- •Matlab r2013a стр. 225
- •Continue Long Statements on Multiple Lines
- •Creating and Concatenating Matrices
- •Overview
- •Constructing a Simple Matrix
- •Entering Signed Numbers
- •Specialized Matrix Functions
- •Examples
- •Concatenating Matrices
- •Keeping Matrices Rectangular
- •Matrix Concatenation Functions
- •Examples
- •Generating a Numeric Sequence
- •The Colon Operator
- •Using the Colon Operator with a Step Value
- •Matrix Indexing
- •Accessing Single Elements
- •Linear Indexing
- •Functions That Control Indexing Style
- •Accessing Multiple Elements
- •Nonconsecutive Elements
- •The end Keyword
- •Specifying All Elements of a Row or Column
- •Using Logicals in Array Indexing
- •Logical Indexing – Example 1
- •Logical Indexing – Example 2
- •Logical Indexing with a Smaller Array
- •Single-Colon Indexing with Different Array Types
- •Indexing on Assignment
- •Arithmetic Operators
- •Arithmetic Operators and Arrays
- •Operator Precedence
- •Precedence of and and or Operators
- •Overriding Default Precedence
- •Relational Operators and Arrays
- •Relational Operators and Empty Arrays
- •Overview of the Logical Class
- •Logical Operators
- •Element-Wise Operators and Functions
- •Short-Circuit Operators
- •Precedence of and and or Operators
- •Symbol Reference
- •Asterisk — *
- •Filename Wildcard
- •Function Handle Constructor
- •Class Folder Designator
- •Line Continuation
- •Dynamic Structure Fields
- •Exclamation Point — !
- •Semicolon — ;
- •Array Row Separator
- •Output Suppression
- •Command or Statement Separator
- •Single Quotes — ' '
- •Square Brackets — [ ]
- •Fundamental matlab Classes
- •More About
- •Overview of Numeric Classes
- •Integers
- •Integer Classes
- •Creating Integer Data
- •Arithmetic Operations on Integer Classes
- •Largest and Smallest Values for Integer Classes
- •Integer Functions
- •Floating-Point Numbers
- •Double-Precision Floating Point
- •Single-Precision Floating Point
- •Creating Floating-Point Data
- •Creating Double-Precision Data
- •Creating Single-Precision Data
- •Arithmetic Operations on Floating-Point Numbers
- •Double-Precision Operations
- •Single-Precision Operations
- •Largest and Smallest Values for Floating-Point Classes
- •Largest and Smallest Double-Precision Values
- •Largest and Smallest Single-Precision Values
- •Accuracy of Floating-Point Data
- •Double-Precision Accuracy
- •Single-Precision Accuracy
- •Avoiding Common Problems with Floating-Point Arithmetic
- •Example 1 — Round-Off or What You Get Is Not What You Expect
- •Example 2 — Catastrophic Cancellation
- •Example 3 — Floating-Point Operations and Linear Algebra
- •Floating-Point Functions
- •Creating a Rectangular Character Array
- •Combining Strings Vertically
- •Combining Strings Horizontally
- •Identifying Characters in a String
- •Working with Space Characters
- •Expanding Character Arrays
- •String Comparisons
- •Comparing Strings for Equality
- •Comparing for Equality Using Operators
- •Categorizing Characters Within a String
- •Create a Structure Array
- •Access Data in a Structure Array
- •Concatenate Structures
- •Generate Field Names from Variables
- •Access Data in Nested Structures
- •Access Elements of a Nonscalar Struct Array
- •Create a Cell Array
- •Access Data in a Cell Array
- •Add Cells to a Cell Array
- •Delete Data from a Cell Array
- •Combine Cell Arrays
- •Pass Contents of Cell Arrays to Functions
- •Multilevel Indexing to Access Parts of Cells
- •Related Examples
- •What Is a Function Handle?
- •Creating a Function Handle
- •Maximum Length of a Function Name
- •The Role of Scope, Precedence, and Overloading When Creating a Function Handle
- •Obtaining Permissions from Class Methods
- •Example
- •Using Function Handles for Anonymous Functions
- •Arrays of Function Handles
- •Calling a Function Using Its Handle
- •Calling Syntax
- •Calling a Function with Multiple Outputs
- •Returning a Handle for Use Outside of a Function File
- •Example — Using Function Handles in Optimization
- •Preserving Data from the Workspace
- •Preserving Data with Anonymous Functions
- •Preserving Data with Nested Functions
- •Loading a Saved Handle to a Nested Function
- •Applications of Function Handles
- •Example of Passing a Function Handle
- •Pass a Function to Another Function
- •Example 1 — Run integral on Varying Functions
- •Example 2 — Run integral on Anonymous Functions
- •Example 3 — Compare integral Results on Different Functions
- •Capture Data Values For Later Use By a Function
- •Example 1 — Constructing a Function Handle that Preserves Its Variables
- •Example 2 — Varying Data Values Stored in a Function Handle
- •Example 3 — You Cannot Vary Data in a Handle to an Anonymous Function
- •Call Functions Outside of Their Normal Scope
- •Save the Handle in a mat-File for Use in a Later matlab Session
- •Parameterizing Functions
- •Overview
- •Parameterizing Using Nested Functions
- •Parameterizing Using Anonymous Functions
- •See Also
- •More About
- •Saving and Loading Function Handles
- •Invalid or Obsolete Function Handles
- •Advanced Operations on Function Handles
- •Examining a Function Handle
- •Converting to and from a String
- •Converting a String to a Function Handle
- •Converting a Function Handle to a String
- •Comparing Function Handles
- •Comparing Handles Constructed from a Named Function
- •Comparing Handles to Anonymous Functions
- •Comparing Handles to Nested Functions
- •Comparing Handles Saved to a mat-File
- •Overview of the Map Data Structure
- •Description of the Map Class
- •Properties of the Map Class
- •Methods of the Map Class
- •Creating a Map Object
- •Constructing an Empty Map Object
- •Constructing An Initialized Map Object
- •Combining Map Objects
- •Examining the Contents of the Map
- •Reading and Writing Using a Key Index
- •Reading From the Map
- •Adding Key/Value Pairs
- •Building a Map with Concatenation
- •Modifying Keys and Values in Map
- •Removing Keys and Values from the Map
- •Modifying Values
- •Modifying Keys
- •Modifying a Copy of the Map
- •Mapping to Different Value Types
- •Mapping to a Structure Array
- •Mapping to a Cell Array
Constructing a Simple Matrix
The simplest way to create a matrix in MATLAB is to use the matrix constructor operator, [] (или {} - для массива ячеек). Create a row in the matrix by entering elements (shown as E below) within the brackets. Separate each element with a comma or space:
row = [E1, E2, ..., Em] row = [E1 E2 ... Em]
For example, to create a one row matrix of five elements, type
A = [12 62 93 -8 22];
To start a new row, terminate the current row with a semicolon:
A = [row1; row2; ...; rown]
This example constructs a 3 row, 5 column (or 3-by-5) matrix of numbers. Note that all rows must have the same number of elements:
A = [12 62 93 -8 22; 16 2 87 43 91; -4 17 -72 95 6]
A =
12 62 93 -8 22
16 2 87 43 91
-4 17 -72 95 6
The square brackets operator constructs two-dimensional matrices only, (including 0-by-0, 1-by-1, and 1-by-n (и n-by-1 ) matrices). To construct arrays of more than two dimensions, see Creating Multidimensional Arrays (R2013a>MATLAB>Language Fundamentals>Matrices and Arrays>Sorting and Reshaping Arrays>Multidimensional Arrays).
For instructions on how to read or overwrite any matrix element, see Matrix Indexing (R2013a>MATLAB>Language Fundamentals>Matrices and Arrays>Indexing).
Entering Signed Numbers
When entering signed numbers into a matrix, make sure that the sign immediately precedes the numeric value. Note that while the following two expressions are equivalent,
7 -2 +5 7 - 2 + 5
ans = ans =
10 10
the next two are not:
[7 -2 +5] [7 - 2 + 5]
ans = ans =
7 -2 5 10
Specialized Matrix Functions
MATLAB has a number of functions that create different kinds of matrices. Some create specialized matrices like the Hankel or Vandermonde matrix. The functions shown in the table below create matrices for more general use.
|
Function |
Description |
|
ones |
Create a matrix or array of all ones. |
|
zeros |
Create a matrix or array of all zeros. |
|
eye |
Create a matrix with ones on the diagonal and zeros elsewhere. |
|
accumarray |
Distribute elements of an input matrix to specified locations in an output matrix, also allowing for accumulation. |
|
diag |
Create a diagonal matrix from a vector. |
|
magic |
Create a square matrix with rows, columns, and diagonals that add up to the same number. |
|
rand |
Create a matrix or array of uniformly distributed random numbers. |
|
randn |
Create a matrix or array of normally distributed random numbers and arrays. |
|
randperm |
Create a vector (1-by-n matrix) containing a random permutation of the specified integers. |
Most of these functions return matrices of type double (double-precision floating point). However, you can easily build basic arrays of any numeric type using the ones, zeros, and eye functions.
To do this, specify the MATLAB class (тип данных) name as the last argument:
A = zeros(4, 6, 'uint32') % Матрица 4х6 беззнаковых 32-разрядных целых чисел:
A =
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0