Emacs Calc Tricks

I like calc so much that I recently replaced the Galculator launcher in my desktop environment with this script:

#!/bin/sh
emacs -g 40x20-0-0 -eval '(progn (calc) (message "") (delete-other-windows))' &

This starts a small Emacs window in the bottom right corner of my screen and clears the default welcome message. I also have the following snippet in my .emacs.d/calc.el file so that the paper trail isn't displayed:

(setq calc-display-trail nil)

I recently did some work defining partition table sizes, and it was useful to define these units in my calc.el:

(setq math-additional-units '(
  (GiB "1024 * MiB" "Giga Byte")
  (MiB "1024 * KiB" "Mega Byte")
  (KiB "1024 * B" "Kilo Byte")
  (B nil "Byte")
  (Gib "1024 * Mib" "Giga Bit")
  (Mib "1024 * Kib" "Mega Bit")
  (Kib "1024 * b" "Kilo Bit")
  (b "B / 8" "Bit")))
(setq math-units-table nil) ; Clear the units table cache

(Lifted from: https://www.reddit.com/r/emacs/comments/31xezm/common_byte_units_in_calc/cq6ef06/)

What really convinced me to stick with calc mode was a recent struggle with LibreOffice Calc. I wanted to do a polynomial curve fit of some data (to use as input into a circuit simulation), but after I setup a chart and plotted the fit, I was unable to copy the formula as text. If I attempted to paste it in another program it would paste as an image. This was less than helpful.

The workaround for LibreOffice Calc was to learn and use the LINEST function, which is an array function. That was a new trick for me, but it certainly wasn't intuitive to setup, and the output wasn't in a particularly useful format. There was one coefficient per cell, but no labeling for which term the coefficient applied to, and in fact the coefficients were in reverse order from the way I supplied the terms to LINEST. I was not happy with this solution.

A bit of research showed that calc could find and plot curve fits as well: https://www.gnu.org/software/emacs/manual/html_mono/calc.html#Curve-Fitting

The input points can be entered as a Nx2 matrix like below, and then transposed into the format calc expects with v t ("vector, transpose").

[
[ 1000,lufquant(-193.5dB,1)],
[ 2000,lufquant(-191.0dB,1)],
[ 2500,lufquant(-190.0dB,1)],
[ 3000,lufquant(-190.5dB,1)],
[ 4000,lufquant(-190.5dB,1)],
[ 5000,lufquant(-189.5dB,1)],
[ 6000,lufquant(-188.5dB,1)],
[ 7000,lufquant(-187.5dB,1)],
[ 8000,lufquant(-183.0dB,1)],
[ 9000,lufquant(-182.5dB,1)],
[10000,lufquant(-181.5dB,1)],
[11000,lufquant(-182.0dB,1)],
[12000,lufquant(-183.0dB,1)],
[13000,lufquant(-190.0dB,1)],

[15000,lufquant(-194.0dB,1)],

[18000,lufquant(-200.0dB,1)],

[20000,lufquant(-250.0dB,1)]
]

The lufquant is a calc function that will convert a decibel value (\(20\log_{10}(x)\)) into the corresponding field quantity, with default reference and units set by the calc-lu-field-reference variable in Emacs. But here I'm passing in a unitless `1` to do the ratio calculation without units.

The a F command will take a 2D matrix of data (2xN), then ask what type of fit you would like to perform. I entered "P" to request a graphical plot using gnuplot, then "5" for a 5th order-polynomial fit, and finally entered "F" to be used as the variable of the polynomial, and calc output a polynomial in a convenient text format. Minimal edits allowed that to be understood by my circuit simulation program, and I now had a voltage source whose amplitude was a function of the simulation frequency.

3.64573332806e-31 F^5 + 1.20125808335e-25 F^4 - 5.36854825319e-21 F^3 
  + 6.69611214816e-17 F^2 - 2.32309953748e-13 F + 4.68451430373e-10

And it even generates a plot of the input data and the fit at the same time. Very handy.