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DescriptionComparison of simple power law curves in original and log-log scale.png |
English: R code to reproduce the image:
``` options( repr.plot.width = 10, # in inches (default = 7) repr.plot.height = 13 # in inches (default = 7) ) library(ggplot2) library(gridExtra)
linear_function <- function(x) x concave_function <- function(x) sqrt(x) convex_function <- function(x) x^2 identity_line <- function(x) x
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))
plot_linear <- ggplot(data_linear, aes(x, y)) + geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Linear: y = x") + ylim(0,10) + xlim(0,10) plot_concave <- ggplot(data_concave, aes(x, y)) + geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Concave: y = x^(1/2)") + ylim(0,10) + xlim(0,10) plot_convex <- ggplot(data_convex, aes(x, y)) + geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Convex: y = x^2") + ylim(0,10) + xlim(0,10)
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))) plot_linear_log <- ggplot(data_linear_log, aes(x, y)) + geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Linear (Log10-Log10): y = x") + ylim(0,1) + xlim(0,1) plot_concave_log <- ggplot(data_concave_log, aes(x, y)) + 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) plot_convex_log <- ggplot(data_convex_log, aes(x, y)) + 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)
grid.arrange(plot_linear, plot_linear_log, 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") ``` 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 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. 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). - Each plot has a title describing the function and indicating whether it is in the original scale or in the log10-log10 scale. 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. |
Date | |
Source | Own work |
Author | Talgalili |
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 13:21, 4 March 2024 |
![]() | 1,200 × 1,560 (110 KB) | Talgalili | Uploaded own work with UploadWizard |
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
If the file has been modified from its original state, some details may not fully reflect the modified file.
Horizontal resolution | 47.24 dpc |
---|---|
Vertical resolution | 47.24 dpc |
Original file (1,200 × 1,560 pixels, file size: 110 KB, MIME type: image/png)
![]() | This is a file from the
Wikimedia Commons. Information from its
description page there is shown below. Commons is a freely licensed media file repository. You can help. |
DescriptionComparison of simple power law curves in original and log-log scale.png |
English: R code to reproduce the image:
``` options( repr.plot.width = 10, # in inches (default = 7) repr.plot.height = 13 # in inches (default = 7) ) library(ggplot2) library(gridExtra)
linear_function <- function(x) x concave_function <- function(x) sqrt(x) convex_function <- function(x) x^2 identity_line <- function(x) x
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))
plot_linear <- ggplot(data_linear, aes(x, y)) + geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Linear: y = x") + ylim(0,10) + xlim(0,10) plot_concave <- ggplot(data_concave, aes(x, y)) + geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Concave: y = x^(1/2)") + ylim(0,10) + xlim(0,10) plot_convex <- ggplot(data_convex, aes(x, y)) + geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Convex: y = x^2") + ylim(0,10) + xlim(0,10)
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))) plot_linear_log <- ggplot(data_linear_log, aes(x, y)) + geom_line() + geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") + ggtitle("Linear (Log10-Log10): y = x") + ylim(0,1) + xlim(0,1) plot_concave_log <- ggplot(data_concave_log, aes(x, y)) + 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) plot_convex_log <- ggplot(data_convex_log, aes(x, y)) + 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)
grid.arrange(plot_linear, plot_linear_log, 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") ``` 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 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. 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). - Each plot has a title describing the function and indicating whether it is in the original scale or in the log10-log10 scale. 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. |
Date | |
Source | Own work |
Author | Talgalili |
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 13:21, 4 March 2024 |
![]() | 1,200 × 1,560 (110 KB) | Talgalili | Uploaded own work with UploadWizard |
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
If the file has been modified from its original state, some details may not fully reflect the modified file.
Horizontal resolution | 47.24 dpc |
---|---|
Vertical resolution | 47.24 dpc |