MATLAB低级数组操作精华指南：实用技巧与高效方法

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本篇"MATLAB精简版使用指南"由Peter J. Acklam撰写，旨在提供一系列关于如何在MATLAB中高效进行低级数组操作的实用技巧和窍门。这些操作包括但不限于：数组复制、旋转、插入、提取、元素排列和移动、生成元素组合与排列、数据压缩（如行长度编码和解码）、矩阵乘法与除法，以及计算距离矩阵等。编写快速MATLAB代码的其他一些策略也在此文中得到探讨。作者强调，这份文档的内容主要是为了帮助用户提升在MATLAB中的实践效率，特别是对于那些需要处理大量数组或执行复杂操作的工程师和研究人员而言，这些技巧将大有裨益。文档中还提到，未经许可，个人或教育用途下可以复制或重复使用文档中的材料，但必须尊重版权。值得注意的是，MATLAB是The MathWorks公司的注册商标，而TEX则是美国数学学会的商标。此外，作者特别感谢了Ken Doniger博士、Dr. Denis Gilbert等人，他们在文档的完善过程中提供了宝贵的意见、纠正了错误并做出了其他贡献。本指南是一份详实的MATLAB使用指南，适合希望提高编程效率和理解MATLAB底层操作的读者参考。通过学习和应用其中的技巧，用户将能够更好地利用MATLAB的强大功能，并在实际工作中实现更高效的代码编写。

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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