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From Sébastien Brisard (Updated) (JIRA) <j...@apache.org>
Subject [jira] [Updated] (MATH-765) Refactoring the vector and matrix classes
Date Thu, 15 Mar 2012 06:41:38 GMT

     [ https://issues.apache.org/jira/browse/MATH-765?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]

Sébastien Brisard updated MATH-765:
-----------------------------------

    Description: 
{panel:title=Warning|borderStyle=solid}
This is not a bug report, but rather a summary of all discussions which have taken place on
the mailing list regarding the refactoring of the vector and matrix classes. Indeed, it has
been argued many times that the {{RealVector}} and {{RealMatrix}} interfaces are really cluttered,
and could benefit from other approaches (like functional programming). 

The description of this ticket will be updated as the discussion progresses on the mailing-list,
and new JIRA tickets will be created to carry out the "real" work. {color:red}In order to
keep this ticket tidy, contributors should refrain from commenting on this website. Instead,
messages should be posted on the dev mailing-list{color}.
{panel}


h1. The current API (version 3.0)

In this section, the current interfaces for vectors and matrices are compared. Vectors and
matrices are two mathematical objects which are very close in nature. Their implementations
should therefore be as similar as possible. The methods will be sorted as follows
* methods reflecting the mathematical structure of vector space: addition, multiplication
by a scalar, matrix-vector product, ...
* methods reflecting the mathematical structure of euclidean space
* ...

h2. Methods reflecting the mathematical structure of vector space
h3. List of the methods
|| {{RealVector}}                            || {{RealMatrix}}                           
               || Comments ||
| {{RealVector add(RealVector v)}}           | {{RealMatrix add(RealMatrix m)}}          
               |           |
| {{RealVector subtract(RealVector v)}}      | {{RealMatrix subtract(RealMatrix m)}}     
               |           |
| {{int getDimension()}}                     | {{int getRowDimension()}},\\ {{int getColumnDimension()}}
|           |
| {{RealVector mapMultiply(double d)}}       | {{scalarMultiply(double d)}}              
               | (1)       |
| {{RealVector mapMultiplyToSelf(double d)}} |                                           
               |           |
| {{RealVector outerProduct(RealVector v)}}  |                                           
               |           |
|                                            | {{double getTrace()}}                     
               |           |
|                                            | {{multiply(RealMatrix m)}}                
               |           |
|                                            | {{double[] operate(double[])}}            
               | (2)       |
|                                            | {{RealVector operate(RealVector)}}        
               |           |
|                                            | {{RealMatrix power(int p)}}               
               |           |
|                                            | {{double[] preMultiply(double[])}}        
               | (2)       |
|                                            | {{RealMatrix preMultiply(RealMatrix)}}    
               |           |
|                                            | {{RealVector preMultiply(RealVector)}}    
               |           |
|                                            | {{RealMatrix transpose()}}                
               |           |

h3. Comments on the above methods
h4. Comment (1)
{{RealVector RealVector.mapMultiply(double)}} and {{RealMatrix RealMatrix.scalarMultiply(double)}}
perform essentially the same task. Readibility of the classes would be improved if they add
the same name. This is very important since these methods reflect the fact that the space
of vectors as well as the space of matrices are two vector spaces.

h4. Comment (2)
Prior to the release of version 3.0, all methods taking as argument, or returning, {{double[]}}
as a representation of vectors were removed. The rationale for this is that calling {{new
ArrayRealVector(double[], false)}} is very easy, and comes at virtually no cost (see MATH-653
and MATH-660). It might be worth considering the same simplification for the {{RealMatrix}}
interface.

h2. Methods reflecting the mathematical structure of euclidean space
h3. List of the methods
|| {{RealVector}}                         || {{RealMatrix}}               || Comments ||
| {{double cosine(RealVector v)}}         |                               |           |
| {{double dotProduct(RealVector v)}}     |                               | (3)       |
| {{double getDistance(RealVector v)}}    |                               |           |
| {{double getNorm()}}                    | {{double getFrobeniusNorm()}} |           |
| {{RealVector projection(RealVector v)}} |                               |           |
| {{void unitize()}}                      |                               | (4)       |
| {{RealVector unitVector()}}             |                               |           |

h3. Comments on the above methods
h4. Comment (3)
In a way, {{RealMatrix RealMatrix.transpose()}} could be seen as a method inherent to the
euclidean structure, and the generalization of the dot product. For this reason, {{transpose()}}
should probably _not_ be externalized.

h4. Comment (4)
This could be externalized with the visitor pattern (see below).

h4. Comment (5)
Could be externalized in a factory class.

h2. Constructors, factory methods and related methods
h3. List of the methods
|| {{RealVector}}                                || {{RealMatrix}}                       
                                                                  || Comments ||
| {{RealVector append(double d)}}                |                                       
                                                                  | |
| {{RealVector append(RealVector v)}}            |                                       
                                                                  | |
| {{RealVector copy()}}                          | {{RealMatrix copy()}}                 
                                                                  | |
|                                                | {{void copySubMatrix(int[] selectedRows,
int[] selectedColumns, double[][] destination)}}                | (6), (7) |
|                                                | {{void copySubMatrix(int startRow, int
endRow, int startColumn, int endColumn, double[][] destination)}} | (7) |
|                                                | {{createMatrix(int rowDimension, int columnDimension)}}
                                                 | (9) |
|                                                | {{double[] getColumn(int column)}}    
                                                                  | (6) |
|                                                | {{RealMatrix getColumnMatrix(int column)}}
                                                              | |
|                                                | {{RealVector getColumnVector(int column)}}
                                                              | |
|                                                | {{double[] getRow(int row)}}          
                                                                  | (6) |
|                                                | {{RealMatrix getRowMatrix(int row)}}  
                                                                  | |
|                                                | {{RealVector getRowVector(int row)}}  
                                                                  | |
|                                                | {{RealMatrix getSubMatrix(int[] selectedRows,
int[] selectedColumns)}}                                   | |
| {{RealVector getSubVector(int index, int n)}}  | {{RealMatrix getSubMatrix(int startRow,
int endRow, int startColumn, int endColumn)}}                    | (8) |
|                                                | {{void setColumn(int column, double[] array)}}
                                                          | (6) |
|                                                | {{void setColumnMatrix(int column, RealMatrix
matrix)}}                                                  | |
|                                                | {{void setColumnVector(int column, RealVector
vector)}}                                                  | |
|                                                | {{void setRow(int row, double[] array)}}
                                                                | (6) |
|                                                | {{void setRowMatrix(int row, RealMatrix
matrix)}}                                                        | |
|                                                | {{void setRowVector(int row, RealVector
vector)}}                                                        | |
| {{void setSubVector(int index, RealVector v)}} | {{void setSubMatrix(double[][] subMatrix,
int row, int column)}}                                         | (6) |
| {{unmodifiableRealVector(RealVector v)}} |                                             
                                                                  | |

h3. Comments on the above methods
h4. Comment (6)
Prior to the release of version 3.0, all methods taking as argument, or returning, {{double[]}}
as a representation of vectors were removed. The rationale for this is that calling {{new
ArrayRealVector(double[], false)}} is very easy, and comes at virtually no cost (see MATH-653
and MATH-660). It might be worth considering the same simplification for the {{RealMatrix}}
interface.

h4. Comment (7)
The signature of this method is rather unusual in Commons-Math, as one of the parameters is
modified, and nothing is returned.

h4. Comment (8)
Inconsistency: in {{getSubVector(int, int)}}, the second parameter is the number of entries
to be copied, while in {{getSubMatrix(int, int, int, int)}} the second (resp. fourth) parameters
are the indices of the last row (resp. column).

h4. Comment (9)
This is a very useful method: one often needs to create a new vector/matrix with same data
layout as an existing vector/matrix. This method should probably be generalized to {{RealVector}}
as well.

h2. Manipulation of entries
h3. List of the methods
|| {{RealVector}}                                  || {{RealMatrix}}                     
                      || Comments ||
| {{double getEntry(int index)}}                   | {{double getEntry(int row, int column)}}
                  |           |
| {{void set(double value)}}                       |                                     
                      | (10)      |
| {{void setEntry(int index, double value)}}       | {{void setEntry(int row, int column,
double value)}}       |           |
| {{void addToEntry(int index, double increment)}} | {{void addToEntry(int row, int column,
double increment)}} | (11)      |
|                                                  | {{void multiplyEntry(int row, int column,
double factor)}} | (11)      |

h3. Comments on these methods
h4. Comment (10)
This useful method could be extended to {{RealMatrix}} as well. However, it could be argued
that this method is superfluous, as the visitor pattern (or indeed the {{mapToSelf()}} method)
would do in this case.

h4. Comment (11)
These are typical examples of useful methods which can lead to uncontrolled growth of the
APIs.

h2. Various norms and related methods
h3. List of the methods
|| {{RealVector}}                          || {{RealMatrix}}      || Comments ||
| {{double getL1Distance(RealVector v)}}   |                      | (13)      |
| {{double getL1Norm()}}                   |                      | (12)      |
| {{double getLInfDistance(RealVector v)}} |                      | (13)      |
| {{double getLInfNorm()}}                 | {{double getNorm()}} | (12), (14)|
| {{int getMaxIndex()}}                    |                      | (12), (15)|
| {{double getMaxValue()}}                 |                      | (12), (15)|
| {{int getMinIndex()}}                    |                      | (12), (15)|
| {{int getMinValue()}}                    |                      | (12), (15)|

h3. Comments on these methods
h4. Comment (12)
This method could be removed from the {{RealVector}} API. Visitors should be implemented instead.

h4. Comment (13)
This method could be removed from the {{RealVector}} API. Alternative functional approach
should be proposed (e.g. [zip|http://stackoverflow.com/questions/1115563/what-is-zip-functional-programming]).

h4. Comment (14)
Inconsistencies: {{getNorm()}} does not refer to the same type of norm.

h4. Comment (15)
Methods {{int getXXXIndex()}} and {{double getXXXValue()}} could be merged, the returned type
might be a {{Pair<Integer, Double>}}. This would avoid inefficient duplicate sweep of
the vector if both the value and the index are needed.

h2. Functional-programming-like methods
h3. List of the methods
The methods listed below are both "truly" FP methods, as well as methods which could benefit
from a FP approach.

|| {{RealVector}}                                                || {{RealMatrix}}       
            || Comments ||
| {{Iterator<RealVector.Entry> iterator()}}                      |                 
                  |           |
| {{Iterator<RealVector.Entry> sparseIterator()}}                |                 
                  |           |
| {{RealVector map(UnivariateFunction function)}}                |                       
            | (18)      |
| {{RealVector mapToSelf(UnivariateFunction function)}}          |                       
            | (18)      |
| {{RealVector mapAdd(double d)}}                                | {{RealMatrix scalarAdd(double
d)}} | (16)      |
| {{RealVector mapAddToSelf(double d)}}                          |                       
            | (16)      |
| {{RealVector mapDivide(double d)}}                             |                       
            | (16)      |
| {{RealVector mapDivideToSelf(double d)}}                       |                       
            | (16)      |
| {{RealVector mapSubtract(double d)}}                           |                       
            | (16)      |
| {{RealVector mapSubtractToSelf(double d)}}                     |                       
            | (16)      |
| {{RealVector ebeDivide(RealVector v)}}                         |                       
            | (17)      |
| {{RealVector ebeMultiply(RealVector v)}}                       |                       
            | (17)      |
| {{RealVector combine(double a, double b, RealVector y)}}       |                       
            | (17)      |
| {{RealVector combineToSelf(double a, double b, RealVector y)}} |                       
            | (17)      |
| | {{double walkInColumnOrder(RealMatrixChangingVisitor visitor)}}                      
                                         | (18)      |
| | {{double walkInColumnOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow,
int startColumn, int endColumn)}}      | (18)      |
| | {{double walkInColumnOrder(RealMatrixPreservingVisitor visitor)}}                    
                                         | (18)      |
| | {{double walkInColumnOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow,
int startColumn, int endColumn)}}    | (18)      |
| | {{double walkInOptimizedOrder(RealMatrixChangingVisitor visitor)}}                   
                                         | (18)      |
| | {{double walkInOptimizedOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow,
int startColumn, int endColumn)}}   | (18)      |
| | {{double walkInOptimizedOrder(RealMatrixPreservingVisitor visitor)}}                 
                                         | (18)      |
| | {{double walkInOptimizedOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow,
int startColumn, int endColumn)}} | (18)      |
| | {{double walkInRowOrder(RealMatrixChangingVisitor visitor)}}                         
                                         | (18)      |
| | {{double walkInRowOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int
startColumn, int endColumn)}}         | (18)      |
| | {{double walkInRowOrder(RealMatrixPreservingVisitor visitor)}}                       
                                         | (18)      |
| | {{double walkInRowOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow,
int startColumn, int endColumn)}}       | (18)      |

h3. Comments on these methods
h4. Comment (16)
These methods could be removed, as a call to {{map()}}{{mapToSelf()}}.

h4. Comment (17)
These methods could benefit from a FP approach (e.g. [zip|http://stackoverflow.com/questions/1115563/what-is-zip-functional-programming]).

h4. Comment (18)
{{map()}} and {{visit()}} are similar concepts, which are both useful. Should {{map()}} be
implemented for {{RealMatrix}}? Should {{visit()}} be implemented for {{RealVector}}?

h2. Data conversion methods
h3. List of the methods
|| {{RealVector}}    || {{RealMatrix}}      || Comments ||
| double[] toArray() | double[][] getData() |           |

  was:
{panel:title=Warning|borderStyle=solid}
This is not a bug report, but rather a summary of all discussions which have taken place on
the mailing list regarding the refactoring of the vector and matrix classes. Indeed, it has
been argued many times that the {{RealVector}} and {{RealMatrix}} interfaces are really cluttered,
and could benefit from other approaches (like functional programming). 

The description of this ticket will be updated as the discussion progresses on the mailing-list,
and new JIRA tickets will be created to carry out the "real" work. {color:red}In order to
keep this ticket tidy, contributors should refrain from commenting on this website. Instead,
messages should be posted on the dev mailing-list{color}.
{panel}


h1. The current API (version 3.0)

In this section, the current interfaces for vectors and matrices are compared. Vectors and
matrices are two mathematical objects which are very close in nature. Their implementations
should therefore be as similar as possible. The methods will be sorted as follows
* methods reflecting the mathematical structure of vector space: addition, multiplication
by a scalar, matrix-vector product, ...
* methods reflecting the mathematical structure of euclidean space
* ...

h2. Methods reflecting the mathematical structure of vector space
h3. List of the methods
|| {{RealVector}}                            || {{RealMatrix}}                           
               || Comments ||
| {{RealVector add(RealVector v)}}           | {{RealMatrix add(RealMatrix m)}}          
               |           |
| {{int getDimension()}}                     | {{int getRowDimension()}},\\ {{int getColumnDimension()}}
|           |
| {{RealVector mapMultiply(double d)}}       | {{scalarMultiply(double d)}}              
               | (1)       |
| {{RealVector mapMultiplyToSelf(double d)}} |                                           
               |           |
| {{RealVector outerProduct(RealVector v)}}  |                                           
               |           |
|                                            | {{double getTrace()}}                     
               |           |
|                                            | {{multiply(RealMatrix m)}}                
               |           |
|                                            | {{double[] operate(double[])}}            
               | (2)       |
|                                            | {{RealVector operate(RealVector)}}        
               |           |
|                                            | {{RealMatrix power(int p)}}               
               |           |
|                                            | {{double[] preMultiply(double[])}}        
               | (2)       |
|                                            | {{RealMatrix preMultiply(RealMatrix)}}    
               |           |
|                                            | {{RealVector preMultiply(RealVector)}}    
               |           |
|                                            | {{RealMatrix transpose()}}                
               |           |

h3. Comments on the above methods
h4. Comment (1)
{{RealVector RealVector.mapMultiply(double)}} and {{RealMatrix RealMatrix.scalarMultiply(double)}}
perform essentially the same task. Readibility of the classes would be improved if they add
the same name. This is very important since these methods reflect the fact that the space
of vectors as well as the space of matrices are two vector spaces.

h4. Comment (2)
Prior to the release of version 3.0, all methods taking as argument, or returning, {{double[]}}
as a representation of vectors were removed. The rationale for this is that calling {{new
ArrayRealVector(double[], false)}} is very easy, and comes at virtually no cost (see MATH-653
and MATH-660). It might be worth considering the same simplification for the {{RealMatrix}}
interface.

h2. Methods reflecting the mathematical structure of euclidean space
h3. List of the methods
|| {{RealVector}}                         || {{RealMatrix}}               || Comments ||
| {{double cosine(RealVector v)}}         |                               |           |
| {{double dotProduct(RealVector v)}}     |                               | (3)       |
| {{double getDistance(RealVector v)}}    |                               |           |
| {{double getNorm()}}                    | {{double getFrobeniusNorm()}} |           |
| {{RealVector projection(RealVector v)}} |                               |           |
| {{void unitize()}}                      |                               | (4)       |
| {{RealVector unitVector()}}             |                               |           |

h3. Comments on the above methods
h4. Comment (3)
In a way, {{RealMatrix RealMatrix.transpose()}} could be seen as a method inherent to the
euclidean structure, and the generalization of the dot product. For this reason, {{transpose()}}
should probably _not_ be externalized.

h4. Comment (4)
This could be externalized with the visitor pattern (see below).

h4. Comment (5)
Could be externalized in a factory class.

h2. Constructors, factory methods and related methods
h3. List of the methods
|| {{RealVector}}                                || {{RealMatrix}}                       
                                                                  || Comments ||
| {{RealVector append(double d)}}                |                                       
                                                                  | |
| {{RealVector append(RealVector v)}}            |                                       
                                                                  | |
| {{RealVector copy()}}                          | {{RealMatrix copy()}}                 
                                                                  | |
|                                                | {{void copySubMatrix(int[] selectedRows,
int[] selectedColumns, double[][] destination)}}                | (6), (7) |
|                                                | {{void copySubMatrix(int startRow, int
endRow, int startColumn, int endColumn, double[][] destination)}} | (7) |
|                                                | {{createMatrix(int rowDimension, int columnDimension)}}
                                                 | (9) |
|                                                | {{double[] getColumn(int column)}}    
                                                                  | (6) |
|                                                | {{RealMatrix getColumnMatrix(int column)}}
                                                              | |
|                                                | {{RealVector getColumnVector(int column)}}
                                                              | |
|                                                | {{double[] getRow(int row)}}          
                                                                  | (6) |
|                                                | {{RealMatrix getRowMatrix(int row)}}  
                                                                  | |
|                                                | {{RealVector getRowVector(int row)}}  
                                                                  | |
|                                                | {{RealMatrix getSubMatrix(int[] selectedRows,
int[] selectedColumns)}}                                   | |
| {{RealVector getSubVector(int index, int n)}}  | {{RealMatrix getSubMatrix(int startRow,
int endRow, int startColumn, int endColumn)}}                    | (8) |
|                                                | {{void setColumn(int column, double[] array)}}
                                                          | (6) |
|                                                | {{void setColumnMatrix(int column, RealMatrix
matrix)}}                                                  | |
|                                                | {{void setColumnVector(int column, RealVector
vector)}}                                                  | |
|                                                | {{void setRow(int row, double[] array)}}
                                                                | (6) |
|                                                | {{void setRowMatrix(int row, RealMatrix
matrix)}}                                                        | |
|                                                | {{void setRowVector(int row, RealVector
vector)}}                                                        | |
| {{void setSubVector(int index, RealVector v)}} | {{void setSubMatrix(double[][] subMatrix,
int row, int column)}}                                         | (6) |
| {{unmodifiableRealVector(RealVector v)}} |                                             
                                                                  | |

h3. Comments on the above methods
h4. Comment (6)
Prior to the release of version 3.0, all methods taking as argument, or returning, {{double[]}}
as a representation of vectors were removed. The rationale for this is that calling {{new
ArrayRealVector(double[], false)}} is very easy, and comes at virtually no cost (see MATH-653
and MATH-660). It might be worth considering the same simplification for the {{RealMatrix}}
interface.

h4. Comment (7)
The signature of this method is rather unusual in Commons-Math, as one of the parameters is
modified, and nothing is returned.

h4. Comment (8)
Inconsistency: in {{getSubVector(int, int)}}, the second parameter is the number of entries
to be copied, while in {{getSubMatrix(int, int, int, int)}} the second (resp. fourth) parameters
are the indices of the last row (resp. column).

h4. Comment (9)
This is a very useful method: one often needs to create a new vector/matrix with same data
layout as an existing vector/matrix. This method should probably be generalized to {{RealVector}}
as well.

h2. Manipulation of entries
h3. List of the methods
|| {{RealVector}}                                  || {{RealMatrix}}                     
                      || Comments ||
| {{double getEntry(int index)}}                   | {{double getEntry(int row, int column)}}
                  |           |
| {{void set(double value)}}                       |                                     
                      | (10)      |
| {{void setEntry(int index, double value)}}       | {{void setEntry(int row, int column,
double value)}}       |           |
| {{void addToEntry(int index, double increment)}} | {{void addToEntry(int row, int column,
double increment)}} | (11)      |
|                                                  | {{void multiplyEntry(int row, int column,
double factor)}} | (11)      |

h3. Comments on these methods
h4. Comment (10)
This useful method could be extended to {{RealMatrix}} as well. However, it could be argued
that this method is superfluous, as the visitor pattern (or indeed the {{mapToSelf()}} method)
would do in this case.

h4. Comment (11)
These are typical examples of useful methods which can lead to uncontrolled growth of the
APIs.

h2. Various norms and related methods
h3. List of the methods
|| {{RealVector}}                          || {{RealMatrix}}      || Comments ||
| {{double getL1Distance(RealVector v)}}   |                      | (13)      |
| {{double getL1Norm()}}                   |                      | (12)      |
| {{double getLInfDistance(RealVector v)}} |                      | (13)      |
| {{double getLInfNorm()}}                 | {{double getNorm()}} | (12), (14)|
| {{int getMaxIndex()}}                    |                      | (12), (15)|
| {{double getMaxValue()}}                 |                      | (12), (15)|
| {{int getMinIndex()}}                    |                      | (12), (15)|
| {{int getMinValue()}}                    |                      | (12), (15)|

h3. Comments on these methods
h4. Comment (12)
This method could be removed from the {{RealVector}} API. Visitors should be implemented instead.

h4. Comment (13)
This method could be removed from the {{RealVector}} API. Alternative functional approach
should be proposed (e.g. [zip|http://stackoverflow.com/questions/1115563/what-is-zip-functional-programming]).

h4. Comment (14)
Inconsistencies: {{getNorm()}} does not refer to the same type of norm.

h4. Comment (15)
Methods {{int getXXXIndex()}} and {{double getXXXValue()}} could be merged, the returned type
might be a {{Pair<Integer, Double>}}. This would avoid inefficient duplicate sweep of
the vector if both the value and the index are needed.

h2. Functional-programming-like methods

    
> Refactoring the vector and matrix classes
> -----------------------------------------
>
>                 Key: MATH-765
>                 URL: https://issues.apache.org/jira/browse/MATH-765
>             Project: Commons Math
>          Issue Type: Improvement
>    Affects Versions: 4.0
>            Reporter: Sébastien Brisard
>              Labels: api-change, linear
>
> {panel:title=Warning|borderStyle=solid}
> This is not a bug report, but rather a summary of all discussions which have taken place
on the mailing list regarding the refactoring of the vector and matrix classes. Indeed, it
has been argued many times that the {{RealVector}} and {{RealMatrix}} interfaces are really
cluttered, and could benefit from other approaches (like functional programming). 
> The description of this ticket will be updated as the discussion progresses on the mailing-list,
and new JIRA tickets will be created to carry out the "real" work. {color:red}In order to
keep this ticket tidy, contributors should refrain from commenting on this website. Instead,
messages should be posted on the dev mailing-list{color}.
> {panel}
> h1. The current API (version 3.0)
> In this section, the current interfaces for vectors and matrices are compared. Vectors
and matrices are two mathematical objects which are very close in nature. Their implementations
should therefore be as similar as possible. The methods will be sorted as follows
> * methods reflecting the mathematical structure of vector space: addition, multiplication
by a scalar, matrix-vector product, ...
> * methods reflecting the mathematical structure of euclidean space
> * ...
> h2. Methods reflecting the mathematical structure of vector space
> h3. List of the methods
> || {{RealVector}}                            || {{RealMatrix}}                      
                    || Comments ||
> | {{RealVector add(RealVector v)}}           | {{RealMatrix add(RealMatrix m)}}     
                    |           |
> | {{RealVector subtract(RealVector v)}}      | {{RealMatrix subtract(RealMatrix m)}}
                    |           |
> | {{int getDimension()}}                     | {{int getRowDimension()}},\\ {{int getColumnDimension()}}
|           |
> | {{RealVector mapMultiply(double d)}}       | {{scalarMultiply(double d)}}         
                    | (1)       |
> | {{RealVector mapMultiplyToSelf(double d)}} |                                      
                    |           |
> | {{RealVector outerProduct(RealVector v)}}  |                                      
                    |           |
> |                                            | {{double getTrace()}}                
                    |           |
> |                                            | {{multiply(RealMatrix m)}}           
                    |           |
> |                                            | {{double[] operate(double[])}}       
                    | (2)       |
> |                                            | {{RealVector operate(RealVector)}}   
                    |           |
> |                                            | {{RealMatrix power(int p)}}          
                    |           |
> |                                            | {{double[] preMultiply(double[])}}   
                    | (2)       |
> |                                            | {{RealMatrix preMultiply(RealMatrix)}}
                   |           |
> |                                            | {{RealVector preMultiply(RealVector)}}
                   |           |
> |                                            | {{RealMatrix transpose()}}           
                    |           |
> h3. Comments on the above methods
> h4. Comment (1)
> {{RealVector RealVector.mapMultiply(double)}} and {{RealMatrix RealMatrix.scalarMultiply(double)}}
perform essentially the same task. Readibility of the classes would be improved if they add
the same name. This is very important since these methods reflect the fact that the space
of vectors as well as the space of matrices are two vector spaces.
> h4. Comment (2)
> Prior to the release of version 3.0, all methods taking as argument, or returning, {{double[]}}
as a representation of vectors were removed. The rationale for this is that calling {{new
ArrayRealVector(double[], false)}} is very easy, and comes at virtually no cost (see MATH-653
and MATH-660). It might be worth considering the same simplification for the {{RealMatrix}}
interface.
> h2. Methods reflecting the mathematical structure of euclidean space
> h3. List of the methods
> || {{RealVector}}                         || {{RealMatrix}}               || Comments
||
> | {{double cosine(RealVector v)}}         |                               |         
 |
> | {{double dotProduct(RealVector v)}}     |                               | (3)     
 |
> | {{double getDistance(RealVector v)}}    |                               |         
 |
> | {{double getNorm()}}                    | {{double getFrobeniusNorm()}} |         
 |
> | {{RealVector projection(RealVector v)}} |                               |         
 |
> | {{void unitize()}}                      |                               | (4)     
 |
> | {{RealVector unitVector()}}             |                               |         
 |
> h3. Comments on the above methods
> h4. Comment (3)
> In a way, {{RealMatrix RealMatrix.transpose()}} could be seen as a method inherent to
the euclidean structure, and the generalization of the dot product. For this reason, {{transpose()}}
should probably _not_ be externalized.
> h4. Comment (4)
> This could be externalized with the visitor pattern (see below).
> h4. Comment (5)
> Could be externalized in a factory class.
> h2. Constructors, factory methods and related methods
> h3. List of the methods
> || {{RealVector}}                                || {{RealMatrix}}                  
                                                                       || Comments ||
> | {{RealVector append(double d)}}                |                                  
                                                                       | |
> | {{RealVector append(RealVector v)}}            |                                  
                                                                       | |
> | {{RealVector copy()}}                          | {{RealMatrix copy()}}            
                                                                       | |
> |                                                | {{void copySubMatrix(int[] selectedRows,
int[] selectedColumns, double[][] destination)}}                | (6), (7) |
> |                                                | {{void copySubMatrix(int startRow,
int endRow, int startColumn, int endColumn, double[][] destination)}} | (7) |
> |                                                | {{createMatrix(int rowDimension, int
columnDimension)}}                                                  | (9) |
> |                                                | {{double[] getColumn(int column)}}
                                                                      | (6) |
> |                                                | {{RealMatrix getColumnMatrix(int column)}}
                                                              | |
> |                                                | {{RealVector getColumnVector(int column)}}
                                                              | |
> |                                                | {{double[] getRow(int row)}}     
                                                                       | (6) |
> |                                                | {{RealMatrix getRowMatrix(int row)}}
                                                                    | |
> |                                                | {{RealVector getRowVector(int row)}}
                                                                    | |
> |                                                | {{RealMatrix getSubMatrix(int[] selectedRows,
int[] selectedColumns)}}                                   | |
> | {{RealVector getSubVector(int index, int n)}}  | {{RealMatrix getSubMatrix(int startRow,
int endRow, int startColumn, int endColumn)}}                    | (8) |
> |                                                | {{void setColumn(int column, double[]
array)}}                                                           | (6) |
> |                                                | {{void setColumnMatrix(int column,
RealMatrix matrix)}}                                                  | |
> |                                                | {{void setColumnVector(int column,
RealVector vector)}}                                                  | |
> |                                                | {{void setRow(int row, double[] array)}}
                                                                | (6) |
> |                                                | {{void setRowMatrix(int row, RealMatrix
matrix)}}                                                        | |
> |                                                | {{void setRowVector(int row, RealVector
vector)}}                                                        | |
> | {{void setSubVector(int index, RealVector v)}} | {{void setSubMatrix(double[][] subMatrix,
int row, int column)}}                                         | (6) |
> | {{unmodifiableRealVector(RealVector v)}} |                                        
                                                                       | |
> h3. Comments on the above methods
> h4. Comment (6)
> Prior to the release of version 3.0, all methods taking as argument, or returning, {{double[]}}
as a representation of vectors were removed. The rationale for this is that calling {{new
ArrayRealVector(double[], false)}} is very easy, and comes at virtually no cost (see MATH-653
and MATH-660). It might be worth considering the same simplification for the {{RealMatrix}}
interface.
> h4. Comment (7)
> The signature of this method is rather unusual in Commons-Math, as one of the parameters
is modified, and nothing is returned.
> h4. Comment (8)
> Inconsistency: in {{getSubVector(int, int)}}, the second parameter is the number of entries
to be copied, while in {{getSubMatrix(int, int, int, int)}} the second (resp. fourth) parameters
are the indices of the last row (resp. column).
> h4. Comment (9)
> This is a very useful method: one often needs to create a new vector/matrix with same
data layout as an existing vector/matrix. This method should probably be generalized to {{RealVector}}
as well.
> h2. Manipulation of entries
> h3. List of the methods
> || {{RealVector}}                                  || {{RealMatrix}}                
                           || Comments ||
> | {{double getEntry(int index)}}                   | {{double getEntry(int row, int column)}}
                  |           |
> | {{void set(double value)}}                       |                                
                           | (10)      |
> | {{void setEntry(int index, double value)}}       | {{void setEntry(int row, int column,
double value)}}       |           |
> | {{void addToEntry(int index, double increment)}} | {{void addToEntry(int row, int column,
double increment)}} | (11)      |
> |                                                  | {{void multiplyEntry(int row, int
column, double factor)}} | (11)      |
> h3. Comments on these methods
> h4. Comment (10)
> This useful method could be extended to {{RealMatrix}} as well. However, it could be
argued that this method is superfluous, as the visitor pattern (or indeed the {{mapToSelf()}}
method) would do in this case.
> h4. Comment (11)
> These are typical examples of useful methods which can lead to uncontrolled growth of
the APIs.
> h2. Various norms and related methods
> h3. List of the methods
> || {{RealVector}}                          || {{RealMatrix}}      || Comments ||
> | {{double getL1Distance(RealVector v)}}   |                      | (13)      |
> | {{double getL1Norm()}}                   |                      | (12)      |
> | {{double getLInfDistance(RealVector v)}} |                      | (13)      |
> | {{double getLInfNorm()}}                 | {{double getNorm()}} | (12), (14)|
> | {{int getMaxIndex()}}                    |                      | (12), (15)|
> | {{double getMaxValue()}}                 |                      | (12), (15)|
> | {{int getMinIndex()}}                    |                      | (12), (15)|
> | {{int getMinValue()}}                    |                      | (12), (15)|
> h3. Comments on these methods
> h4. Comment (12)
> This method could be removed from the {{RealVector}} API. Visitors should be implemented
instead.
> h4. Comment (13)
> This method could be removed from the {{RealVector}} API. Alternative functional approach
should be proposed (e.g. [zip|http://stackoverflow.com/questions/1115563/what-is-zip-functional-programming]).
> h4. Comment (14)
> Inconsistencies: {{getNorm()}} does not refer to the same type of norm.
> h4. Comment (15)
> Methods {{int getXXXIndex()}} and {{double getXXXValue()}} could be merged, the returned
type might be a {{Pair<Integer, Double>}}. This would avoid inefficient duplicate sweep
of the vector if both the value and the index are needed.
> h2. Functional-programming-like methods
> h3. List of the methods
> The methods listed below are both "truly" FP methods, as well as methods which could
benefit from a FP approach.
> || {{RealVector}}                                                || {{RealMatrix}}  
                 || Comments ||
> | {{Iterator<RealVector.Entry> iterator()}}                      |            
                       |           |
> | {{Iterator<RealVector.Entry> sparseIterator()}}                |            
                       |           |
> | {{RealVector map(UnivariateFunction function)}}                |                  
                 | (18)      |
> | {{RealVector mapToSelf(UnivariateFunction function)}}          |                  
                 | (18)      |
> | {{RealVector mapAdd(double d)}}                                | {{RealMatrix scalarAdd(double
d)}} | (16)      |
> | {{RealVector mapAddToSelf(double d)}}                          |                  
                 | (16)      |
> | {{RealVector mapDivide(double d)}}                             |                  
                 | (16)      |
> | {{RealVector mapDivideToSelf(double d)}}                       |                  
                 | (16)      |
> | {{RealVector mapSubtract(double d)}}                           |                  
                 | (16)      |
> | {{RealVector mapSubtractToSelf(double d)}}                     |                  
                 | (16)      |
> | {{RealVector ebeDivide(RealVector v)}}                         |                  
                 | (17)      |
> | {{RealVector ebeMultiply(RealVector v)}}                       |                  
                 | (17)      |
> | {{RealVector combine(double a, double b, RealVector y)}}       |                  
                 | (17)      |
> | {{RealVector combineToSelf(double a, double b, RealVector y)}} |                  
                 | (17)      |
> | | {{double walkInColumnOrder(RealMatrixChangingVisitor visitor)}}                 
                                              | (18)      |
> | | {{double walkInColumnOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow,
int startColumn, int endColumn)}}      | (18)      |
> | | {{double walkInColumnOrder(RealMatrixPreservingVisitor visitor)}}               
                                              | (18)      |
> | | {{double walkInColumnOrder(RealMatrixPreservingVisitor visitor, int startRow, int
endRow, int startColumn, int endColumn)}}    | (18)      |
> | | {{double walkInOptimizedOrder(RealMatrixChangingVisitor visitor)}}              
                                              | (18)      |
> | | {{double walkInOptimizedOrder(RealMatrixChangingVisitor visitor, int startRow, int
endRow, int startColumn, int endColumn)}}   | (18)      |
> | | {{double walkInOptimizedOrder(RealMatrixPreservingVisitor visitor)}}            
                                              | (18)      |
> | | {{double walkInOptimizedOrder(RealMatrixPreservingVisitor visitor, int startRow,
int endRow, int startColumn, int endColumn)}} | (18)      |
> | | {{double walkInRowOrder(RealMatrixChangingVisitor visitor)}}                    
                                              | (18)      |
> | | {{double walkInRowOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow,
int startColumn, int endColumn)}}         | (18)      |
> | | {{double walkInRowOrder(RealMatrixPreservingVisitor visitor)}}                  
                                              | (18)      |
> | | {{double walkInRowOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow,
int startColumn, int endColumn)}}       | (18)      |
> h3. Comments on these methods
> h4. Comment (16)
> These methods could be removed, as a call to {{map()}}{{mapToSelf()}}.
> h4. Comment (17)
> These methods could benefit from a FP approach (e.g. [zip|http://stackoverflow.com/questions/1115563/what-is-zip-functional-programming]).
> h4. Comment (18)
> {{map()}} and {{visit()}} are similar concepts, which are both useful. Should {{map()}}
be implemented for {{RealMatrix}}? Should {{visit()}} be implemented for {{RealVector}}?
> h2. Data conversion methods
> h3. List of the methods
> || {{RealVector}}    || {{RealMatrix}}      || Comments ||
> | double[] toArray() | double[][] getData() |           |

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