesian(ylim = c(-0.05, 1.05), xlim=c(-0.05,1.05)) +
+ annotate('text', x = .5, y = .5, angle=45, label = "f(x)==sum(paste(c[i],v[i]), i)+k", parse = T,size=10)
+
+ function.plot =
+ ggplot(data=data.frame(x=0,y=0)) +
+ geom_point(aes(x=0,y=0), size=0) +
+ ylab(expression(f(x))) + xlab('x') +
+ coord_cartesian(ylim = c(-0.05, 1.05), xlim=c(-0.05,1.05)) +
+ annotate('text', x = .5, y = .5, label = "f:x %->% f(x)", parse = T,size=10)
+
+
+########## Vertical layout
+ terms.grid = plot_grid(
+
+triangle.plot, bell.plot, piShape.plot,
+trapezoid.plot, cosine.plot, sigmoidDifference.plot,
+rectangle.plot, gaussian.plot, sigmoidProduct.plot,
+discrete.plot, gaussianProduct.plot, spike.plot,
+binary.plot, ramp.plot, sShape.plot,
+concave.plot, sigmoid.plot, zShape.plot,
+function.plot, linear.plot, constant.plot,
+
+ ncol=3, nrow=7, scale=1, label_size=12, vjust=1.25, align='v',
+ #hjust=.5, # align='hv',
+
+ labels=c(
+'Triangle', 'Bell', 'PiShape',
+'Trapezoid', 'Cosine', 'SigmoidDifference',
+'Rectangle', 'Gaussian', 'SigmoidProduct',
+'Discrete', 'GaussianProduct', 'Spike',
+'Binary', 'Ramp', 'SShape',
+'Concave', 'Sigmoid', 'ZShape',
+'Function', 'Linear', 'Constant'
+ )
+ )
+
+ save_plot('figure/terms.svg', terms.grid, ncol=3, nrow=7, scale=.75)
+
+ stop('Script successfully executed')
+
+
+##########Horizontal layout
+ terms.grid = plot_grid(
+
+ triangle.plot, trapezoid.plot, rectangle.plot, discrete.plot, function.plot, binary.plot , concave.plot,
+
+ bell.plot, cosine.plot, gaussian.plot, gaussianProduct.plot, linear.plot, ramp.plot, sigmoid.plot,
+
+ piShape.plot, sigmoidDifference.plot, sigmoidProduct.plot, spike.plot, constant.plot, sShape.plot, zShape.plot,
+
+ ncol=7, nrow=3, scale=1, label_size=12, vjust=1.25, align='v',
+ #hjust=.5, # align='hv',
+
+labels=c(
+'Triangle', 'Trapezoid', 'Rectangle', 'Discrete', 'Function', 'Binary', 'Concave',
+'Bell', 'Cosine', 'Gaussian', 'GaussianProduct', 'Linear', 'Ramp', 'Sigmoid',
+'PiShape', 'SigmoidDifference', 'SigmoidProduct','Spike', 'Constant', 'SShape', 'ZShape')
+)
+
+save_plot('figure/terms.svg', terms.grid, ncol=7, nrow=3, scale=.75)
+
+stop('Script successfully executed')
+
+
+
+
+
+
+
+
+
+
+
+
+# X1234X
+# 123456
+# 7 8
+# 123456
+
+constant.plot =
+ ggplot(data=data.frame(x=0,y=0)) +
+ geom_point(aes(x=0,y=0), size=0) +
+ ylab(expression(mu(x))) + xlab('x') +
+ coord_cartesian(ylim = c(-0.05, 1.05), xlim=c(-0.05,1.05)) +
+ annotate('text', x = .5, y = .5, label = "mu(x)==k", parse = T,size=10)
+
+linear.plot =
+ ggplot(data=data.frame(x=0,y=0)) +
+ geom_point(aes(x=0,y=0), size=0) +
+ ylab(expression(mu(x))) + xlab('x') +
+ coord_cartesian(ylim = c(-0.05, 1.05), xlim=c(-0.05,1.05)) +
+ annotate('text', x = .5, y = .5, angle=45, label = "mu(x)==sum(c[i] %.% x[i], i)+k", parse = T,size=5)
+
+function.plot =
+ ggplot(data=data.frame(x=0,y=0)) +
+ geom_point(aes(x=0,y=0), size=0) +
+ ylab(expression(mu(x))) + xlab('x') +
+ coord_cartesian(ylim = c(-0.05, 1.05), xlim=c(-0.05,1.05)) +
+ annotate('text', x = .5, y = .5, label = "f:x %->% mu(x)", parse = T,size=5)
+
+
+terms.grid = plot_grid(
+
+NULL, triangle.plot, trapezoid.plot, rectangle.plot, discrete.plot, NULL,
+
+bell.plot, cosine.plot, gaussian.plot, gaussianProduct.plot, piShape.plot, sigmoidDifference.plot,
+
+sigmoidProduct.plot, spike.plot, NULL, constant.plot, linear.plot, function.plot,
+
+binary.plot, concave.plot, ramp.plot, sigmoid.plot, sShape.plot, zShape.plot,
+
+nrow=4, ncol=6, scale=1, label_size=12, vjust=1.25,
+#hjust=.5, # align='hv',
+
+labels=c(
+'', 'Triangle', 'Trapezoid', 'Rectangle', 'Discrete', '',
+'Bell', 'Cosine', 'Gaussian', 'GaussianProduct', 'PiShape', 'SigmoidDifference',
+'SigmoidProduct','Spike', '', 'Constant', 'Linear', 'Function',
+'Binary', 'Concave', 'Ramp', 'Sigmoid', 'SShape', 'ZShape')
+)
+
+save_plot('figure/terms.svg', terms.grid,
+ ncol=6, nrow=4, scale=.5)
+
+
+
+
generated by cgit v1.2.3 (git 2.25.1) at 2024-04-19 19:35:13 +0000