使用矢量化

马铃薯^®is optimized for operations involving matrices and vectors. The process of revising loop-based, scalar-oriented code to use MATLAB matrix and vector operations is calledvectorization。Vectorizing your code is worthwhile for several reasons:

我= 0;对于t = 0：.01：10 i = i + 1;y（i）= sin（t）;结束

t = 0：.01：10;y = sin（t）;

x = 1:10000; ylength = (length(x) - mod(length(x),5))/5; y(1:ylength) = 0; for n= 5:5:length(x) y(n/5) = sum(x(1:n)); end

x = 1:10000; xsums = cumsum(x); y = xsums(5:5:length(x));

Array Operations

Array operators perform the same operation for all elements in the data set. These types of operations are useful for repetitive calculations. For example, suppose you collect the volume (V) of various cones by recording their diameter (D) and height (H). If you collect the information for just one cone, you can calculate the volume for that single cone:

V = 1/12*pi*(D^2)*H;

Now, collect information on 10,000 cones. The vectorsDandHeach contain 10,000 elements, and you want to calculate 10,000 volumes. In most programming languages, you need to set up a loop similar to this MATLAB code:

对于n = 1：10000 V（n）= 1/12 * pi *（d（n）^ 2）* h（n））;结束

With MATLAB, you can perform the calculation for each element of a vector with similar syntax as the scalar case:

% Vectorized Calculationv = 1/12 * pi *（d。^ 2）。* h;

Array operators also enable you to combine matrices of different dimensions. This automatic expansion of size-1 dimensions is useful for vectorizing grid creation, matrix and vector operations, and more.

假设矩阵A代表测试分数，其中的行表示不同的类别。您希望计算每个类的平均分数和各个分数之间的差异。使用循环，操作看起来像：

A = [97 89 84; 95 82 92; 64 80 99;76 77 67;。。。88 59 74; 78 66 87; 55 93 85]; mA = mean(A); B = zeros(size(A));对于n = 1:size(A,2) B(:,n) = A(:,n) - mA(n);结束

A more direct way to do this is witha - 平均（a）, which avoids the need of a loop and is significantly faster.

deva = a  - 意思是（a）

Deva = 18 11 0 16 4 8 -15 2 15 -3 -1 -17 9 -19 -10 -1 -12 3 -24 15 1

Even thoughA是一个7×3矩阵和mean(A)是一个1-×3矢量，MATLAB隐式扩展矢量，因为它与矩阵具有与矩阵相同的尺寸，并且操作执行为正常元素 - WISE减去操作。

操作数的大小要求是，对于每个维度，阵列必须具有相同的大小或其中一个。如果满足此要求，则阵列之一具有大小1的尺寸将扩展为相同的大小作为其他阵列中的相应维度。有关更多信息，请参阅兼容数组大小，用于基本操作。

如果您正在使用多维数据，则隐式扩展非常有用的另一个区域。假设您想要评估函数，F, of two variables,xandy。

F(x,y) = x*exp(-x2- y2)

To evaluate this function at every combination of points in thexandy向量,您需要定义一个网格的值。为this task you should avoid using loops to iterate through the point combinations. Instead, if one of the vectors is a column and the other is a row, then MATLAB automatically constructs the grid when the vectors are used with an array operator, such asx+yorx-y。在这个例子中，xis a 21-by-1 vector andyis a 1-by-16 vector, so the operation produces a 21-by-16 matrix by expanding the second dimension ofxand the first dimension ofy。

x = (-2:0.2:2)';％21-by-1y = -1.5:0.2:1.5;％1-by-16F = x.*exp(-x.^2-y.^2);％21-by-16

在您想要显式创建网格的情况下，您可以使用meshgrid.andndgridfunctions.

Logical Array Operations

阵列的批量处理的逻辑扩展是矢量化比较和决策。Matlab比较运算符接受向量输入和返回向量输出。

为example, suppose while collecting data from 10,000 cones, you record several negative values for the diameter. You can determine which values in a vector are valid with the>=操作员：

D = [-0.2 1.0 1.5 3.0 -1.0 4.2 3.14]; D >= 0

ans = 0 1 1 1 0 1 1

vgood.= V(D >= 0);

MATLAB允许您使用函数执行整个向量的逻辑且或或或或上的元素allandany, respectively. You can throw a warning if all values ofD低于零：

如果所有（d <0）警告（'All values of diameter are negative.')返回结束

马铃薯can also compare two vectors with compatible sizes, allowing you to impose further restrictions. This code finds all the values where V is nonnegative andDis greater thanH:

V((V >= 0) & (D > H))

为了帮助比较，MATLAB包含特殊值，以表示溢出，下溢和未定义的运算符，例如Infand南。Logical operatorsisinfandisnanexist to help perform logical tests for these special values. For example, it is often useful to exclude南计算中的值：

x = [2 -1 0 3 nan 2 nan 11 4 inf];xvalid = x（〜isnan（x））

xvalid = 2 -1 0 3 2 11 4 inf

Matrix Operations

When vectorizing code, you often need to construct a matrix with a particular size or structure. Techniques exist for creating uniform matrices. For instance, you might need a 5-by-5 matrix of equal elements:

A = ones(5,5)*10;

v = 1:5; A = repmat(v,3,1)

A = 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

The functionrepmatpossesses flexibility in building matrices from smaller matrices or vectors.repmat通过重复输入矩阵创建矩阵：

A = repmat(1:3,5,2) B = repmat([1 2; 3 4],2,2)

A = 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 B = 1 2 1 2 3 4 3 4 1 2 1 2 3 4 3 4

Ordering, Setting, and Counting Operations

在许多应用中，在向量的元素上完成的计算取决于同一向量中的其他元素。例如，一个向量，x，可能代表一组。如何迭代一套没有a对于orwhileloop is not obvious. The process becomes much clearer and the syntax less cumbersome when you use vectorized code.

x = [2 1 2 2 3 1 3 2 1 3]; x = sort(x); difference = diff([x,NaN]); y = x(difference~=0)

y = 1 2 3

Y =唯一（x）;

x = [2 1 2 2 3 1 3 2 1 3]; x = sort(x); difference = diff([x,max(x)+1]); count = diff(find([1,difference])) y = x(find(difference))

count = 3 4 3 y = 1 2 3

count_nans = sum(isnan(x(:))); count_infs = sum(isinf(x(:)));

Functions Commonly Used in Vectorization