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Diffstat (limited to 'documentation')
53 files changed, 10575 insertions, 0 deletions
diff --git a/documentation/ui/figure.R b/documentation/ui/figure.R new file mode 100644 index 0000000..88cef79 --- /dev/null +++ b/documentation/ui/figure.R @@ -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) + + + + diff --git a/documentation/ui/figure/bell.svg b/documentation/ui/figure/bell.svg new file mode 100644 index 0000000..9709cf5 --- /dev/null +++ b/documentation/ui/figure/bell.svg @@ -0,0 +1,260 @@ +<?xml version="1.0" encoding="UTF-8"?> +<svg xmlns="http://www.w3.org/2000/svg" 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