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In each plot: - The data is represented by a black line. - A dashed red line is included in each plot, representing a line with a 0 intercept and a slope of 1, for reference. - The x-axis and y-axis are labeled appropriately, with the axes in the log10-log10 plots labeled as log10(x) and log10(y). -
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The R code provided above generates a grid of six plots, arranged in two columns and three rows, showcasing different mathematical functions both in their original scale and in a log10-log10 scale. The functions displayed include a linear function (y = x), a concave function (y = sqrt(x)), and a
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data_linear_log <- data.frame(x = log10(x_values), y = log10(linear_function(x_values))) data_concave_log <- data.frame(x = log10(x_values), y = log10(concave_function(x_values))) data_convex_log <- data.frame(x = log10(x_values), y = log10(convex_function(x_values)))
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x_values <- seq(0.001, 10, length.out = 1000) data_linear <- data.frame(x = x_values, y = linear_function(x_values)) data_concave <- data.frame(x = x_values, y = concave_function(x_values)) data_convex <- data.frame(x = x_values, y = convex_function(x_values))
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plot_concave, plot_concave_log, plot_convex, plot_convex_log, ncol = 2, top = "Comparison of Linear, Concave, and Convex
Functions\nIn original (left) and log10 (right) scales")
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convex function (y = x^2). Each of these functions is depicted in two plots: one showing the relationship in its original scale and the other showing the relationship in a log10-log10 scale.
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This visualization serves to demonstrate how different types of mathematical relationships are represented both in their normal scale and when transformed into a logarithmic scale.
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geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Concave (Log10-Log10): y = x^(1/2)") + ylim(0,1) + xlim(0,1)
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geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Convex (Log10-Log10): y = x^2") + ylim(0,1) + xlim(0,1)
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geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Linear (Log10-Log10): y = x") + ylim(0,1) + xlim(0,1)
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linear_function <- function(x) x concave_function <- function(x) sqrt(x) convex_function <- function(x) x^2 identity_line <- function(x) x
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geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Concave: y = x^(1/2)") + ylim(0,10) + xlim(0,10)
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geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Convex: y = x^2") + ylim(0,10) + xlim(0,10)
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geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Linear: y = x") + ylim(0,10) + xlim(0,10)
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Each plot has a title describing the function and indicating whether it is in the original scale or in the log10-log10 scale.
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This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
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repr.plot.width = 10, # in inches (default = 7) repr.plot.height = 13 # in inches (default = 7)
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Comparison of Linear, Concave, and Convex
Functions\nIn original (left) and log10 (right) scales
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I, the copyright holder of this work, hereby publish it under the following license:
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Comparison of simple power law curves in original and log-log scale.png
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Click on a date/time to view the file as it appeared at that time.
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plot_concave_log <- ggplot(data_concave_log, aes(x, y)) +
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plot_convex_log <- ggplot(data_convex_log, aes(x, y)) +
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plot_linear_log <- ggplot(data_linear_log, aes(x, y)) +
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Creative
Commons Attribution-ShareAlike 4.0 International
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User:Talgalili/sandbox/Log transformation (statistics)
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plot_concave <- ggplot(data_concave, aes(x, y)) +
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Commons is a freely licensed media file repository.
192:plot_convex <- ggplot(data_convex, aes(x, y)) +
180:plot_linear <- ggplot(data_linear, aes(x, y)) +
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640:4 March 2024
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960:47.24 dpc
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489:URL
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
