MATLAB课程：代码示例之Mathematics（三）

widen我的世界

1895

收藏 2016-03-07

MATLAB课程：代码示例之Mathematics（三）

Single Precision Math

This example shows how to perform arithmetic and linear algebra with single precision data. It also shows how the results are computed appropriately in single-precision or double-precision, depending on the input.

Create Double Precision Data

Let's first create some data, which is double precision by default.

Ad = [1 2 0; 2 5 -1; 4 10 -1]

Ad = 1 2 0 2 5 -1 4 10 -1

Convert to Single Precision

We can convert data to single precision with the single function.

A = single(Ad); % or A = cast(Ad,'single');

Create Single Precision Zeros and Ones

We can also create single precision zeros and ones with their respective functions.

n = 1000;Z = zeros(n,1,'single');O = ones(n,1,'single');

Let's look at the variables in the workspace.

whos A Ad O Z n

Name Size Bytes Class Attributes A 3x3 36 single Ad 3x3 72 double O 1000x1 4000 single Z 1000x1 4000 single n 1x1 8 double

We can see that some of the variables are of type single and that the variable A (the single precision version of Ad) takes half the number of bytes of memory to store because singles require just four bytes (32-bits), whereas doubles require 8 bytes (64-bits).

Arithmetic and Linear Algebra

We can perform standard arithmetic and linear algebra on singles.

B = A' % Matrix Transpose

B = 1 2 4 2 5 10 0 -1 -1

whos B

Name Size Bytes Class Attributes B 3x3 36 single

We see the result of this operation, B, is a single.

C = A * B % Matrix multiplication

C =    5 12 24 12 30 59 24 59 117

C = A .* B % Elementwise arithmetic

C =    1    4    0    4 25 -10    0 -10    1

X = inv(A) % Matrix inverse

X =    5    2 -2 -2 -1    1    0 -2    1

I = inv(A) * A % Confirm result is identity matrix

I =    1    0    0    0    1    0    0    0    1

I = A \ A  % Better way to do matrix division than inv

I =    1    0    0    0    1    0    0    0    1

E = eig(A) % Eigenvalues

E = 3.7321 0.2679 1.0000

F = fft(A(:,1)) % FFT

F = 7.0000 + 0.0000i  -2.0000 + 1.7321i  -2.0000 - 1.7321i

S = svd(A) % Singular value decomposition

S = 12.3171 0.5149 0.1577

P = round(poly(A)) % The characteristic polynomial of a matrix

P =    1 -5    5 -1

R = roots(P) % Roots of a polynomial

R = 3.7321 1.0000 0.2679

Q = conv(P,P) % Convolve two vectorsR = conv(P,Q)

Q =    1 -10 35 -52 35 -10    1R =    1 -15 90  -278 480  -480 278 -90 15 -1

stem(R); % Plot the result

A Program that Works for Either Single or Double Precision

Now let's look at a function to compute enough terms in the Fibonacci sequence so the ratio is less than the correct machine epsilon (eps) for datatype single or double.

% How many terms needed to get single precision results?fibodemo('single')% How many terms needed to get double precision results?fibodemo('double')% Now let's look at the working code.type fibodemo% Notice that we initialize several of our variables, |fcurrent|,% |fnext|, and |goldenMean|, with values that are dependent on the% input datatype, and the tolerance |tol| depends on that type as% well. Single precision requires that we calculate fewer terms than% the equivalent double precision calculation.

ans = 19ans = 41function nterms = fibodemo(dtype)%FIBODEMO Used by SINGLEMATH demo.% Calculate number of terms in Fibonacci sequence.% Copyright 1984-2014 The MathWorks, Inc.fcurrent = ones(dtype);fnext = fcurrent;goldenMean = (ones(dtype)+sqrt(5))/2;tol = eps(goldenMean);nterms = 2;while abs(fnext/fcurrent - goldenMean) >= tol nterms = nterms + 1; temp = fnext; fnext = fnext + fcurrent; fcurrent = temp;end

扫码加我拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

扫码加我 拉你入群

分享

扫码加好友，拉您进群

扫码加我拉你入群