Real Statistics Release 9.0

The following is an overview of the new features in Release 9.0. 

Neural Networks

The new release adds the following two new data analysis tools that can be accessed from Corr tab to support the building of neural networks with one hidden layer in Excel.

Training a Neural Network: enables you to train a neural network using training data contained in an Excel spreadsheet

Testing a Neural Network: enables you to test how well the neural network that you have built and trained is performing

See Neural Networks for more information about these new capabilities, including an example that shows how to construct a neural network that can be used to recognize hand-written digits 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.

Painting and Coding Images

The new release adds the following three new data analysis tools that can be accessed from Corr tab to support the processing of images constructed by filling cells in an Excel spreadsheet (i.e. pixel art)

Scanning an Image: enables you to code an Excel-based image into RGB or greyscale codes; includes the ability to code a compressed version of the image

Painting an Image: enables you to display an Excel-based image based on a range containing RGB or greyscale codes.

Converting an Image to Greyscale: enables you to replace an Excel-based color image with a greyscale equivalent.

In addition, the new release provides the following new worksheet function:

CodeImage: returns an RGB or greyscale coding of an image

These capabilities have been developed to support neural networks that perform image recognition.

See Coding an Image for more information about these new capabilities.

Greyscale support

Real Statistics supports 66 named colors, including the color “grey” (also labeled “gray”). This color is characterized by an RGB code whose red, green, and blue components are all 128. This results in an RGB code of 128(2562 + 256 + 1) = 8421504.

We will use 128 as the greyscale code for this color. In fact, there are several shades of grey whose greyscale code varies from 0 (black) to 255 (white). All these colors are characterized by the fact that the red, green, and blue components are the same; i.e. each such component is the greyscale code. Starting with this release we add these shades of grey to the list of 66 named colors. E.g. the color “grey150” is the grey color whose greyscale code is 150.

The following new worksheet functions have been added to support greyscale:

Convert2Grey(rgb1) = the greyscale code of the greyscale equivalent of the color with RGB code rgb1.

See Greyscale for additional information about these new capabilities.

Enhanced color support

This release adds the following two worksheet functions that measure the difference between two colors (called the “squared distance”).

ColorDistSq(color1, color2, type) = the squared distance between the two named colors color1 and color2

RGBDistSq(rgb1, rgb2, type) = the squared distance between colors with RGB codes rgb1 and rgb2

type specifies one of three ways of calculating the squared distance between two colors.

The existing FillColor and FontColor worksheet functions have been modified to use these squared distance functions to identify the named color that is closest to a specified color.

See Colors for additional information about these new capabilities.

Rational numbers

This release adds new capabilities that support rational numbers, i.e. a quotient of integers. These capabilities extend existing prime number support.

The new release supports the following new worksheet functions where

Q_n = {h/k : 0 < h < k ≤ n and gcd(h, k) = 1}

FRACS(n): returns an array with three columns. Column 1 contains the values in Q_n in decimal form, and the other two columns contain the corresponding h and k values for an h/k in Q_n

NFRAC(n) = the number of unique elements in Q_n

FRAC2DEC(n, m) = a text representation of m/n as a decimal where 1 ≤ m < n

FRAC_REP(n, m) = the number of repeating digits in the decimal representation of m/n

FRAC_FIXED(n, m) = the number of fixed digits in the decimal representation of m/n

EULER(n) = the Euler number at the positive integer n = # of integers h such that 1 ≤ h < n and gcd(h, n) = 1 

See Rational Numbers for more information about these new capabilities.

New prime number capabilities

This release adds the following new worksheet functions where n is a positive integer:

Divisors(n): returns a column array with the divisors of n

PrimeFactors(n): returns a column array with the prime factors of n

See Prime Numbers for more information about these new capabilities.

Enhancement to eigenvalue/vector functions

The existing eigVAL, eigVALReal, eigVALSym, eigVECT, eigVECTReal, eigVECTSym, SCHUR, and SCHURQ worksheet functions take an order argument. If order = TRUE or -1 (default) then the eigenvalues are arranged in descending order based on the absolute values of their real part; if order = FALSE or 0 then the eigenvalues are arranged in descending order of their real parts.

With this release, we add a third option, namely if order  = +1 then the eigenvalues are not sorted at all. 

Bug-fixes

This release fixes a bug in the HNORM_DIST(x, σ, cum) function when cum = FALSE.