- •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
Examples
Here are some examples of how you can use these functions.
Concatenating Matrices and Arrays. An alternative to using the [] operator for concatenation are the three functions cat, horzcat, and vertcat. With these functions, you can construct matrices (or multidimensional arrays) along a specified dimension. Either of the following commands accomplish the same task as the command C = [A; B] used in the section on Concatenating Matrices (см. выше):
C = cat(1, A, B); % Concatenate along the first dimension
C = vertcat(A, B); % Concatenate vertically
Replicating a Matrix. Use the repmat function to create a matrix composed of copies of an existing matrix. When you enter
repmat(M, v, h)
MATLAB replicates input matrix M v times vertically and h times horizontally. For example, to replicate existing matrix A into a new matrix B, use
A = [8 1 6; 3 5 7; 4 9 2]
A =
8 1 6
3 5 7
4 9 2
B = repmat(A, 2, 4)
B =
8 1 6 8 1 6 8 1 6 8 1 6
3 5 7 3 5 7 3 5 7 3 5 7
4 9 2 4 9 2 4 9 2 4 9 2
8 1 6 8 1 6 8 1 6 8 1 6
3 5 7 3 5 7 3 5 7 3 5 7
4 9 2 4 9 2 4 9 2 4 9 2
Creating a Block Diagonal Matrix. The blkdiag function combines matrices in a diagonal direction, creating what is called a block diagonal matrix. All other elements of the newly created matrix are set to zero:
A = magic(3);
B = [-5 -6 -9; -4 -4 -2];
C = eye(2) * 8;
D = blkdiag(A, B, C)
D =
8 1 6 0 0 0 0 0
3 5 7 0 0 0 0 0
4 9 2 0 0 0 0 0
0 0 0 -5 -6 -9 0 0
0 0 0 -4 -4 -2 0 0
0 0 0 0 0 0 8 0
0 0 0 0 0 0 0 8
Generating a Numeric Sequence
Because numeric sequences can often be useful in constructing and indexing into matrices and arrays, MATLAB provides a special operator to assist in creating them.
This section covers
The Colon Operator (R2013a>MATLAB>Language Fundamentals>Matrices and Arrays>Array Creation and Concatenation>Creating and Concatenating Matrices)
Using the Colon Operator with a Step Value (R2013a>MATLAB>Language Fundamentals>Matrices and Arrays>Array Creation and Concatenation>Creating and Concatenating Matrices)
The Colon Operator
The colon operator (first:last) generates a 1-by-n matrix (or vector) of sequential numbers from the first value to the last. The default sequence is made up of incremental values, each 1 greater than the previous one:
A = 10:15
A =
10 11 12 13 14 15
The numeric sequence does not have to be made up of positive integers. It can include negative numbers and fractional numbers as well:
A = -2.5:2.5
A =
-2.5000 -1.5000 -0.5000 0.5000 1.5000 2.5000
By default, MATLAB always increments by exactly 1 when creating the sequence, even if the ending value is not an integral distance from the start:
A = 1:6.3
A =
1 2 3 4 5 6
Also, the default series generated by the colon operator always increments rather than decrementing. The operation shown in this example attempts to increment from 9 to 1 and thus MATLAB returns an empty matrix (R2013a>MATLAB>Language Fundamentals>Matrices and Arrays>Sorting and Reshaping Arrays>Empty Matrices, Scalars, and Vectors):
A = 9:1
A =
Empty matrix: 1-by-0
The next section explains how to generate a nondefault numeric series.