# Blog Archives

## Exponentiation of a matrix (including pseudoinverse)

March 22, 2012
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The following function "exp.mat" allows for the exponentiation of a matrix (i.e. calculation of a matrix to a given power). The function follows three steps:1) Singular Value Decomposition (SVD) of the matrix2) Exponentiation of the singular values3) Re-calculation of the matrix with the new singular valuesThe most common case where the method is applied...

## A ridiculous proof of concept: xyz interpolation

March 14, 2012
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Ridiculous OrbThis is really the last one on this theme for a while... I had alluded to a combination of methods regarding xyz interpolation at the end of my last post and wanted to demonstrate this in a final example.The ridiculousness that you see above involved two interpolation steps. First,...

## XYZ geographic data interpolation, part 3

March 12, 2012
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This will be probably be a final posting on interpolation of xyz data as I believe I have come to some conclusions to my original issues. I show three methods of xyz interpolation:1. The quick and dirty method of interpolating projected xyz points (bi-linear)2. Interpolation using Cartesian coordinates (bi-linear)3. Interpolation using spherical coordinates and...

## XYZ geographic data interpolation, part 2

February 29, 2012
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Having recently received a comment on a post regarding geographic xyz data interpolation, I decided to return to my original "xyz.map" function and open it up for easier interpretation. This should make the method easier to adapt and follow.The above graph shows the distance to Mecca as interpolated from 1000 randomly generated lat/lon...

## Maximal Information Coefficient (MIC)

December 19, 2011
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Pearson r correlation coefficients for various distributions of paired data (Credit: Denis Boigelot, Wikimedia Commons)A paper published this week in Science outlines a new statistic called the maximal information coefficient (MIC), which is able to equally describe the correlation between paired variables regardless of linear or nonlinear relationship. In...

## Maximum Covariance Analysis (MCA)

December 13, 2011
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Maximum Covariance Analysis (MCA) (Mode 1; scaled) of Sea Level Pressure (SLP) and Sea Surface Temperature (SST) monthly anomalies for the region between -180 °W to -70 °W and +30 °N to -30 °S.  MCA coefficients (scaled) are below. The mode represents 94% of the squared covariance fraction (SCF).Maximum Correlation Analysis...

## Another aspect of speeding up loops in R

November 28, 2011
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Any frequent reader of R-bloggers will have come across several posts concerning the optimization of code - in particular, the avoidance of loops.Here's another aspect of the same issue. If you have experience programming in other languages besides R, this is probably a no-brainer, but for laymen, like myself, the following example was...

## Define intermediate color steps for colorRampPalette

November 24, 2011
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The following function, color.palette(), is a wrapper for colorRampPalette() and allows some increased flexibility in defining the spacing between main color levels. One defines both the main color levels (as with colorRampPalette) and an optional vector containing the number of color levels that should be put in between at equal distances.     The above...

## Empirical Orthogonal Function (EOF) Analysis for gappy data

November 24, 2011
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The following is a function for the calculation of Empirical Orthogonal Functions (EOF). For those coming from a more biologically-oriented background and are familiar with Principal Component Analysis (PCA), the methods are similar. In the climate sciences the method is usually used for the decomposition of a data field into dominant spatial-temporal modes. Read...

## Propagation of error

November 11, 2011
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At the onset, this was strictly an excercise of my own curiosity and I didn't imagine writing this down in any form at all. As someone who has done some modelling work in the past, I'm embarrassed to say that I had never fully grasped how one can gauge the error of a...