有童鞋问我这里面的0, 1, 2是什么意思, permute(x, (1, 0, 2))在我们的数据里(深度2 x 高度3 x 宽度4)指的是0索引的轴(即深度)跟1索引的轴(即高度)做转置。所以,括号里面的数字,代表的是索引及其对应的度量量!. Petsc-3.14.1 2020-11-03. Report Typos and Errors. the matrix to permute row - row permutation, each processor supplies only the permutation for its rows.
- Matlab Tutorial
- MATLAB Advanced
- MATLAB Useful Resources
- Selected Reading
All variables of all data types in MATLAB are multidimensional arrays. A vector is a one-dimensional array and a matrix is a two-dimensional array.
We have already discussed vectors and matrices. In this chapter, we will discuss multidimensional arrays. However, before that, let us discuss some special types of arrays.
Special Arrays in MATLAB
In this section, we will discuss some functions that create some special arrays. For all these functions, a single argument creates a square array, double arguments create rectangular array.
The zeros() function creates an array of all zeros −
For example −
MATLAB will execute the above statement and return the following result −
The ones() function creates an array of all ones −
For example −
MATLAB will execute the above statement and return the following result −
The eye() function creates an identity matrix.
For example −
MATLAB will execute the above statement and return the following result −
The rand() function creates an array of uniformly distributed random numbers on (0,1) −
For example −
MATLAB will execute the above statement and return the following result −
A Magic Square
A magic square is a square that produces the same sum, when its elements are added row-wise, column-wise or diagonally.
The magic() function creates a magic square array. It takes a singular argument that gives the size of the square. The argument must be a scalar greater than or equal to 3.
MATLAB will execute the above statement and return the following result −
Multidimensional Arrays
An array having more than two dimensions is called a multidimensional array in MATLAB. Multidimensional arrays in MATLAB are an extension of the normal two-dimensional matrix.
Generally to generate a multidimensional array, we first create a two-dimensional array and extend it.
For example, let's create a two-dimensional array a.
MATLAB will execute the above statement and return the following result −
The array a is a 3-by-3 array; we can add a third dimension to a, by providing the values like −
MATLAB will execute the above statement and return the following result −
We can also create multidimensional arrays using the ones(), zeros() or the rand() functions.
For example,
MATLAB will execute the above statement and return the following result −
We can also use the cat() function to build multidimensional arrays. It concatenates a list of arrays along a specified dimension −
Syntax for the cat() function is −
Where,
B is the new array created
A1, A2, .. are the arrays to be concatenated
dim is the dimension along which to concatenate the arrays
Example
Create a script file and type the following code into it −
When you run the file, it displays −
Array Functions
MATLAB provides the following functions to sort, rotate, permute, reshape, or shift array contents.
Function | Purpose |
---|---|
length | Length of vector or largest array dimension |
ndims | Number of array dimensions |
numel | Number of array elements |
size | Array dimensions |
iscolumn | Determines whether input is column vector |
isempty | Determines whether array is empty |
ismatrix | Determines whether input is matrix |
isrow | Determines whether input is row vector |
isscalar | Determines whether input is scalar |
isvector | Determines whether input is vector |
blkdiag | Constructs block diagonal matrix from input arguments |
circshift | Shifts array circularly |
ctranspose | Complex conjugate transpose |
diag | Diagonal matrices and diagonals of matrix |
flipdim | Flips array along specified dimension |
fliplr | Flips matrix from left to right |
flipud | Flips matrix up to down |
ipermute | Inverses permute dimensions of N-D array |
permute | Rearranges dimensions of N-D array |
repmat | Replicates and tile array |
reshape | Reshapes array |
rot90 | Rotates matrix 90 degrees |
shiftdim | Shifts dimensions |
issorted | Determines whether set elements are in sorted order |
sort | Sorts array elements in ascending or descending order |
sortrows | Sorts rows in ascending order |
squeeze | Removes singleton dimensions |
transpose | Transpose |
vectorize | Vectorizes expression |
Examples
The following examples illustrate some of the functions mentioned above.
Length, Dimension and Number of elements −
Create a script file and type the following code into it −
When you run the file, it displays the following result −
Permute 2 2 3 7 As A Fraction
Circular Shifting of the Array Elements −
Create a script file and type the following code into it −
When you run the file, it displays the following result −
Syntax for the cat() function is −
Where,
B is the new array created
A1, A2, .. are the arrays to be concatenated
dim is the dimension along which to concatenate the arrays
Example
Create a script file and type the following code into it −
When you run the file, it displays −
Array Functions
MATLAB provides the following functions to sort, rotate, permute, reshape, or shift array contents.
Function | Purpose |
---|---|
length | Length of vector or largest array dimension |
ndims | Number of array dimensions |
numel | Number of array elements |
size | Array dimensions |
iscolumn | Determines whether input is column vector |
isempty | Determines whether array is empty |
ismatrix | Determines whether input is matrix |
isrow | Determines whether input is row vector |
isscalar | Determines whether input is scalar |
isvector | Determines whether input is vector |
blkdiag | Constructs block diagonal matrix from input arguments |
circshift | Shifts array circularly |
ctranspose | Complex conjugate transpose |
diag | Diagonal matrices and diagonals of matrix |
flipdim | Flips array along specified dimension |
fliplr | Flips matrix from left to right |
flipud | Flips matrix up to down |
ipermute | Inverses permute dimensions of N-D array |
permute | Rearranges dimensions of N-D array |
repmat | Replicates and tile array |
reshape | Reshapes array |
rot90 | Rotates matrix 90 degrees |
shiftdim | Shifts dimensions |
issorted | Determines whether set elements are in sorted order |
sort | Sorts array elements in ascending or descending order |
sortrows | Sorts rows in ascending order |
squeeze | Removes singleton dimensions |
transpose | Transpose |
vectorize | Vectorizes expression |
Examples
The following examples illustrate some of the functions mentioned above.
Length, Dimension and Number of elements −
Create a script file and type the following code into it −
When you run the file, it displays the following result −
Permute 2 2 3 7 As A Fraction
Circular Shifting of the Array Elements −
Create a script file and type the following code into it −
When you run the file, it displays the following result −
Permute 2 2 3 7 X
Sorting Arrays
Create a script file and type the following code into it −
When you run the file, it displays the following result −
Cell Array
Cell arrays are arrays of indexed cells where each cell can store an array of a different dimensions and data types.
Permute 2 2 3 700
The cell function is used for creating a cell array. Syntax for the cell function is −
Where,
C is the cell array;
dim is a scalar integer or vector of integers that specifies the dimensions of cell array C;
dim1, .. , dimN are scalar integers that specify the dimensions of C;
obj is One of the following −
- Java array or object
- .NET array of type System.String or System.Object
Example
Create a script file and type the following code into it −
When you run the file, it displays the following result −
Accessing Data in Cell Arrays
There are two ways to refer to the elements of a cell array −
- Enclosing the indices in first bracket (), to refer to sets of cells
- Enclosing the indices in braces {}, to refer to the data within individual cells
When you enclose the indices in first bracket, it refers to the set of cells.
Permute 2
Cell array indices in smooth parentheses refer to sets of cells.
Movavi video editor 15 2 0 download. For example −
MATLAB will execute the above statement and return the following result −
Permute 2 2 3 70
You can also access the contents of cells by indexing with curly braces.
For example −
MATLAB will execute the above statement and return the following result −
Calculator Use
Like the Combinations Calculator the Permutations Calculator finds the number of subsets that can be taken from a larger set. However, the order of the subset matters. The Permutations Calculator finds the number of subsets that can be created including subsets of the same items in different orders.
- Factorial
- There are n! ways of arranging n distinct objects into an ordered sequence, permutations where n = r.
- Combination
- The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.
- Permutation
- The number of ways to choose a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed. When n = r this reduces to n!, a simple factorial of n.
- Combination Replacement
- The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are allowed.
- Permutation Replacement
- The number of ways to choose a sample of r elements from a set of n distinct objects where order does matter and replacements are allowed.
- n
- the set or population
- r
- subset of n or sample set
Permutations Formula:
For n ≥ r ≥ 0.
Calculate the permutations for P(n,r) = n! / (n - r)!. 'The number of ways of obtaining an ordered subset of r elements from a set of n elements.'[1]
Permutation Problem 1
Choose 3 horses from group of 4 horses
In a race of 15 horses you beleive that you know the best 4 horses and that 3 of them will finish in the top spots: win, place and show (1st, 2nd and 3rd). So out of that set of 4 horses you want to pick the subset of 3 winners and the order in which they finish. How many different permutations are there for the top 3 from the 4 best horses?
For this problem we are looking for an ordered subset of 3 horses (r) from the set of 4 best horses (n). We are ignoring the other 11 horses in this race of 15 because they do not apply to our problem. We must calculate P(4,3) in order to find the total number of possible outcomes for the top 3 winners.
P(4,3) = 4! / (4 - 3)! = 24 Possible Race Results
If our 4 top horses have the numbers 1, 2, 3 and 4 our 24 potential permutations for the winning 3 are {1,2,3}, {1,3,2}, {1,2,4}, {1,4,2}, {1,3,4}, {1,4,3}, {2,1,3}, {2,3,1}, {2,1,4}, {2,4,1}, {2,3,4}, {2,4,3}, {3,1,2}, {3,2,1}, {3,1,4}, {3,4,1}, {3,2,4}, {3,4,2}, {4,1,2}, {4,2,1}, {4,1,3}, {4,3,1}, {4,2,3}, {4,3,2}
Permutation Problem 2
Choose 3 contestants from group of 12 contestants
At a high school track meet the 400 meter race has 12 contestants. The top 3 will receive points for their team. How many different permutations are there for the top 3 from the 12 contestants?
For this problem we are looking for an ordered subset 3 contestants (r) from the 12 contestants (n). We must calculate P(12,3) in order to find the total number of possible outcomes for the top 3.
P(12,3) = 12! / (12-3)! = 1,320 Possible Outcomes
Permutation Problem 3
Choose 5 players from a set of 10 players
An NFL team has the 6th pick in the draft, meaning there are 5 other teams drafting before them. If the team believes that there are only 10 players that have a chance of being chosen in the top 5, how many different orders could the top 5 be chosen?
For this problem we are finding an ordered subset of 5 players (r) from the set of 10 players (n).
P(10,5)=10!/(10-5)!= 30,240 Possible Orders
References
[1] For more information on permutations and combinations please see Wolfram MathWorld: Permutation.