Class MatrixFeatures_FDRM
Used to compute features that describe the structure of a matrix.
Unless explicitly stated otherwise it is assumed that the elements of input matrices contain only real numbers. If an element is NaN or infinite then the behavior is undefined. See IEEE 754 for more information on this issue.
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Method Summary
Modifier and TypeMethodDescriptionstatic int
Counts the number of elements in A which are not zero.static boolean
Checks to see if any element in the matrix is NaN.static boolean
Checks to see if any element in the matrix is NaN of Infinite.static boolean
isConstantVal
(FMatrixRMaj mat, float val, float tol) Checks to see if every value in the matrix is the specified value.static boolean
Checks to see if diagonal element are all not negative, i.e.static boolean
Checks to see if all the diagonal elements in the matrix are positive.static boolean
isEquals
(BMatrixRMaj a, BMatrixRMaj b) Checks to see if each element in the two matrices are equal: aij == bijstatic boolean
Checks to see if each element in the two matrices are equal: aij == bijstatic boolean
Checks to see if each element in the two matrices are within tolerance of each other: tol ≥ |aij - bij|.static boolean
isEqualsTriangle
(FMatrix a, FMatrix b, boolean upper, float tol) Checks to see if each element in the upper or lower triangular portion of the two matrices are within tolerance of each other: tol ≥ |aij - bij|.static boolean
static boolean
isIdentical
(FMatrixD1 a, FMatrixD1 b, float tol) Checks to see if each corresponding element in the two matrices are within tolerance of each other or have the some symbolic meaning.static boolean
isIdentity
(FMatrixRMaj mat, float tol) Checks to see if the provided matrix is within tolerance to an identity matrix.static boolean
isInverse
(FMatrixRMaj a, FMatrixRMaj b, float tol) Checks to see if the two matrices are inverses of each other.static boolean
isLowerTriangle
(FMatrixRMaj A, int hessenberg, float tol) Checks to see if a matrix is lower triangular or Hessenberg.static boolean
isNegative
(FMatrixD1 a, FMatrixD1 b, float tol) Checks to see if the two matrices are the negative of each other:
aij = -bijstatic boolean
isOrthogonal
(FMatrixRMaj Q, float tol) Checks to see if a matrix is orthogonal or isometric.static boolean
Checks to see if the matrix is positive definite.static boolean
Checks to see if the matrix is positive semidefinite:static boolean
Checks to see if the rows of the provided matrix are linearly independent.static boolean
isSkewSymmetric
(FMatrixRMaj A, float tol) Checks to see if a matrix is skew symmetric with in tolerance:
-A = AT
or
|aij + aji| ≤ tolstatic boolean
Checks to see if it is a square matrix.static boolean
Returns true if the matrix is perfectly symmetric.static boolean
isSymmetric
(FMatrixRMaj m, float tol) Returns true if the matrix is symmetric within the tolerance.static boolean
isUpperTriangle
(FMatrixRMaj A, int hessenberg, float tol) Checks to see if a matrix is upper triangular or Hessenberg.static boolean
Checks to see if the matrix is a vector or not.static boolean
Checks to see all the elements in the matrix are zerosstatic int
Computes the nullity of a matrix using the default tolerance.static int
nullity
(FMatrixRMaj A, float threshold) Computes the nullity of a matrix using the specified tolerance.static int
rank
(FMatrixRMaj A) Computes the rank of a matrix using a default tolerance.static int
rank
(FMatrixRMaj A, float threshold) Computes the rank of a matrix using the specified tolerance.
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Method Details
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hasNaN
Checks to see if any element in the matrix is NaN.- Parameters:
m
- A matrix. Not modified.- Returns:
- True if any element in the matrix is NaN.
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hasUncountable
Checks to see if any element in the matrix is NaN of Infinite.- Parameters:
m
- A matrix. Not modified.- Returns:
- True if any element in the matrix is NaN of Infinite.
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isZeros
Checks to see all the elements in the matrix are zeros- Parameters:
m
- A matrix. Not modified.- Returns:
- True if all elements are zeros or false if not
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isVector
Checks to see if the matrix is a vector or not.- Parameters:
mat
- A matrix. Not modified.- Returns:
- True if it is a vector and false if it is not.
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isPositiveDefinite
Checks to see if the matrix is positive definite.
xT A x > 0
for all x where x is a non-zero vector and A is a symmetric matrix.- Parameters:
A
- square symmetric matrix. Not modified.- Returns:
- True if it is positive definite and false if it is not.
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isPositiveSemidefinite
Checks to see if the matrix is positive semidefinite:
xT A x ≥ 0
for all x where x is a non-zero vector and A is a symmetric matrix.- Parameters:
A
- square symmetric matrix. Not modified.- Returns:
- True if it is positive semidefinite and false if it is not.
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isSquare
Checks to see if it is a square matrix. A square matrix has the same number of rows and columns.- Parameters:
mat
- A matrix. Not modified.- Returns:
- True if it is a square matrix and false if it is not.
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isSymmetric
Returns true if the matrix is symmetric within the tolerance. Only square matrices can be symmetric.
A matrix is symmetric if:
|aij - aji| ≤ tol- Parameters:
m
- A matrix. Not modified.tol
- Tolerance for how similar two elements need to be.- Returns:
- true if it is symmetric and false if it is not.
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isSymmetric
Returns true if the matrix is perfectly symmetric. Only square matrices can be symmetric.
A matrix is symmetric if:
aij == aji- Parameters:
m
- A matrix. Not modified.- Returns:
- true if it is symmetric and false if it is not.
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isSkewSymmetric
Checks to see if a matrix is skew symmetric with in tolerance:
-A = AT
or
|aij + aji| ≤ tol- Parameters:
A
- The matrix being tested.tol
- Tolerance for being skew symmetric.- Returns:
- True if it is skew symmetric and false if it is not.
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isInverse
Checks to see if the two matrices are inverses of each other.- Parameters:
a
- A matrix. Not modified.b
- A matrix. Not modified.
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isEquals
Checks to see if each element in the two matrices are within tolerance of each other: tol ≥ |aij - bij|.
NOTE: If any of the elements are not countable then false is returned.
NOTE: If a tolerance of zero is passed in this is equivalent to callingisEquals(FMatrixD1, FMatrixD1)
- Parameters:
a
- A matrix. Not modified.b
- A matrix. Not modified.tol
- How close to being identical each element needs to be.- Returns:
- true if equals and false otherwise.
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isEqualsTriangle
Checks to see if each element in the upper or lower triangular portion of the two matrices are within tolerance of each other: tol ≥ |aij - bij|.
NOTE: If any of the elements are not countable then false is returned.
NOTE: If a tolerance of zero is passed in this is equivalent to callingisEquals(FMatrixD1, FMatrixD1)
- Parameters:
a
- A matrix. Not modified.b
- A matrix. Not modified.upper
- true of upper triangular and false for lower.tol
- How close to being identical each element needs to be.- Returns:
- true if equals and false otherwise.
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isEquals
Checks to see if each element in the two matrices are equal: aij == bij
NOTE: If any of the elements are NaN then false is returned. If two corresponding elements are both positive or negative infinity then they are equal.
- Parameters:
a
- A matrix. Not modified.b
- A matrix. Not modified.- Returns:
- true if identical and false otherwise.
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isEquals
Checks to see if each element in the two matrices are equal: aij == bij
NOTE: If any of the elements are NaN then false is returned. If two corresponding elements are both positive or negative infinity then they are equal.
- Parameters:
a
- A matrix. Not modified.b
- A matrix. Not modified.- Returns:
- true if identical and false otherwise.
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isIdentical
Checks to see if each corresponding element in the two matrices are within tolerance of each other or have the some symbolic meaning. This can handle NaN and Infinite numbers.
If both elements are countable then the following equality test is used:
|aij - bij| ≤ tol.
Otherwise both numbers must both be Float.NaN, Float.POSITIVE_INFINITY, or Float.NEGATIVE_INFINITY to be identical.- Parameters:
a
- A matrix. Not modified.b
- A matrix. Not modified.tol
- Tolerance for equality.- Returns:
- true if identical and false otherwise.
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isOrthogonal
Checks to see if a matrix is orthogonal or isometric.
- Parameters:
Q
- The matrix being tested. Not modified.tol
- Tolerance.- Returns:
- True if it passes the test.
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isRowsLinearIndependent
Checks to see if the rows of the provided matrix are linearly independent.- Parameters:
A
- Matrix whose rows are being tested for linear independence.- Returns:
- true if linearly independent and false otherwise.
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isIdentity
Checks to see if the provided matrix is within tolerance to an identity matrix.- Parameters:
mat
- Matrix being examined. Not modified.tol
- Tolerance.- Returns:
- True if it is within tolerance to an identify matrix.
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isConstantVal
Checks to see if every value in the matrix is the specified value.- Parameters:
mat
- The matrix being tested. Not modified.val
- Checks to see if every element in the matrix has this value.tol
- True if all the elements are within this tolerance.- Returns:
- true if the test passes.
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isDiagonalNotNegative
Checks to see if diagonal element are all not negative, i.e. greater than or equal to 0.- Parameters:
a
- A matrix. Not modified.- Returns:
- True if diagonal element are all not negative. False otherwise.
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isDiagonalPositive
Checks to see if all the diagonal elements in the matrix are positive.- Parameters:
a
- A matrix. Not modified.- Returns:
- true if all the diagonal elements are positive, false otherwise.
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isFullRank
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isNegative
Checks to see if the two matrices are the negative of each other:
aij = -bij- Parameters:
a
- First matrix. Not modified.b
- Second matrix. Not modified.tol
- Numerical tolerance.- Returns:
- True if they are the negative of each other within tolerance.
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isUpperTriangle
Checks to see if a matrix is upper triangular or Hessenberg. A Hessenberg matrix of degree N has the following property:
aij ≤ 0 for all i < j+N
A triangular matrix is a Hessenberg matrix of degree 0.- Parameters:
A
- Matrix being tested. Not modified.hessenberg
- The degree of being hessenberg.tol
- How close to zero the lower left elements need to be.- Returns:
- If it is an upper triangular/hessenberg matrix or not.
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isLowerTriangle
Checks to see if a matrix is lower triangular or Hessenberg. A Hessenberg matrix of degree N has the following property:
aij ≤ 0 for all i < j+N
A triangular matrix is a Hessenberg matrix of degree 0.- Parameters:
A
- Matrix being tested. Not modified.hessenberg
- The degree of being hessenberg.tol
- How close to zero the lower left elements need to be.- Returns:
- If it is an upper triangular/hessenberg matrix or not.
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rank
Computes the rank of a matrix using a default tolerance.- Parameters:
A
- Matrix whose rank is to be calculated. Not modified.- Returns:
- The matrix's rank.
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rank
Computes the rank of a matrix using the specified tolerance.- Parameters:
A
- Matrix whose rank is to be calculated. Not modified.threshold
- The numerical threshold used to determine a singular value.- Returns:
- The matrix's rank.
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nullity
Computes the nullity of a matrix using the default tolerance.- Parameters:
A
- Matrix whose rank is to be calculated. Not modified.- Returns:
- The matrix's nullity.
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nullity
Computes the nullity of a matrix using the specified tolerance.- Parameters:
A
- Matrix whose rank is to be calculated. Not modified.threshold
- The numerical threshold used to determine a singular value.- Returns:
- The matrix's nullity.
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countNonZero
Counts the number of elements in A which are not zero.- Parameters:
A
- A matrix- Returns:
- number of non-zero elements
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