public class DiagonalMatrix extends AbstractRealMatrix implements SymmetricMatrix
This implementation only stores the diagonal elements of the matrix. Setting any off-diagonal element to a value that is not 0 is forbidden (otherwise the matrix would not be diagonal anymore) and attempting to do so will systematically result in a MathUnsupportedOperationException being thrown. As a result, any method which modifies the entries of the matrix (setRow, setColumn, setSubMatrix, etc) will most likely fail, unless only the diagonal elements are actually modified.
This class is up-to-date with commons-math 3.6.1, but has been mostly rewritten since.
| Constructor and Description |
|---|
DiagonalMatrix(double[] diagonalElements)
Creates a matrix using the value of the provided array as diagonal elements.
|
DiagonalMatrix(double[] diagonalElements,
boolean copyArray)
Creates a matrix using the value of the provided array as diagonal elements.
|
DiagonalMatrix(int n)
Creates a matrix with the supplied dimension.
|
| Modifier and Type | Method and Description |
|---|---|
DiagonalMatrix |
add(DiagonalMatrix m)
Returns the result of adding the diagonal matrix
m to this matrix. |
RealMatrix |
add(RealMatrix m)
Returns the result of adding the matrix
m to this matrix. |
SymmetricMatrix |
add(SymmetricMatrix m)
Returns the result of adding the symmetric matrix
m to this matrix. |
void |
addToEntry(int row,
int column,
double increment)
Adds (in place) a given value to the specified entry of this matrix.
|
protected static void |
checkDataArray(double[] data)
Checks the validity of the provided data array.
|
RealMatrix |
concatenateDiagonally(RealMatrix m,
boolean rightConcatenation,
boolean lowerConcatenation)
Diagonally or anti-diagonally concatenates this matrix and another matrix
m. |
RealMatrix |
concatenateHorizontally(RealMatrix m,
boolean rightConcatenation)
Horizontally concatenates this matrix and another matrix
m, , placing it in the left
or right part of the concatenated matrix. |
RealMatrix |
concatenateVertically(RealMatrix m,
boolean lowerConcatenation)
Vertically concatenates this matrix and another matrix
m, placing it in the lower or
upper part of the concatenated matrix. |
DiagonalMatrix |
copy()
Returns a deep copy of this matrix.
|
static DiagonalMatrix |
createIdentityMatrix(int n)
Creates an identity matrix of the specified dimension.
|
DiagonalMatrix |
createMatrix(int rowDimension,
int columnDimension)
Creates a new matrix of the same type as this matrix.
|
boolean |
equals(Object object)
Returns
true if the provided object is a RealMatrix instance with the
same dimensions as this matrix, whose entries are strictly equal to the entries of this
matrix (no absolute or relative tolerance is taken into account when comparing the entries). |
double[] |
getColumn(int column)
Gets the entries of a given column.
|
int |
getColumnDimension()
Returns the dimension of the domain of this operator.
|
RealMatrix |
getColumnMatrix(int column)
Gets the entries of a given column as a column matrix.
|
RealVector |
getColumnVector(int column)
Gets the entries of a given column as a vector.
|
double[][] |
getData()
Returns a 2D array containing the entries of the matrix.
|
double[] |
getDataRef()
Gets a reference to the internal data array storing the diagonal elements of the matrix.
|
double[] |
getDiagonal()
Gets the diagonal vector from this matrix.
|
double |
getEntry(int row,
int column)
Gets the entry at the specified row and column.
|
double |
getFrobeniusNorm()
Returns the Frobenius norm of
the matrix.
|
DiagonalMatrix |
getInverse()
Gets the inverse (or pseudo-inverse) of this matrix using the default decomposition.
|
DiagonalMatrix |
getInverse(Function<RealMatrix,Decomposition> decompositionBuilder)
Gets the inverse (or pseudo-inverse) of this matrix using the given decomposition algorithm.
|
double |
getMax()
Returns the maximum value of the matrix.
|
double |
getMin()
Returns the minimum value of the matrix.
|
double |
getNorm()
Returns the maximum
absolute row sum norm of the matrix.
|
double[] |
getRow(int row)
Gets the entries of a given row.
|
int |
getRowDimension()
Returns the dimension of the codomain of this operator.
|
RealMatrix |
getRowMatrix(int row)
Gets the entries of a given row as a row matrix.
|
RealVector |
getRowVector(int row)
Gets the entries of a given row as a vector.
|
ArrayRowSymmetricMatrix |
getSubMatrix(int[] indices)
Extracts the submatrix corresponding to the specified indices.
|
RealMatrix |
getSubMatrix(int[] selectedRows,
int[] selectedColumns)
Gets a submatrix.
|
DiagonalMatrix |
getSubMatrix(int startIndex,
int endIndex)
Extracts the submatrix corresponding to the specified indices.
|
RealMatrix |
getSubMatrix(int startRow,
int endRow,
int startColumn,
int endColumn)
Gets a submatrix.
|
double |
getTrace()
Returns the trace of the matrix
(the sum of the elements on the main diagonal).
|
int |
hashCode()
Computes a hash code for the matrix.
|
boolean |
isAntisymmetric(double absoluteTolerance)
Checks if this is an antisymmetric matrix.
|
boolean |
isAntisymmetric(double relativeTolerance,
double absoluteTolerance)
Is this a antisymmetric matrix?
|
boolean |
isDiagonal(double threshold)
Is this a diagonal matrix?
|
boolean |
isInvertible()
Checks if the matrix is invertible.
|
boolean |
isInvertible(double absoluteTolerance)
Checks if the matrix is invertible.
|
boolean |
isOrthogonal(double thresholdNorm,
double thresholdOrthogonality)
Is this an orthogonal matrix?
|
boolean |
isSingular()
Checks whether this diagonal matrix is singular or not.
|
boolean |
isSingular(double absoluteTolerance)
Checks whether this diagonal matrix is singular or not.
|
boolean |
isSquare()
Is this a square matrix?
|
boolean |
isSymmetric()
Is this a symmetric matrix?
|
boolean |
isSymmetric(double relativeTolerance)
Is this a symmetric matrix?
|
boolean |
isSymmetric(double relativeTolerance,
double absoluteTolerance)
Is this a symmetric matrix?
|
DiagonalMatrix |
multiply(DiagonalMatrix m,
double d)
Returns the result of postmultiplying this matrix by the diagonal matrix
m, then by
the scalar d. |
RealMatrix |
multiply(RealMatrix m,
boolean toTranspose,
double d)
Returns the result of postmultiplying this matrix by the matrix
m or its transpose
mT, then by the scalar d. |
void |
multiplyEntry(int row,
int column,
double factor)
Multiplies (in place) the specified entry of
this matrix by a given value. |
double[] |
operate(double[] v)
Returns the result of postmultiplying this matrix by the vector
v. |
RealVector |
operate(RealVector v)
Returns the result of multiplying
this by the vector x. |
DiagonalMatrix |
power(int p)
Returns the the result of multiplying this matrix with itself
p times. |
double[] |
preMultiply(double[] v)
Returns the result of premultiplying this matrix by the vector
v. |
RealVector |
preMultiply(RealVector v)
Returns the result of premultiplying this matrix by the vector
v. |
ArrayRowSymmetricMatrix |
quadraticMultiplication(RealMatrix m)
Returns the result of the quadratic multiplication M×
this×MT,
where M is the provided matrix. |
ArrayRowSymmetricMatrix |
quadraticMultiplication(RealMatrix m,
boolean isTranspose)
Returns the result of the quadratic multiplication M×
this×MT,
where M or MT is the provided matrix. |
ArrayRowSymmetricMatrix |
scalarAdd(double d)
Returns the result of adding a scalar
d to the entries of this matrix. |
DiagonalMatrix |
scalarMultiply(double d)
Returns the result of multiplying the entries of this matrix by the scalar
d. |
void |
setEntry(int row,
int column,
double value)
Sets the entry at the specified row and column to a new value.
|
void |
setSubMatrix(double[][] subMatrix,
int row,
int column)
Replaces part of the matrix with a given submatrix, starting at the specified row and column.
|
DiagonalMatrix |
subtract(DiagonalMatrix m)
Returns the result of subtracting the diagonal matrix
m from this matrix. |
RealMatrix |
subtract(RealMatrix m)
Returns the result of subtracting the matrix
m from this matrix. |
SymmetricMatrix |
subtract(SymmetricMatrix m)
Returns the result of subtracting the symmetric matrix
m from this matrix. |
DiagonalMatrix |
transpose()
Returns the transpose of this matrix.
|
DiagonalMatrix |
transpose(boolean forceCopy)
Returns the transpose of this matrix.
|
checkDestinationArray, checkSquare, concatenateDiagonally, concatenateDiagonally, concatenateHorizontally, concatenateVertically, copySubMatrix, copySubMatrix, copySubMatrix, copySubMatrix, equals, getData, getDefaultDecomposition, multiply, multiply, preMultiply, setColumn, setColumnMatrix, setColumnVector, setDefaultDecomposition, setRow, setRowMatrix, setRowVector, toString, toString, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInRowOrder, walkInRowOrder, walkInRowOrder, walkInRowOrderisTransposable, operateTransposeclone, finalize, getClass, notify, notifyAll, wait, wait, waitconcatenateDiagonally, concatenateDiagonally, concatenateHorizontally, concatenateVertically, copySubMatrix, copySubMatrix, copySubMatrix, copySubMatrix, equals, getData, getDefaultDecomposition, multiply, multiply, preMultiply, setColumn, setColumnMatrix, setColumnVector, setDefaultDecomposition, setRow, setRowMatrix, setRowVector, toString, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInRowOrder, walkInRowOrder, walkInRowOrder, walkInRowOrderpublic DiagonalMatrix(int n)
n - the dimension of the matrixNotStrictlyPositiveException - if the provided dimension is not positivepublic DiagonalMatrix(double[] diagonalElements)
The input array is copied, not referenced.
diagonalElements - the diagonal elements of the matrixNullArgumentException - if diagonalElements is nullpublic DiagonalMatrix(double[] diagonalElements,
boolean copyArray)
If an array is created specifically for this constructor (in order to be embedded in the
created instance and not used directly), copyArray may be set to false. This
will improve performance as no new array will be built and no data will be copied.
diagonalElements - the diagonal elements of the matrixcopyArray - if true, the input array will be copied, otherwise it will be referencedNullArgumentException - if diagonalElements is nullprotected static void checkDataArray(double[] data)
To be valid, the array must not be null or empty.
data - the data array to be checkedNullArgumentException - if the data array is nullNoDataException - if the data array is emptypublic int getRowDimension()
getRowDimension in interface AnyMatrixgetRowDimension in class AbstractRealMatrixpublic int getColumnDimension()
getColumnDimension in interface AnyMatrixgetColumnDimension in class AbstractRealMatrixpublic double getMin()
getMin in interface RealMatrixgetMin in class AbstractRealMatrixpublic double getMax()
getMax in interface RealMatrixgetMax in class AbstractRealMatrixpublic double getTrace()
The trace of the matrix is only defined for square matrices.
getTrace in interface RealMatrixgetTrace in class AbstractRealMatrixpublic double getNorm()
getNorm in interface RealMatrixgetNorm in class AbstractRealMatrixpublic double getFrobeniusNorm()
getFrobeniusNorm in interface RealMatrixgetFrobeniusNorm in class AbstractRealMatrixpublic double[][] getData()
getData in interface RealMatrixgetData in class AbstractRealMatrixpublic double[] getDataRef()
This method is only provided for optimization purposes.
Any modification made on the returned array will change the values of this matrix.
public double[] getDiagonal()
Note: The matrix needs to be square.
getDiagonal in interface RealMatrixgetDiagonal in interface SymmetricMatrixgetDiagonal in class AbstractRealMatrixpublic double getEntry(int row,
int column)
Row and column indices start at 0.
getEntry in interface RealMatrixgetEntry in class AbstractRealMatrixrow - the row index of entry to be fetchedcolumn - the column index of entry to be fetchedpublic void setEntry(int row,
int column,
double value)
Row and column indices start at 0.
Important:
This method throws a NumberIsTooLargeException when asked to set an
extra-diagonal element to a non-zero value, since this operation is not allowed when dealing
with diagonal matrices (the properties of the matrix are not guaranteed to be preserved).
setEntry in interface RealMatrixsetEntry in class AbstractRealMatrixrow - the row index of entry to be setcolumn - the column index of entry to be setvalue - the new value of the entryNumberIsTooLargeException - if the method is asked to set an extra-diagonal element to a non-zero valuepublic void addToEntry(int row,
int column,
double increment)
Row and column indices start at 0.
Important:
This method throws a NumberIsTooLargeException when asked to add a non-zero
value to an extra-diagonal element, since this operation is not allowed when dealing with
diagonal matrices (the properties of the matrix are not guaranteed to be preserved).
addToEntry in interface RealMatrixaddToEntry in class AbstractRealMatrixrow - the row index of the entry to be modifiedcolumn - the column index of the entry to be modifiedincrement - the value to add to the matrix entryNumberIsTooLargeException - if the method is asked to add a non-zero value to an extra-diagonal elementpublic void multiplyEntry(int row,
int column,
double factor)
this matrix by a given value.
Row and column indices start at 0.
multiplyEntry in interface RealMatrixmultiplyEntry in class AbstractRealMatrixrow - the row index of the entry to be modifiedcolumn - the column index of the entry to be modifiedfactor - the multiplication factor for the matrix entrypublic double[] getRow(int row)
Row indices start at 0.
getRow in interface RealMatrixgetRow in class AbstractRealMatrixrow - the index of the row to be fetchedpublic RealVector getRowVector(int row)
Row indices start at 0.
getRowVector in interface RealMatrixgetRowVector in class AbstractRealMatrixrow - the index of the row to be fetchedpublic RealMatrix getRowMatrix(int row)
Row indices start at 0.
getRowMatrix in interface RealMatrixgetRowMatrix in class AbstractRealMatrixrow - the index of the row to be fetchedpublic double[] getColumn(int column)
Column indices start at 0.
getColumn in interface RealMatrixgetColumn in class AbstractRealMatrixcolumn - the index of the column to be fetchedpublic RealVector getColumnVector(int column)
Column indices start at 0.
getColumnVector in interface RealMatrixgetColumnVector in class AbstractRealMatrixcolumn - the index of the column to be fetchedpublic RealMatrix getColumnMatrix(int column)
Column indices start at 0.
getColumnMatrix in interface RealMatrixgetColumnMatrix in class AbstractRealMatrixcolumn - the index of the column to be fetchedpublic RealMatrix getSubMatrix(int startRow, int endRow, int startColumn, int endColumn)
Rows and columns are indicated counting from 0 to n-1.
The returned matrix is a DiagonalMatrix if the selected rows and columns are the same, and an Array2DRowRealMatrix or a BlockRealMatrix otherwise.
getSubMatrix in interface RealMatrixgetSubMatrix in class AbstractRealMatrixstartRow - the initial row indexendRow - the final row index (inclusive)startColumn - the initial column indexendColumn - the final column index (inclusive)public RealMatrix getSubMatrix(int[] selectedRows, int[] selectedColumns)
Rows and columns are indicated counting from 0 to n-1.
The returned matrix is an ArrayRowSymmetricMatrix if the selected rows and columns are the same (same indices, same order), and an Array2DRowRealMatrix or a BlockRealMatrix otherwise.
getSubMatrix in interface RealMatrixgetSubMatrix in class AbstractRealMatrixselectedRows - the selected row indicesselectedColumns - the selected column indicespublic DiagonalMatrix getSubMatrix(int startIndex, int endIndex)
This method uses the same start/end indices to select the rows and columns to be extracted. These indices must be valid indices with respect to the dimensions of the matrix (valid indices range from 0 to n-1, with n the row/column dimension of the matrix). Calling this method is equivalent to calling RealMatrix.getSubMatrix(int, int, int, int) using the same start/end indices for the rows and columns. The extracted submatrix is guaranteed to be symmetric. It will also remain positive semi-definite if the initial matrix originally is.
Usage examples:
// Initial matrix
matrix = [a00, a10, a20]
[a10, a11, a21]
[a20, a21, a22]
// Submatrix extraction
matrix.getSubMatrix(1, 2) => [a11, a21]
[a21, a22]
getSubMatrix in interface SymmetricMatrixstartIndex - the initial row/column indexendIndex - the final row/column index (inclusive)public ArrayRowSymmetricMatrix getSubMatrix(int[] indices)
This method uses a single index array to select the rows and columns to be extracted. All indices must be valid indices with respect to the dimensions of the matrix (valid indices range from 0 to n-1, with n the row/column dimension of the matrix). The provided index array is allowed to contain duplicates. Calling this method is equivalent to calling RealMatrix.getSubMatrix(int[], int[]) using the provided index array for the selected rows and columns. This method can be used to extract any submatrix and perform a symmetric reordering of its rows/columns. The extracted submatrix is guaranteed to be symmetric. It will also remain positive semi-definite if the initial matrix originally is.
Usage examples:
// Initial matrix
matrix = [a00, a10, a20]
[a10, a11, a21]
[a20, a21, a22]
// Submatrix extraction
matrix.getSubMatrix([1, 2]) => [a11, a21]
[a21, a22]
// Rows/Columns permutation
matrix.getSubMatrix([1, 2, 0]) => [a11, a21, a10]
[a21, a22, a20]
[a10, a20, a00]
// Submatrix extraction (with duplicated indices)
matrix.getSubMatrix([1, 2, 0, 1, 0])
=> [a11, a21, a10, a11, a10]
[a21, a22, a20, a21, a20]
[a10, a20, a00, a10, a00]
[a11, a21, a10, a11, a10]
[a10, a20, a00, a10, a00]
getSubMatrix in interface SymmetricMatrixindices - the selected indicespublic void setSubMatrix(double[][] subMatrix,
int row,
int column)
Important:
This method systematically throws a MathUnsupportedOperationException since this
operation is not safe when dealing with diagonal matrices (the properties of the matrix are
not guaranteed to be preserved).
setSubMatrix in interface RealMatrixsetSubMatrix in class AbstractRealMatrixsubMatrix - the array containing the replacement data of the targeted submatrixrow - the row coordinate of the top, left element to be replacedcolumn - the column coordinate of the top, left element to be replacedMathUnsupportedOperationException - systematically, since this operation is not supportedpublic ArrayRowSymmetricMatrix scalarAdd(double d)
d to the entries of this matrix.
The returned matrix is an ArrayRowSymmetricMatrix.
scalarAdd in interface RealMatrixscalarAdd in interface SymmetricMatrixscalarAdd in class AbstractRealMatrixd - the scalar value to be added to the entries of this matrixthis+dpublic DiagonalMatrix scalarMultiply(double d)
d.scalarMultiply in interface RealMatrixscalarMultiply in interface SymmetricMatrixscalarMultiply in class AbstractRealMatrixd - the scalar value by which to multiply the entries of this matrix bythis×dpublic RealMatrix add(RealMatrix m)
m to this matrix.
The returned matrix is, in order of priority:
add in interface RealMatrixadd in class AbstractRealMatrixm - the matrix to be addedthis+mpublic SymmetricMatrix add(SymmetricMatrix m)
m to this matrix.
The returned matrix is, in order of priority:
add in interface SymmetricMatrixm - the matrix to be addedthis+mpublic DiagonalMatrix add(DiagonalMatrix m)
m to this matrix.m - the matrix to be addedthis+mMatrixDimensionMismatchException - if the matrix m is not the same size as this matrixpublic RealMatrix subtract(RealMatrix m)
m from this matrix.
The returned matrix is, in order of priority:
subtract in interface RealMatrixsubtract in class AbstractRealMatrixm - the matrix to be subtractedthis-mpublic SymmetricMatrix subtract(SymmetricMatrix m)
m from this matrix.
The returned matrix is, in order of priority:
subtract in interface SymmetricMatrixm - the matrix to be subtractedthis-mpublic DiagonalMatrix subtract(DiagonalMatrix m)
m from this matrix.m - the matrix to be subtractedthis - mMatrixDimensionMismatchException - if the matrix m is not the same size as this matrixpublic RealMatrix multiply(RealMatrix m, boolean toTranspose, double d)
m or its transpose
mT, then by the scalar d.multiply in interface RealMatrixmultiply in class AbstractRealMatrixm - the matrix by which to multiply this matrix bytoTranspose - whether to compute the product this×m×d (
toTranspose=false), or the product this×m
T×d (toTranspose=true)d - the scalar by which to multiply the resulting matrix bythis×m×d or
this×mT×dpublic DiagonalMatrix multiply(DiagonalMatrix m, double d)
m, then by
the scalar d.multiply in class AbstractRealMatrixm - the diagonal matrix by which to multiply this matrix byd - the scalar by which to multiply the resulting matrix bythis×m×d or
this×mT×dpublic ArrayRowSymmetricMatrix quadraticMultiplication(RealMatrix m)
this×MT,
where M is the provided matrix.quadraticMultiplication in interface SymmetricMatrixm - the matrix Mthis
×MTpublic ArrayRowSymmetricMatrix quadraticMultiplication(RealMatrix m, boolean isTranspose)
this×MT,
where M or MT is the provided matrix.quadraticMultiplication in interface SymmetricMatrixm - the matrix M or the matrix MTisTranspose - if true, assumes the provided matrix is MT, otherwise assumes it is
Mthis
×MTpublic double[] operate(double[] v)
v.operate in interface RealMatrixoperate in class AbstractRealMatrixv - the vector by which to multiply this matrix bythis×vpublic RealVector operate(RealVector v)
this by the vector x.operate in interface RealMatrixoperate in class AbstractRealMatrixv - the vector to operate onthis instance with xpublic double[] preMultiply(double[] v)
v.preMultiply in interface RealMatrixpreMultiply in class AbstractRealMatrixv - the row vector by which to premultiply this matrix byv×thispublic RealVector preMultiply(RealVector v)
v.preMultiply in interface RealMatrixpreMultiply in class AbstractRealMatrixv - the vector by which to premultiply this matrix byv×thispublic DiagonalMatrix power(int p)
p times.
The exponent p must be positive or equal to zero.
This operation is only supported for square matrices.
Depending on the underlying storage, numerical instabilities might occur for high powers.
power in interface RealMatrixpower in interface SymmetricMatrixpower in class AbstractRealMatrixp - the exponent p to which this matrix is to be raisedppublic DiagonalMatrix createMatrix(int rowDimension, int columnDimension)
The returned matrix is filled with zeros. Its size is determined by the specified row and column dimensions, which must both be strictly positive. Additional constraints on the dimensions may apply depending on the implementation (for example, symmetric matrices must be square, which implies that the row and column dimensions must be equal).
createMatrix in interface RealMatrixcreateMatrix in interface SymmetricMatrixcreateMatrix in class AbstractRealMatrixrowDimension - the number of rows in the new matrixcolumnDimension - the number of columns in the new matrixpublic static DiagonalMatrix createIdentityMatrix(int n)
n - the dimension of the identity matrixpublic DiagonalMatrix copy()
copy in interface RealMatrixcopy in interface SymmetricMatrixcopy in class AbstractRealMatrixpublic DiagonalMatrix transpose()
transpose in interface RealMatrixtranspose in interface SymmetricMatrixtranspose in class AbstractRealMatrixpublic DiagonalMatrix transpose(boolean forceCopy)
If forceCopy is true, the returned matrix is guaranteed to be a new instance,
which can be modified without any risk of impacting the current instance. Otherwise, this
method may simply return the current instance when the matrix is its own transpose (symmetric
matrix).
transpose in interface RealMatrixtranspose in interface SymmetricMatrixtranspose in class AbstractRealMatrixforceCopy - if true, the transpose of the matrix is systematically stored in a new matrix;
otherwise the method may return the current instance when the matrix is its own
transposepublic RealMatrix concatenateHorizontally(RealMatrix m, boolean rightConcatenation)
m, , placing it in the left
or right part of the concatenated matrix.
The way the two matrices are concatenated depends on the provided argument:
The matrix m is placed in the right part of the concatenated matrix if
rightConcatenation is set to true, and in its left part if it is set to
false.
Usage examples:
this.concatenateHorizontally(m, true) => [this, m] this.concatenateHorizontally(m, false) => [m, this]
concatenateHorizontally in interface RealMatrixconcatenateHorizontally in class AbstractRealMatrixm - the matrix to be concatenated with this matrixrightConcatenation - whether the matrix m is to be placed in the right (true) or left (
false) part of the concatenated matrixpublic RealMatrix concatenateVertically(RealMatrix m, boolean lowerConcatenation)
m, placing it in the lower or
upper part of the concatenated matrix.
The way the two matrices are concatenated depends on the provided argument:
The matrix m is placed in the lower part of the concatenated matrix if
lowerConcatenation is set to true, and in its upper part if it is set to
false.
Usage examples:
this.concatenateVertically(m, true) => [this]
[ m]
this.concatenateVertically(m, false) => [ m]
[this]
concatenateVertically in interface RealMatrixconcatenateVertically in class AbstractRealMatrixm - the matrix to be concatenated with this matrixlowerConcatenation - whether the matrix m is to be placed in the lower (true) or upper (
false) part of the concatenated matrixpublic RealMatrix concatenateDiagonally(RealMatrix m, boolean rightConcatenation, boolean lowerConcatenation)
m.
The way the two matrices are concatenated depends on the provided arguments:
The matrix m is placed in the right part of the concatenated matrix if
rightConcatenation is set to true, and in its left part if it is set to
false. Similarly, the matrix m is placed in the lower part of the
concatenated matrix if lowerConcatenation is set to true, and in its upper
part if it is set to false. This matrix is then placed in the opposite part of the
concatenated matrix (as an example, if the provided matrix is placed in the upper left part,
this matrix will be placed in the lower right part, the remaining parts being filled with
zeros).
Usage examples:
// Diagonal concatenation
this.concatenateDiagonally(m, true, true) => [this, 0]
[ 0, m]
this.concatenateDiagonally(m, false, false) => [m, 0]
[0, this]
// Anti-diagonal concatenation
this.concatenateDiagonally(m, false, true) => [0, this]
[m, 0]
this.concatenateDiagonally(m, true, false) => [ 0, m]
[this, 0]
concatenateDiagonally in interface RealMatrixconcatenateDiagonally in class AbstractRealMatrixm - the matrix to be concatenated with this matrixrightConcatenation - whether the matrix m is to be placed in the right (true) or left (
false) part of the concatenated matrixlowerConcatenation - whether the matrix m is to be placed in the lower (true) or upper (
false) part of the concatenated matrixpublic DiagonalMatrix getInverse()
The default decomposition builder can be changed using the
setDefaultDecomposition method.
getInverse in interface RealMatrixgetInverse in interface SymmetricMatrixgetInverse in class AbstractRealMatrixRealMatrix.getDefaultDecomposition(),
RealMatrix.setDefaultDecomposition(Function)public DiagonalMatrix getInverse(Function<RealMatrix,Decomposition> decompositionBuilder)
The decomposition builder is a function capable of generating new instances of the decomposition algorithm to be used for the computation of the inverse matrix (like the QRDecomposition or the EigenDecomposition, for instance).
The provided decomposition algorithm is never used, since the computation of the inverse is straightforward for diagonal matrices.
getInverse in interface RealMatrixgetInverse in interface SymmetricMatrixgetInverse in class AbstractRealMatrixdecompositionBuilder - the decomposition builder to usepublic boolean isDiagonal(double threshold)
This method indicates if the matrix is diagonal, taking into account the specified tolerance.
To do so, the method checks if the off-diagonal elements are numerically equal to zero.
This method systematically returns false for non-square matrices.
isDiagonal in interface RealMatrixisDiagonal in class AbstractRealMatrixthreshold - the absolute threshold above which the absolute value of an off-diagonal element is
considered to be strictly positivetrue if this is a diagonal matrix, false otherwisepublic boolean isSquare()
isSquare in interface AnyMatrixisSquare in class AbstractRealMatrixpublic boolean isSymmetric()
This method indicates if the matrix is symmetric.
To do so, the method checks that symmetric off-diagonal elements are numerically equal. Two
elements are considered to have different values if their absolute and relative differences
are both above the default tolerances.
This method systematically returns false for non-square matrices.
The absolute and relative tolerances both default to Precision.DOUBLE_COMPARISON_EPSILON.
isSymmetric in interface RealMatrixisSymmetric in class AbstractRealMatrixtrue if this is a symmetric matrix, false otherwisepublic boolean isSymmetric(double relativeTolerance)
This method indicates if the matrix is symmetric.
To do so, the method checks that symmetric off-diagonal elements are numerically equal. Two
elements are considered to have different values if their relative difference is above the
specified tolerance.
This method systematically returns false for non-square matrices.
isSymmetric in interface RealMatrixisSymmetric in class AbstractRealMatrixrelativeTolerance - the relative tolerance to take into account when comparing off-diagonal elementstrue if this is a symmetric matrix, false otherwisepublic boolean isSymmetric(double relativeTolerance,
double absoluteTolerance)
This method indicates if the matrix is symmetric.
To do so, the method checks that symmetric off-diagonal elements are numerically equal. Two
elements are considered to have different values if their absolute and relative differences
are both above the specified tolerances.
This method systematically returns false for non-square matrices.
isSymmetric in interface RealMatrixisSymmetric in class AbstractRealMatrixrelativeTolerance - the relative tolerance to take into account when comparing off-diagonal elementsabsoluteTolerance - the absolute tolerance to take into account when comparing off-diagonal elementstrue if this is a symmetric matrix, false otherwisepublic boolean isAntisymmetric(double absoluteTolerance)
A diagonal matrix can only be antisymmetric if its diagonal elements are all equal to zero.
The specified absolute threshold is taken into account to assess if this is the case or not.
absoluteTolerance - the absolute threshold to take into account when checking if the diagonal elements are
equal to zerotrue if the matrix is antisymmetric, false otherwisepublic boolean isAntisymmetric(double relativeTolerance,
double absoluteTolerance)
This method indicates if the matrix is antisymmetric.
To do so, the method checks that symmetric off-diagonal elements have numerically equal
values but opposite signs, and that diagonal elements are numerically equal to zero. Two
off-diagonal elements are considered to have different values if their absolute and relative
differences are both above the specified tolerances. Diagonal elements are considered to be
different from zero if their absolute value is greater than the specified absolute tolerance.
This method systematically returns false for non-square matrices.
A diagonal matrix can only be antisymmetric if its diagonal elements are all equal to zero.
Only the absolute threshold is taken into account to assess if this is the case or not.
isAntisymmetric in interface RealMatrixisAntisymmetric in class AbstractRealMatrixrelativeTolerance - the relative tolerance to take into account when comparing off-diagonal elementsabsoluteTolerance - the absolute tolerance to take into account when comparing off-diagonal elements, and
when checking if diagonal elements are
equal to zerotrue if this is an antisymmetric matrix, false otherwisepublic boolean isOrthogonal(double thresholdNorm,
double thresholdOrthogonality)
This method indicates if this matrix is orthogonal, taking into account the specified
tolerances.
To do so, the method checks if the columns of the matrix form an orthonormal set (that is,
the column vectors are orthogonal to each other and their norm is numerically equal to 1).
This method systematically returns false for non-square matrices.
A diagonal matrix can only be orthogonal if its diagonal elements are all equal to +1 or -1.
isOrthogonal in interface RealMatrixisOrthogonal in class AbstractRealMatrixthresholdNorm - the relative tolerance to take into account when checking the normality of the the
column vectorsthresholdOrthogonality - the absolute tolerance to take into account when checking the mutual orthogonality of
the the column vectorstrue if this is an orthogonal matrix, false otherwisepublic boolean isSingular()
A diagonal matrix is singular if any of its diagonal elements is equal to 0.
The default absolute tolerance (Precision.SAFE_MIN) is taken into account when
checking the values.
true if the matrix is singular, false otherwisepublic boolean isSingular(double absoluteTolerance)
A diagonal matrix is singular if any of its diagonal elements is equal to 0.
The specified absolute tolerance is taken into account when checking the values.
absoluteTolerance - the absolute tolerance to take into account when checking if an element is equal to 0true if the matrix is singular, false otherwisepublic boolean isInvertible()
A diagonal matrix is invertible if its diagonal elements are all different from zero.
The default absolute tolerance (Precision.SAFE_MIN) is taken into account when
checking the values.
true if the matrix is invertible, false otherwisepublic boolean isInvertible(double absoluteTolerance)
A diagonal matrix is invertible if its diagonal elements are all different from zero.
The specified absolute tolerance is taken into account when checking the values.
isInvertible in interface RealMatrixisInvertible in class AbstractRealMatrixabsoluteTolerance - the absolute tolerance to take into account when checking if an element is equal to 0true if the matrix is invertible, false otherwisepublic boolean equals(Object object)
true if the provided object is a RealMatrix instance with the
same dimensions as this matrix, whose entries are strictly equal to the entries of this
matrix (no absolute or relative tolerance is taken into account when comparing the entries).equals in class AbstractRealMatrixobject - the object to be tested for equalitytrue if the provided object is equal to this matrixpublic int hashCode()
hashCode in class AbstractRealMatrixCopyright © 2023 CNES. All rights reserved.