MATLAB高效数组操作技巧合集

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MATLAB.amtt是由Peter J. Acklam编写的，于2002年8月14日发布的一份文档，专注于提供一系列MATLAB编程中的数组操作技巧和窍门。这份文档主要关注低级别的数组操作，包括但不限于：数组复制、旋转、插入、提取、元素排列、位移、生成元素组合和排列、行长度编码和解码、数组乘法和除法、距离矩阵计算等基础任务。"Manipulation"一词在此指的是对MATLAB中数据结构进行精确、高效的操作。文档不仅涉及基本的数组处理技术，还涵盖了如何编写快速且高效的MATLAB代码的其他方面。作者Peter J. Acklam特别感谢了那些通过提供建议、纠正错误或贡献其他内容的人，按照字母顺序列举了他们的名字，以表示对他们帮助的感激。版权方面，所有内容受2000年至2002年Peter J. Acklam的保留，允许个人或教育用途的复制或复制品制作，但需尊重版权。值得注意的是，MATLAB是The MathWorks, Inc.的注册商标，而TEX则是美国数学学会的商标。这些提及表明在使用这份文档中的内容时，应遵守相应的知识产权规定，链接到各自的官方网站以确保合法合规。这份文档对于MATLAB使用者来说是一份宝贵的资源，尤其对于那些希望提高编程效率、掌握高级数组操作技巧的程序员，它提供了实用的工具和最佳实践，帮助他们优化代码性能。

2 OPERATORS, FUNCTIONS AND SPECIAL CHARACTERS

2.2 Built-in functions

all True if all elements of a vector are nonzero.

any True if any element of a vector is nonzero.

cumsum Cumulative sum of elements.

diag Diagonal matrices and diagonals of a matrix.

diff Difference and approximate derivative.

end Last index in an indexing expression.

eye Identity matrix.

find Find indices of nonzero elements.

isempty True for empty matrix.

isequal True if arrays are numerically equal.

isfinite True for ﬁnite elements.

isinf True for inﬁnite elements.

islogical True for logical array.

isnan True for Not-a-Number.

isnumeric True for numeric arrays.

length Length of vector.

logical Convert numeric values to logical.

ndims Number of dimensions.

numel Number of elements in a matrix.

ones Ones array.

permute Permute array dimensions.

prod Product of elements.

reshape Change size.

size Size of matrix.

sort Sort in ascending order.

sum Sum of elements.

tril Extract lower triangular part.

triu Extract upper triangular part.

zeros Zeros array.

2.3 M-ﬁle functions

flipdim Flip matrix along speciﬁed dimension.

fliplr Flip matrix in left/right direction.

flipud Flip matrix in up/down direction.

ind2sub Multiple subscripts from linear index.

ipermute Inverse permute array dimensions.

kron Kronecker tensor product.

linspace Linearly spaced vector.

ndgrid Generation of arrays for N-D functions and interpolation.

repmat Replicate and tile an array.

rot90 Rotate matrix 90 degrees.

shiftdim Shift dimensions.

squeeze Remove singleton dimensions.

sub2ind Linear index from multiple subscripts.

3 BASIC ARRAY PROPERTIES

3 Basic array properties

3.1 Size

The size of an array is a row vector with the length along all dimensions. The size of the array x can

be found with

sx = size(x); % size of x (along all dimensions)

The length of the size vector sx is the number of dimensions in x. That is, length(size(x))

is identical to ndims(x) (see section 3.2.1). No builtin array class in MATLAB has less than two

dimensions.

To change the size of an array without changing the number of elements, use reshape.

3.1.1 Size along a speciﬁc dimension

To get the length along a speciﬁc dimension dim, of the array x, use

size(x, dim) % size of x (along a specific dimension)

This will return one for all singleton dimensions (see section 3.2.2), and, in particular, it will return

one for all dim greater than ndims(x).

3.1.2 Size along multiple dimension

Sometimes one needs to get the size along multiple dimensions. It would be nice if we could use

size(x, dims), where dims is a vector of dimension numbers, but alas, size only allows the

dimension argument to be a scalar. We may of course use a for-loop solution:

siz = zeros(size(dims)); % initialize size vector to return

for i = 1 : numel(dims) % loop over the elements in dims

siz(i) = size(x, dims(i)); % get the size along dimension

end % end loop

The above works, but a better solution is:

siz = ones(size(dims)); % initialize size vector to return

sx = size(x); % get size along all dimensions

k = dims <= ndims(x); % dimensions known not to be trailing singleton

siz(k) = sx(dims(k)); % insert size along dimensions of interest

Code like the following is sometimes seen, unfortunately. It might be more intuitive than the above,

but it is more fragile since it might use a lot more memory than necessary when dims contains a

large value.

sx = size(x); % get size along all dimensions

n = max(dims(:)) - ndims(x); % number of dimensions to append

sx = [ sx ones(1, n) ]; % pad size vector

siz = sx(dims); % extract dimensions of interest

An unlikely scenario, but imagine what happens if x and dims both are scalars and that dims is a

million. The above code would require more than 8 MB of memory. The suggested solution further

above requires a negligible amount of memory. There is no reason to write fragile code when it can

easily be avoided.

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