创建双精度数据

首先创建一些数据，默认情况下为双精度。

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

Ad = 3×3

1 2 0

2 5 -1

4 10 -1

转换为单精度

可以使用 single 函数将数据转换为单精度。

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

创建单精度零和一

此外，也可以分别使用函数创建单精度零和一。

n = 1000;

Z = zeros(n,1,'single');

O = ones(n,1,'single');

看一下工作区中的变量。

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

可以看到，部分变量的类型为 single，变量 A(Ad 的单精度版本)需要一半的内存字节数用于存储，因为单精度仅需要四字节(32 位)，而双精度需要 8 字节(64 位)。

算术运算和线性代数运算

可以对单精度数据执行标准算术运算和线性代数运算。

B = A' % Matrix Transpose

B = 3x3 single matrix

1 2 4

2 5 10

0 -1 -1

whos B

Name Size Bytes Class Attributes

B 3x3 36 single

可以看出，此操作的结果 B 为单精度。

C = A * B % Matrix multiplication

C = 3x3 single matrix

5 12 24

12 30 59

24 59 117

C = A .* B % Elementwise arithmetic

C = 3x3 single matrix

1 4 0

4 25 -10

0 -10 1

X = inv(A) % Matrix inverse

X = 3x3 single matrix

5 2 -2

-2 -1 1

0 -2 1

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

I = 3x3 single matrix

1 0 0

0 1 0

0 0 1

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

I = 3x3 single matrix

1 0 0

0 1 0

0 0 1

E = eig(A) % Eigenvalues

E = 3x1 single column vector

3.7321

0.2679

1.0000

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

F = 3x1 single column vector

7.0000 + 0.0000i

-2.0000 + 1.7321i

-2.0000 - 1.7321i

S = svd(A) % Singular value decomposition

S = 3x1 single column vector

12.3171

0.5149

0.1577

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

P = 1x4 single row vector

1 -5 5 -1

R = roots(P) % Roots of a polynomial

R = 3x1 single column vector

3.7321

1.0000

0.2679

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

Q = 1x7 single row vector

1 -10 35 -52 35 -10 1

R = conv(P,Q)

R = 1x10 single row vector

1 -15 90 -278 480 -480 278 -90 15 -1

stem(R); % Plot the result

用于处理单精度或双精度的一个程序

现在来看一个函数，该函数用于计算为使比率小于 single 或 double 数据类型的正确机器精度 (eps)，斐波那契数列需要的足够项数。

% How many terms needed to get single precision results?

fibodemo('single')

ans = 19

% How many terms needed to get double precision results?

fibodemo('double')

ans = 41

% Now let's look at the working code.

type fibodemo

function 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

请注意，我们初始化了几个变量，即 fcurrent、fnext 和 goldenMean，初始化所用的值取决于输入数据类型，容差 tol 也取决于该类型。与等效的双精度计算相比，单精度要求计算的项较少。