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cumsum

Symbolic cumulative sum

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Syntax

B = cumsum(A)
B = cumsum(A,dim)
B = cumsum(___,direction)
B = cumsum(___,nanflag)

Description

example

B= cumsum(A)returns the cumulative sum ofAstarting at the beginning of the first array dimension inAwhose size does not equal 1. The outputBhas the same size asA.

  • IfAis a vector, thencumsum(A)returns a vector containing the cumulative sum of the elements ofA.

  • IfAis a matrix, thencumsum(A)returns a matrix containing the cumulative sums of each column ofA.

  • IfAis a multidimensional array, thencumsum(A)acts along thefirst nonsingleton dimension.

example

B= cumsum(A,dim)returns the cumulative sum along dimensiondim. For example, ifAis a matrix, thencumsum(A,2)returns the cumulative sum of each row.

example

B= cumsum(___,direction)specifies the direction using any of the previous syntaxes. For instance,cumsum(A,2,'reverse')returns the cumulative sum within the rows ofAby working from end to beginning of the second dimension.

example

B= cumsum(___,nanflag)specifies whether to include or omitNaNvalues from the calculation for any of the previous syntaxes.cumsum(A,'includenan')includes allNaN在计算值cumsum(A,'omitnan')ignores them.

Examples

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Open Live Script

Create a symbolic vector. Find the cumulative sum of its elements.

symsxA = (1:5)*x
A =
                       
                        
                         
                          
                           (
                          
                           
                            
                             
                              
                               x
                             
                            
                            
                             
                              
                               
                                
                                 2
                                
                                
                                
                                 x
                               
                              
                             
                            
                            
                             
                              
                               
                                
                                 3
                                
                                
                                
                                 x
                               
                              
                             
                            
                            
                             
                              
                               
                                
                                 4
                                
                                
                                
                                 x
                               
                              
                             
                            
                            
                             
                              
                               
                                
                                 5
                                
                                
                                
                                 x
                               
                              
                             
                            
                           
                          
                          
                           )

In the vector of cumulative sums, elementB(2)is the sum ofA(1)andA(2), whileB(5)is the sum of elementsA(1)throughA(5).

B = cumsum(A)
B =
                       
                        
                         
                          
                           (
                          
                           
                            
                             
                              
                               x
                             
                            
                            
                             
                              
                               
                                
                                 3
                                
                                
                                
                                 x
                               
                              
                             
                            
                            
                             
                              
                               
                                
                                 6
                                
                                
                                
                                 x
                               
                              
                             
                            
                            
                             
                              
                               
                                
                                 10
                                
                                
                                
                                 x
                               
                              
                             
                            
                            
                             
                              
                               
                                
                                 15
                                
                                
                                
                                 x
                               
                              
                             
                            
                           
                          
                          
                           )
Open Live Script

Create a 3-by-3 symbolic matrixAwhose elements are all equal to 1.

A = sym(ones(3))
A =

                       

                        
                         
                          
                           
                            (
                           
                            
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                1
                              
                             
                            
                            
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                1
                              
                             
                            
                            
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                1
                              
                             
                            
                           
                           
                            )

Compute the cumulative sum of elements ofA. By default,cumsumreturns the cumulative sum of each column.

B = cumsum(A)
B =

                       

                        
                         
                          
                           
                            (
                           
                            
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                1
                              
                             
                            
                            
                             
                              
                               
                                2
                              
                             
                             
                              
                               
                                2
                              
                             
                             
                              
                               
                                2
                              
                             
                            
                            
                             
                              
                               
                                3
                              
                             
                             
                              
                               
                                3
                              
                             
                             
                              
                               
                                3
                              
                             
                            
                           
                           
                            )

To compute the cumulative sum of each row, set the value of thedimoption to2.

B = cumsum(A,2)
B =

                       

                        
                         
                          
                           
                            (
                           
                            
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                2
                              
                             
                             
                              
                               
                                3
                              
                             
                            
                            
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                2
                              
                             
                             
                              
                               
                                3
                              
                             
                            
                            
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                2
                              
                             
                             
                              
                               
                                3
                              
                             
                            
                           
                           
                            )
Open Live Script

Create a 3-by-3-by-2 symbolic array.

symsxyA(:,:,1) = [x y 3; 3 x y; y 2 x]; A(:,:,2) = [x y 1/3; 1 y x; 1/3 x 2]; A
A(:,:,1) =

                       

                        
                         
                          
                           
                            (
                           
                            
                             
                              
                               
                                x
                              
                             
                             
                              
                               
                                y
                              
                             
                             
                              
                               
                                3
                              
                             
                            
                            
                             
                              
                               
                                3
                              
                             
                             
                              
                               
                                x
                              
                             
                             
                              
                               
                                y
                              
                             
                            
                            
                             
                              
                               
                                y
                              
                             
                             
                              
                               
                                2
                              
                             
                             
                              
                               
                                x
                              
                             
                            
                           
                           
                            )
                          
                         
                        

                      
A(:,:,2) =

                       

                        
                         
                          
                           
                            (
                           
                            
                             
                              
                               
                                x
                              
                             
                             
                              
                               
                                y
                              
                             
                             
                              
                               
                                
                                 
                                  1
                                
                                
                                 
                                  3
                                
                               
                              
                             
                            
                            
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                y
                              
                             
                             
                              
                               
                                x
                              
                             
                            
                            
                             
                              
                               
                                
                                 
                                  1
                                
                                
                                 
                                  3
                                
                               
                              
                             
                             
                              
                               
                                x
                              
                             
                             
                              
                               
                                2
                              
                             
                            
                           
                           
                            )

Compute the cumulative sum along the rows by specifyingdimas2. Specify the“反向”选择工作right to left in each row. The result is the same size asA.

B = cumsum(A,2,“反向”)
B(:,:,1) =

                       

                        
                         
                          
                           
                            (
                           
                            
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  y
                                 
                                  +
                                 
                                  3
                                
                               
                              
                             
                             
                              
                               
                                
                                 
                                  y
                                 
                                  +
                                 
                                  3
                                
                               
                              
                             
                             
                              
                               
                                3
                              
                             
                            
                            
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  y
                                 
                                  +
                                 
                                  3
                                
                               
                              
                             
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  y
                                
                               
                              
                             
                             
                              
                               
                                y
                              
                             
                            
                            
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  y
                                 
                                  +
                                 
                                  2
                                
                               
                              
                             
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  2
                                
                               
                              
                             
                             
                              
                               
                                x
                              
                             
                            
                           
                           
                            )
                          
                         
                        

                      
B(:,:,2) =

                       

                        
                         
                          
                           
                            (
                           
                            
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  y
                                 
                                  +
                                 
                                  
                                   
                                    1
                                  
                                  
                                   
                                    3
                                  
                                 
                                
                               
                              
                             
                             
                              
                               
                                
                                 
                                  y
                                 
                                  +
                                 
                                  
                                   
                                    1
                                  
                                  
                                   
                                    3
                                  
                                 
                                
                               
                              
                             
                             
                              
                               
                                
                                 
                                  1
                                
                                
                                 
                                  3
                                
                               
                              
                             
                            
                            
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  y
                                 
                                  +
                                 
                                  1
                                
                               
                              
                             
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  y
                                
                               
                              
                             
                             
                              
                               
                                x
                              
                             
                            
                            
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  
                                   
                                    7
                                  
                                  
                                   
                                    3
                                  
                                 
                                
                               
                              
                             
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  2
                                
                               
                              
                             
                             
                              
                               
                                2
                              
                             
                            
                           
                           
                            )

To compute the cumulative sum along the third (page) dimension, specifydimas3. Specify the“反向”选择工作largest page index to smallest page index.

B = cumsum(A,3,“反向”)
B(:,:,1) =

                       

                        
                         
                          
                           
                            (
                           
                            
                             
                              
                               
                                
                                 
                                  2
                                 
                                 
                                 
                                  x
                                
                               
                              
                             
                             
                              
                               
                                
                                 
                                  2
                                 
                                 
                                 
                                  y
                                
                               
                              
                             
                             
                              
                               
                                
                                 
                                  10
                                
                                
                                 
                                  3
                                
                               
                              
                             
                            
                            
                             
                              
                               
                                4
                              
                             
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  y
                                
                               
                              
                             
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  y
                                
                               
                              
                             
                            
                            
                             
                              
                               
                                
                                 
                                  y
                                 
                                  +
                                 
                                  
                                   
                                    1
                                  
                                  
                                   
                                    3
                                  
                                 
                                
                               
                              
                             
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  2
                                
                               
                              
                             
                             
                              
                               
                                
                                 
                                  x
                                 
                                  +
                                 
                                  2
                                
                               
                              
                             
                            
                           
                           
                            )
                          
                         
                        

                      
B(:,:,2) =

                       

                        
                         
                          
                           
                            (
                           
                            
                             
                              
                               
                                x
                              
                             
                             
                              
                               
                                y
                              
                             
                             
                              
                               
                                
                                 
                                  1
                                
                                
                                 
                                  3
                                
                               
                              
                             
                            
                            
                             
                              
                               
                                1
                              
                             
                             
                              
                               
                                y
                              
                             
                             
                              
                               
                                x
                              
                             
                            
                            
                             
                              
                               
                                
                                 
                                  1
                                
                                
                                 
                                  3
                                
                               
                              
                             
                             
                              
                               
                                x
                              
                             
                             
                              
                               
                                2
                              
                             
                            
                           
                           
                            )
Open Live Script

Create a symbolic vector containingNaNvalues. Compute the cumulative sums.

A = [sym('a') sym('b') 1 NaN 2]
A =
                       
                        
                         
                          
                           (
                          
                           
                            
                             
                              
                               a
                             
                            
                            
                             
                              
                               b
                             
                            
                            
                             
                              
                               1
                             
                            
                            
                             
                              
                               NaN
                             
                            
                            
                             
                              
                               2
                             
                            
                           
                          
                          
                           )
                         
                        
                       
B = cumsum(A)
B =
                       
                        
                         
                          
                           (
                          
                           
                            
                             
                              
                               a
                             
                            
                            
                             
                              
                               
                                
                                 a
                                
                                 +
                                
                                 b
                               
                              
                             
                            
                            
                             
                              
                               
                                
                                 a
                                
                                 +
                                
                                 b
                                
                                 +
                                
                                 1
                               
                              
                             
                            
                            
                             
                              
                               NaN
                             
                            
                            
                             
                              
                               NaN
                             
                            
                           
                          
                          
                           )

You can ignoreNaNvalues in the cumulative sum calculation using the'omitnan'option.

B = cumsum(A,'omitnan')
B =
                       
                        
                         
                          
                           (
                          
                           
                            
                             
                              
                               a
                             
                            
                            
                             
                              
                               
                                
                                 a
                                
                                 +
                                
                                 b
                               
                              
                             
                            
                            
                             
                              
                               
                                
                                 a
                                
                                 +
                                
                                 b
                                
                                 +
                                
                                 1
                               
                              
                             
                            
                            
                             
                              
                               
                                
                                 a
                                
                                 +
                                
                                 b
                                
                                 +
                                
                                 1
                               
                              
                             
                            
                            
                             
                              
                               
                                
                                 a
                                
                                 +
                                
                                 b
                                
                                 +
                                
                                 3
                               
                              
                             
                            
                           
                          
                          
                           )

Input Arguments

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Input array, specified as a symbolic vector, matrix, or multidimensional array.

Dimension to operate along, specified as a positive integer scalar. If no value is specified, then the default is the first array dimension whose size does not equal 1.

Consider a two-dimensional input array,A:

  • cumsum(A,1)works on successive elements in the columns ofAand returns the cumulative sum of each column.

  • cumsum(A,2)works on successive elements in the rows ofAand returns the cumulative sum of each row.

cumsumreturnsAifdimis greater thanndims(A).

Direction of cumulation, specified as'forward'(default) or“反向”.

  • 'forward'works from1toendof the active dimension.

  • “反向”works fromendto1of the active dimension.

Data Types:char

NaNcondition, specified as:

  • 'includenan'— IncludeNaNvalues from the input when computing the cumulative sums, resulting inNaNvalues in the output.

  • 'omitnan'— Ignore allNaNvalues in the input. The sum of elements containingNaNvalues is the sum of all non-NaN元素。如果所有elements areNaN, thencumsumreturns 0.

Data Types:char

Output Arguments

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Cumulative sum array, returned as a vector, matrix, or multidimensional array of the same size as the inputA.

More About

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First Nonsingleton Dimension

The first nonsingleton dimension is the first dimension of an array whose size is not equal to 1.

For example:

  • IfXis a 1-by-n row vector, then the second dimension is the first nonsingleton dimension ofX.

  • IfXis a 1-by-0-by-n empty array, then the second dimension is the first nonsingleton dimension ofX.

  • IfXis a 1-by-1-by-3 array, then the third dimension is the first nonsingleton dimension ofX.

Version History

Introduced in R2013b

See Also

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