rats

Rational output

Syntax

S = rats(X)

S = rats(X,strlen)

Description

S = rats(X) returns a character vector containing the rational approximations to the elements of X. Asterisks indicate elements that cannot be printed in the allotted space, but which are not negligible compared to the other elements in X.

S = rats(X,strlen) specifies the length of the character vector to use for the rational approximation. For real inputs strlength(S) is equal to strlen+1, while for complex inputs it is equal to 2*strlen+3. The rational approximation uses a tolerance that is inversely proportional to the specified length, as explained in the Algorithms section.

Examples

Rational Representation of Matrix

Create a 4-by-4 matrix.

format short
X = hilb(4)

X = 4×4

    1.0000    0.5000    0.3333    0.2500
    0.5000    0.3333    0.2500    0.2000
    0.3333    0.2500    0.2000    0.1667
    0.2500    0.2000    0.1667    0.1429

View the rational representation of the matrix using rats. The result is the same as using format rat.

R = rats(X)

R = 4×56 char array
    '       1            1/2           1/3           1/4     '
    '      1/2           1/3           1/4           1/5     '
    '      1/3           1/4           1/5           1/6     '
    '      1/4           1/5           1/6           1/7     '

Adjust Output Vector Length

Find the rational representation of pi with the default character vector length and approximation tolerance. The result is the same as using format rat.

rats(pi)

ans = 
'    355/113   '

Adjust the length of the output, which also adjusts the approximation tolerance.

rats(pi,20)

ans = 
'    104348/33215     '

The resulting rational approximation has greater accuracy. As the output length increases, the tolerance decreases.

Adjust the output length again to achieve greater accuracy.

rats(pi,25)

ans = 
'      1146408/364913      '

The resulting approximation agrees with pi to 10 decimal places.

Input Arguments

X — Input array

array

Input array, specified as an array of class single or double.

Data Types: single | double
Complex Number Support: Yes

strlen — Length of character vector

13 (default) | positive integer

Length of character vector, specified as a positive integer. The length of the character vector you specify controls how precise the rational approximation is. Larger character vectors allow for a more accurate rational approximation.

The default length of 13 produces character vectors of length strlen+1 for real inputs and of length 2*strlen+3 for complex inputs.

Algorithms

rats obtains rational approximations with [N,D] = rat(X,tol), where tol is min(10^(-(strlen-1)/2)*norm(X(isfinite(X)),1),.1). Thus, the tolerance is inversely proportional to the output length, strlen.

Extended Capabilities

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced before R2006a