IntProperty (Parallel Colt 0.10.1

java.lang.Object
- cern.colt.PersistentObject
- - cern.colt.matrix.tint.algo.IntProperty

All Implemented Interfaces:: Serializable, Cloneable

public class IntProperty
extends PersistentObject

Tests matrices for linear algebraic properties (equality, tridiagonality, symmetry, singularity, etc).

Note that this implementation is not synchronized.

Here are some example properties

`matrix`	`4 x 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0`	`4 x 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1`	`4 x 4 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1`	`4 x 4 0 1 1 1 0 1 1 1 0 0 0 1 0 0 0 1`	`4 x 4 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1`	`4 x 4 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1`	`4 x 4 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1`
`upperBandwidth`	`0`	`0`	`1`	`3`	`0`	`1`	`2`
`lowerBandwidth`	`0`	`0`	`1`	`0`	`3`	`3`	`2`
`semiBandwidth`	`1`	`1`	`2`	`4`	`4`	`4`	`3`
`description`	`zero`	`diagonal`	`tridiagonal`	`upper triangular`	`lower triangular`	`unstructured`	`unstructured`

Author:: Piotr Wendykier (piotr.wendykier@gmail.com)
See Also:: Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

static IntProperty DEFAULT
The default Property object;.

Fields
Modifier and Type	Field and Description
`static IntProperty`	`DEFAULT` The default Property object;.

Constructor Summary

Constructors
Constructor and Description

IntProperty()
Constructs an instance with a tolerance of Math.abs(newTolerance).

Constructors
Constructor and Description
`IntProperty()` Constructs an instance with a tolerance of `Math.abs(newTolerance)`.

Method Summary

Methods
Modifier and Type	Method and Description
`void`	`checkRectangular(IntMatrix2D A)` Checks whether the given matrix `A` is rectangular.
`void`	`checkSquare(IntMatrix2D A)` Checks whether the given matrix `A` is square.
`int`	`density(IntMatrix2D A)` Returns the matrix's fraction of non-zero cells; `A.cardinality() / A.size()`.
`boolean`	`equals(IntMatrix1D A, int value)` Returns whether all cells of the given matrix `A` are equal to the given value.
`boolean`	`equals(IntMatrix1D A, IntMatrix1D B)` Returns whether both given matrices `A` and `B` are equal.
`boolean`	`equals(IntMatrix2D A, int value)` Returns whether all cells of the given matrix `A` are equal to the given value.
`boolean`	`equals(IntMatrix2D A, IntMatrix2D B)` Returns whether both given matrices `A` and `B` are equal.
`boolean`	`equals(IntMatrix3D A, int value)` Returns whether all cells of the given matrix `A` are equal to the given value.
`boolean`	`equals(IntMatrix3D A, IntMatrix3D B)` Returns whether both given matrices `A` and `B` are equal.
`void`	`generateNonSingular(IntMatrix2D A)` Modifies the given matrix square matrix `A` such that it is diagonally dominant by row and column, hence non-singular, hence invertible.
`boolean`	`isDiagonal(IntMatrix2D A)` A matrix `A` is diagonal if `A[i,j] == 0` whenever `i != j`.
`boolean`	`isDiagonallyDominantByColumn(IntMatrix2D A)` A matrix `A` is diagonally dominant by column if the absolute value of each diagonal element is larger than the sum of the absolute values of the off-diagonal elements in the corresponding column.
`boolean`	`isDiagonallyDominantByRow(IntMatrix2D A)` A matrix `A` is diagonally dominant by row if the absolute value of each diagonal element is larger than the sum of the absolute values of the off-diagonal elements in the corresponding row.
`boolean`	`isIdentity(IntMatrix2D A)` A matrix `A` is an identity matrix if `A[i,i] == 1` and all other cells are zero.
`boolean`	`isLowerBidiagonal(IntMatrix2D A)` A matrix `A` is lower bidiagonal if `A[i,j]==0` unless `i==j \|\| i==j+1`.
`boolean`	`isLowerTriangular(IntMatrix2D A)` A matrix `A` is lower triangular if `A[i,j]==0` whenever `i < j`.
`boolean`	`isNonNegative(IntMatrix2D A)` A matrix `A` is non-negative if `A[i,j] >= 0` holds for all cells.
`boolean`	`isOrthogonal(IntMatrix2D A)` A square matrix `A` is orthogonal if `A*transpose(A) = I`.
`boolean`	`isPositive(IntMatrix2D A)` A matrix `A` is positive if `A[i,j] > 0` holds for all cells.
`boolean`	`isSkewSymmetric(IntMatrix2D A)` A square matrix `A` is skew-symmetric if `A = -transpose(A)`, that is `A[i,j] == -A[j,i]`.
`boolean`	`isSquare(IntMatrix2D A)` A matrix `A` is square if it has the same number of rows and columns.
`boolean`	`isStrictlyLowerTriangular(IntMatrix2D A)` A matrix `A` is strictly lower triangular if `A[i,j]==0` whenever `i <= j`.
`boolean`	`isStrictlyTriangular(IntMatrix2D A)` A matrix `A` is strictly triangular if it is triangular and its diagonal elements all equal 0.
`boolean`	`isStrictlyUpperTriangular(IntMatrix2D A)` A matrix `A` is strictly upper triangular if `A[i,j]==0` whenever `i >= j`.
`boolean`	`isSymmetric(IntMatrix2D A)` A matrix `A` is symmetric if `A = tranpose(A)`, that is `A[i,j] == A[j,i]`.
`boolean`	`isTriangular(IntMatrix2D A)` A matrix `A` is triangular iff it is either upper or lower triangular.
`boolean`	`isTridiagonal(IntMatrix2D A)` A matrix `A` is tridiagonal if `A[i,j]==0` whenever `Math.abs(i-j) > 1`.
`boolean`	`isUnitTriangular(IntMatrix2D A)` A matrix `A` is unit triangular if it is triangular and its diagonal elements all equal 1.
`boolean`	`isUpperBidiagonal(IntMatrix2D A)` A matrix `A` is upper bidiagonal if `A[i,j]==0` unless `i==j \|\| i==j-1`.
`boolean`	`isUpperTriangular(IntMatrix2D A)` A matrix `A` is upper triangular if `A[i,j]==0` whenever `i > j`.
`boolean`	`isZero(IntMatrix2D A)` A matrix `A` is zero if all its cells are zero.
`int`	`lowerBandwidth(IntMatrix2D A)` The lower bandwidth of a square matrix `A` is the maximum `i-j` for which `A[i,j]` is nonzero and `i > j`.
`int`	`semiBandwidth(IntMatrix2D A)` Returns the semi-bandwidth of the given square matrix `A`.
`String`	`toString(IntMatrix2D A)` Returns summary information about the given matrix `A`.
`int`	`upperBandwidth(IntMatrix2D A)` The upper bandwidth of a square matrix `A` is the maximum `j-i` for which `A[i,j]` is nonzero and `j > i`.

Methods inherited from class cern.colt.PersistentObject
clone

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail
- DEFAULT
```
public static final IntProperty DEFAULT
```
  The default Property object;.

Constructor Detail
- IntProperty
```
public IntProperty()
```
  Constructs an instance with a tolerance of Math.abs(newTolerance).

Method Detail

checkRectangular
```
public void checkRectangular(IntMatrix2D A)
```
Checks whether the given matrix A is rectangular.

Throws:

IllegalArgumentException - if A.rows() < A.columns().

checkSquare
```
public void checkSquare(IntMatrix2D A)
```
Checks whether the given matrix A is square.

Throws:

IllegalArgumentException - if A.rows() != A.columns().

density
```
public int density(IntMatrix2D A)
```
Returns the matrix's fraction of non-zero cells; A.cardinality() / A.size().

equals
```
public boolean equals(IntMatrix1D A,
             int value)
```
Returns whether all cells of the given matrix A are equal to the given value. The result is true if and only if A != null and ! (Math.abs(value - A[i]) > tolerance()) holds for all coordinates.

Parameters:
A - the first matrix to compare.
value - the value to compare against.

Returns:
true if the matrix is equal to the value; false otherwise.

equals
```
public boolean equals(IntMatrix1D A,
             IntMatrix1D B)
```
Returns whether both given matrices A and B are equal. The result is true if A==B. Otherwise, the result is true if and only if both arguments are != null, have the same size and ! (Math.abs(A[i] - B[i]) > tolerance()) holds for all indexes.

Parameters:
A - the first matrix to compare.
B - the second matrix to compare.

Returns:
true if both matrices are equal; false otherwise.

equals
```
public boolean equals(IntMatrix2D A,
             int value)
```
Returns whether all cells of the given matrix A are equal to the given value. The result is true if and only if A != null and ! (Math.abs(value - A[row,col]) > tolerance()) holds for all coordinates.

Parameters:
A - the first matrix to compare.
value - the value to compare against.

Returns:
true if the matrix is equal to the value; false otherwise.

equals
```
public boolean equals(IntMatrix2D A,
             IntMatrix2D B)
```
Returns whether both given matrices A and B are equal. The result is true if A==B. Otherwise, the result is true if and only if both arguments are != null, have the same number of columns and rows and ! (Math.abs(A[row,col] - B[row,col]) > tolerance()) holds for all coordinates.

Parameters:
A - the first matrix to compare.
B - the second matrix to compare.

Returns:
true if both matrices are equal; false otherwise.

equals
```
public boolean equals(IntMatrix3D A,
             int value)
```
Returns whether all cells of the given matrix A are equal to the given value. The result is true if and only if A != null and ! (Math.abs(value - A[slice,row,col]) > tolerance()) holds for all coordinates.

Parameters:
A - the first matrix to compare.
value - the value to compare against.

Returns:
true if the matrix is equal to the value; false otherwise.

equals
```
public boolean equals(IntMatrix3D A,
             IntMatrix3D B)
```
Returns whether both given matrices A and B are equal. The result is true if A==B. Otherwise, the result is true if and only if both arguments are != null, have the same number of columns, rows and slices, and ! (Math.abs(A[slice,row,col] - B[slice,row,col]) > tolerance()) holds for all coordinates.

Parameters:
A - the first matrix to compare.
B - the second matrix to compare.

Returns:
true if both matrices are equal; false otherwise.

generateNonSingular
```
public void generateNonSingular(IntMatrix2D A)
```
Modifies the given matrix square matrix A such that it is diagonally dominant by row and column, hence non-singular, hence invertible. For testing purposes only.

Parameters:
A - the square matrix to modify.

Throws:

IllegalArgumentException - if !isSquare(A).

isDiagonal
```
public boolean isDiagonal(IntMatrix2D A)
```
A matrix A is diagonal if A[i,j] == 0 whenever i != j. Matrix may but need not be square.

isDiagonallyDominantByColumn
```
public boolean isDiagonallyDominantByColumn(IntMatrix2D A)
```
A matrix A is diagonally dominant by column if the absolute value of each diagonal element is larger than the sum of the absolute values of the off-diagonal elements in the corresponding column. returns true if for all i: abs(A[i,i]) > Sum(abs(A[j,i])); j != i. Matrix may but need not be square.
Note: Ignores tolerance.

isDiagonallyDominantByRow
```
public boolean isDiagonallyDominantByRow(IntMatrix2D A)
```
A matrix A is diagonally dominant by row if the absolute value of each diagonal element is larger than the sum of the absolute values of the off-diagonal elements in the corresponding row. returns true if for all i: abs(A[i,i]) > Sum(abs(A[i,j])); j != i. Matrix may but need not be square.
Note: Ignores tolerance.

isIdentity
```
public boolean isIdentity(IntMatrix2D A)
```
A matrix A is an identity matrix if A[i,i] == 1 and all other cells are zero. Matrix may but need not be square.

isLowerBidiagonal
```
public boolean isLowerBidiagonal(IntMatrix2D A)
```
A matrix A is lower bidiagonal if A[i,j]==0 unless i==j || i==j+1. Matrix may but need not be square.

isLowerTriangular
```
public boolean isLowerTriangular(IntMatrix2D A)
```
A matrix A is lower triangular if A[i,j]==0 whenever i < j. Matrix may but need not be square.

isNonNegative
```
public boolean isNonNegative(IntMatrix2D A)
```
A matrix A is non-negative if A[i,j] >= 0 holds for all cells.
Note: Ignores tolerance.

isOrthogonal
```
public boolean isOrthogonal(IntMatrix2D A)
```
A square matrix A is orthogonal if A*transpose(A) = I.

Throws:

IllegalArgumentException - if !isSquare(A).

isPositive
```
public boolean isPositive(IntMatrix2D A)
```
A matrix A is positive if A[i,j] > 0 holds for all cells.
Note: Ignores tolerance.

isSkewSymmetric
```
public boolean isSkewSymmetric(IntMatrix2D A)
```
A square matrix A is skew-symmetric if A = -transpose(A), that is A[i,j] == -A[j,i].

Throws:

IllegalArgumentException - if !isSquare(A).

isSquare
```
public boolean isSquare(IntMatrix2D A)
```
A matrix A is square if it has the same number of rows and columns.

isStrictlyLowerTriangular
```
public boolean isStrictlyLowerTriangular(IntMatrix2D A)
```
A matrix A is strictly lower triangular if A[i,j]==0 whenever i <= j. Matrix may but need not be square.

isStrictlyTriangular
```
public boolean isStrictlyTriangular(IntMatrix2D A)
```
A matrix A is strictly triangular if it is triangular and its diagonal elements all equal 0. Matrix may but need not be square.

isStrictlyUpperTriangular
```
public boolean isStrictlyUpperTriangular(IntMatrix2D A)
```
A matrix A is strictly upper triangular if A[i,j]==0 whenever i >= j. Matrix may but need not be square.

isSymmetric
```
public boolean isSymmetric(IntMatrix2D A)
```
A matrix A is symmetric if A = tranpose(A), that is A[i,j] == A[j,i].

Throws:

IllegalArgumentException - if !isSquare(A).

isTriangular
```
public boolean isTriangular(IntMatrix2D A)
```
A matrix A is triangular iff it is either upper or lower triangular. Matrix may but need not be square.

isTridiagonal
```
public boolean isTridiagonal(IntMatrix2D A)
```
A matrix A is tridiagonal if A[i,j]==0 whenever Math.abs(i-j) > 1. Matrix may but need not be square.

isUnitTriangular
```
public boolean isUnitTriangular(IntMatrix2D A)
```
A matrix A is unit triangular if it is triangular and its diagonal elements all equal 1. Matrix may but need not be square.

isUpperBidiagonal
```
public boolean isUpperBidiagonal(IntMatrix2D A)
```
A matrix A is upper bidiagonal if A[i,j]==0 unless i==j || i==j-1. Matrix may but need not be square.

isUpperTriangular
```
public boolean isUpperTriangular(IntMatrix2D A)
```
A matrix A is upper triangular if A[i,j]==0 whenever i > j. Matrix may but need not be square.

isZero
```
public boolean isZero(IntMatrix2D A)
```
A matrix A is zero if all its cells are zero.

lowerBandwidth
```
public int lowerBandwidth(IntMatrix2D A)
```
The lower bandwidth of a square matrix A is the maximum i-j for which A[i,j] is nonzero and i > j. A banded matrix has a "band" about the diagonal. Diagonal, tridiagonal and triangular matrices are special cases.

Parameters:
A - the square matrix to analyze.

Returns:
the lower bandwith.

Throws:

IllegalArgumentException - if !isSquare(A).
See Also:
semiBandwidth(IntMatrix2D), upperBandwidth(IntMatrix2D)

semiBandwidth

public int semiBandwidth(IntMatrix2D A)

Returns the semi-bandwidth of the given square matrix A. A banded matrix has a "band" about the diagonal. It is a matrix with all cells equal to zero, with the possible exception of the cells along the diagonal line, the k diagonal lines above the diagonal, and the k diagonal lines below the diagonal. The semi-bandwith l is the number k+1. The bandwidth p is the number 2*k + 1. For example, a tridiagonal matrix corresponds to k=1, l=2, p=3, a diagonal or zero matrix corresponds to k=0, l=1, p=1,

The upper bandwidth is the maximum j-i for which A[i,j] is nonzero and j > i. The lower bandwidth is the maximum i-j for which A[i,j] is nonzero and i > j. Diagonal, tridiagonal and triangular matrices are special cases.

Examples:

`matrix`	`4 x 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0`	`4 x 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1`	`4 x 4 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1`	`4 x 4 0 1 1 1 0 1 1 1 0 0 0 1 0 0 0 1`	`4 x 4 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1`	`4 x 4 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1`	`4 x 4 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1`
`upperBandwidth`	`0`	`0`	`1`	`3`	`0`	`1`	`2`
`lowerBandwidth`	`0`	`0`	`1`	`0`	`3`	`3`	`2`
`semiBandwidth`	`1`	`1`	`2`	`4`	`4`	`4`	`3`
`description`	`zero`	`diagonal`	`tridiagonal`	`upper triangular`	`lower triangular`	`unstructured`	`unstructured`

Parameters:: A - the square matrix to analyze.
Returns:: the semi-bandwith l.
Throws:: IllegalArgumentException - if !isSquare(A).
See Also:: lowerBandwidth(IntMatrix2D), upperBandwidth(IntMatrix2D)

toString

public String toString(IntMatrix2D A)

Returns summary information about the given matrix A. That is a String with (propertyName, propertyValue) pairs. Useful for debugging or to quickly get the rough picture of a matrix. For example,

   density                      : 0.9
   isDiagonal                   : false
   isDiagonallyDominantByRow    : false
   isDiagonallyDominantByColumn : false
   isIdentity                   : false
   isLowerBidiagonal            : false
   isLowerTriangular            : false
   isNonNegative                : true
   isOrthogonal                 : Illegal operation or error: Matrix must be square.
   isPositive                   : true
   isSingular                   : Illegal operation or error: Matrix must be square.
   isSkewSymmetric              : Illegal operation or error: Matrix must be square.
   isSquare                     : false
   isStrictlyLowerTriangular    : false
   isStrictlyTriangular         : false
   isStrictlyUpperTriangular    : false
   isSymmetric                  : Illegal operation or error: Matrix must be square.
   isTriangular                 : false
   isTridiagonal                : false
   isUnitTriangular             : false
   isUpperBidiagonal            : false
   isUpperTriangular            : false
   isZero                       : false
   lowerBandwidth               : Illegal operation or error: Matrix must be square.
   semiBandwidth                : Illegal operation or error: Matrix must be square.
   upperBandwidth               : Illegal operation or error: Matrix must be square.

upperBandwidth
```
public int upperBandwidth(IntMatrix2D A)
```
The upper bandwidth of a square matrix A is the maximum j-i for which A[i,j] is nonzero and j > i. A banded matrix has a "band" about the diagonal. Diagonal, tridiagonal and triangular matrices are special cases.

Parameters:
A - the square matrix to analyze.

Returns:
the upper bandwith.

Throws:

IllegalArgumentException - if !isSquare(A).
See Also:
semiBandwidth(IntMatrix2D), lowerBandwidth(IntMatrix2D)

Class IntProperty

Field Summary

Constructor Summary

Method Summary

Methods inherited from class cern.colt.PersistentObject

Methods inherited from class java.lang.Object

Field Detail

DEFAULT

Constructor Detail

IntProperty

Method Detail

checkRectangular

checkSquare

density

equals

equals

equals

equals

equals

equals

generateNonSingular

isDiagonal

isDiagonallyDominantByColumn

isDiagonallyDominantByRow

isIdentity

isLowerBidiagonal

isLowerTriangular

isNonNegative

isOrthogonal

isPositive

isSkewSymmetric

isSquare

isStrictlyLowerTriangular

isStrictlyTriangular

isStrictlyUpperTriangular

isSymmetric

isTriangular

isTridiagonal

isUnitTriangular

isUpperBidiagonal

isUpperTriangular

isZero

lowerBandwidth

semiBandwidth

toString

upperBandwidth