class MatrixD extends MatriD with Error with Serializable
The MatrixD class stores and operates on Numeric Matrices of type Double.
This class follows the gen.MatrixN framework and is provided for efficiency.
Caveat: Only works for rectangular matrices. For matrix-like structures
based on jagged arrays, where the second dimension varies,
- See also
scalation.linalgebra.gen.HMatrix2
- Alphabetic
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- MatrixD
- Serializable
- MatriD
- Error
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Instance Constructors
- new MatrixD(b: MatriD)
Construct a matrix and assign values from matrix 'b'.
Construct a matrix and assign values from matrix 'b'.
- b
the matrix of values to assign
- new MatrixD(dim: (Int, Int), u: Double*)
Construct a matrix from repeated values.
Construct a matrix from repeated values.
- dim
the (row, column) dimensions
- u
the repeated values
- new MatrixD(u: Array[Array[Double]])
Construct a matrix and assign values from array of arrays 'u'.
Construct a matrix and assign values from array of arrays 'u'.
- u
the 2D array of values to assign
- new MatrixD(dim1: Int, dim2: Int, x: Double)
Construct a 'dim1' by 'dim2' matrix and assign each element the value 'x'.
Construct a 'dim1' by 'dim2' matrix and assign each element the value 'x'.
- dim1
the row dimension
- dim2
the column dimension
- x
the scalar value to assign
- new MatrixD(dim1: Int)
Construct a 'dim1' by 'dim1' square matrix.
Construct a 'dim1' by 'dim1' square matrix.
- dim1
the row and column dimension
- new MatrixD(d1: Int, d2: Int, v: Array[Array[Double]] = null)
- d1
the first/row dimension
- d2
the second/column dimension
- v
the 2D array used to store matrix elements
Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def ##: Int
- Definition Classes
- AnyRef → Any
- def *(x: Double): MatrixD
Multiply 'this' matrix by scalar 'x'.
- def *(u: VectoD): VectorD
Multiply 'this' matrix by (column) vector 'u' (vector elements beyond 'dim2' ignored).
- def *(b: MatriD): MatrixD
Multiply 'this' matrix by matrix 'b', transposing 'b' to improve efficiency.
- def *(b: MatrixD): MatrixD
Multiply 'this' matrix by matrix 'b', transposing 'b' to improve efficiency.
Multiply 'this' matrix by matrix 'b', transposing 'b' to improve efficiency. Use 'times' method to skip the transpose step.
- b
the matrix to multiply by (requires 'sameCrossDimensions')
- def **(b: MatriD): MatrixD
Multiply 'this' matrix by matrix 'b' elementwise (Hadamard product).
- def **(u: VectoD): MatrixD
Multiply 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
- def **:(u: VectoD): MatrixD
Multiply vector 'u' by 'this' matrix to produce another matrix 'u_i * a_ij'.
- def **=(u: VectoD): MatrixD
Multiply in-place 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
- def *:(u: VectoD): VectoD
Multiply (row) vector 'u' by 'this' matrix.
Multiply (row) vector 'u' by 'this' matrix. Note '*:' is right associative. vector = vector *: matrix
- u
the vector to multiply by
- Definition Classes
- MatriD
- def *=(x: Double): MatrixD
Multiply in-place 'this' matrix by scalar 'x'.
- def *=(b: MatriD): MatrixD
Multiply in-place 'this' matrix by matrix 'b', transposing 'b' to improve efficiency.
- def *=(b: MatrixD): MatrixD
Multiply in-place 'this' matrix by matrix 'b', transposing 'b' to improve efficiency.
Multiply in-place 'this' matrix by matrix 'b', transposing 'b' to improve efficiency. Use 'times_ip' method to skip the transpose step.
- b
the matrix to multiply by (requires square and 'sameCrossDimensions')
- def +(x: Double): MatrixD
Add 'this' matrix and scalar 'x'.
- def +(u: VectoD): MatrixD
Add 'this' matrix and (row) vector 'u'.
- def +(b: MatriD): MatrixD
Add 'this' matrix and matrix 'b' for any type extending MatriD.
- def +(b: MatrixD): MatrixD
Add 'this' matrix and matrix 'b'.
Add 'this' matrix and matrix 'b'.
- b
the matrix to add (requires 'leDimensions')
- def ++(b: MatriD): MatrixD
Concatenate (row-wise) 'this' matrix and matrix 'b'.
- def ++^(b: MatriD): MatrixD
Concatenate (column-wise) 'this' matrix and matrix 'b'.
- def +:(u: VectoD): MatrixD
Concatenate (row) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.
- def +=(x: Double): MatrixD
Add in-place 'this' matrix and scalar 'x'.
- def +=(u: VectoD): MatrixD
Add in-place 'this' matrix and (row) vector 'u'.
- def +=(b: MatriD): MatrixD
Add in-place 'this' matrix and matrix 'b' for any type extending MatriD.
- def +=(b: MatrixD): MatrixD
Add in-place 'this' matrix and matrix 'b'.
Add in-place 'this' matrix and matrix 'b'.
- b
the matrix to add (requires 'leDimensions')
- def +^:(u: VectoD): MatrixD
Concatenate (column) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.
- def -(x: Double): MatrixD
From 'this' matrix subtract scalar 'x'.
- def -(u: VectoD): MatrixD
From 'this' matrix subtract (row) vector 'u'.
- def -(b: MatriD): MatrixD
From 'this' matrix subtract matrix 'b' for any type extending MatriD.
- def -(b: MatrixD): MatrixD
From 'this' matrix subtract matrix 'b'.
From 'this' matrix subtract matrix 'b'.
- b
the matrix to subtract (requires 'leDimensions')
- def -=(x: Double): MatrixD
From 'this' matrix subtract in-place scalar 'x'.
- def -=(u: VectoD): MatrixD
From 'this' matrix subtract in-place (row) vector 'u'.
- def -=(b: MatriD): MatrixD
From 'this' matrix subtract in-place matrix 'b'.
- def -=(b: MatrixD): MatrixD
From 'this' matrix subtract in-place matrix 'b'.
From 'this' matrix subtract in-place matrix 'b'.
- b
the matrix to subtract (requires 'leDimensions')
- def /(x: Double): MatrixD
Divide 'this' matrix by scalar 'x'.
- def /=(x: Double): MatrixD
Divide in-place 'this' matrix by scalar 'x'.
- def :+(u: VectoD): MatrixD
Concatenate 'this' matrix and (row) vector 'u', i.e., append 'u' to 'this'.
- def :^+(u: VectoD): MatrixD
Concatenate 'this' matrix and (column) vector 'u', i.e., append 'u' to 'this'.
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- def apply(iv: VectoI): MatrixD
Get the rows from 'this' matrix according to the given index/basis.
- def apply(): Array[Array[Double]]
Get the underlying 2D array for 'this' matrix.
- def apply(ir: Range, jr: Range): MatrixD
Get a slice 'this' matrix row-wise on range 'ir' and column-wise on range 'jr'.
- def apply(i: Int): VectorD
Get 'this' matrix's vector at the 'i'-th index position ('i'-th row).
- def apply(i: Int, j: Int): Double
Get 'this' matrix's element at the 'i,j'-th index position.
- def apply(i: Int, jr: Range): VectoD
Get a slice 'this' matrix row-wise at index 'i' and column-wise on range 'jr'.
Get a slice 'this' matrix row-wise at index 'i' and column-wise on range 'jr'. Ex: u = a(2, 3..5)
- i
the row index
- jr
the column range
- Definition Classes
- MatriD
- def apply(ir: Range, j: Int): VectoD
Get a slice 'this' matrix row-wise on range 'ir' and column-wise at index j.
Get a slice 'this' matrix row-wise on range 'ir' and column-wise at index j. Ex: u = a(2..4, 3)
- ir
the row range
- j
the column index
- Definition Classes
- MatriD
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- def bsolve(y: VectoD): VectorD
Solve for 'x' using back substitution in the equation 'u*x = y' where 'this' matrix ('u') is upper triangular (see 'lud_npp' above).
- def clean(thres: Double = TOL, relative: Boolean = true): MatrixD
Clean values in 'this' matrix at or below the threshold 'thres' by setting them to zero.
Clean values in 'this' matrix at or below the threshold 'thres' by setting them to zero. Iterative algorithms give approximate values and if very close to zero, may throw off other calculations, e.g., in computing eigenvectors.
- thres
the cutoff threshold (a small value)
- relative
whether to use relative or absolute cutoff
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
- def col(col: Int, from: Int = 0): VectorD
Get column 'col' from the matrix, returning it as a vector.
- def copy: MatrixD
Create an exact copy of 'this' m-by-n matrix.
- def det: Double
Compute the determinant of 'this' matrix.
- def diag(p: Int, q: Int = 0): MatrixD
Form a matrix '[Ip, this, Iq]' where Ir is a 'r-by-r' identity matrix, by positioning the three matrices 'Ip', 'this' and 'Iq' along the diagonal.
- def diag(b: MatriD): MatrixD
Combine 'this' matrix with matrix 'b', placing them along the diagonal and filling in the bottom left and top right regions with zeros; '[this, b]'.
- lazy val dim1: Int
Dimension 1
- lazy val dim2: Int
Dimension 2
- def dot(b: MatrixD): VectorD
Compute the dot product of 'this' matrix and matrix 'b' that results in a vector, by taking the dot product for each column 'j' of both matrices.
Compute the dot product of 'this' matrix and matrix 'b' that results in a vector, by taking the dot product for each column 'j' of both matrices.
- b
the matrix to multiply by (requires same first dimensions)
- See also
www.mathworks.com/help/matlab/ref/dot.html
- def dot(b: MatriD): VectorD
Compute the dot product of 'this' matrix and matrix 'b' that results in a vector, by taking the dot product for each column 'j' of both matrices.
- def dot(u: VectoD): VectorD
Compute the dot product of 'this' matrix and vector 'u', by first transposing 'this' matrix and then multiplying by 'u' (i.e., 'a dot u = a.t * u').
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def equals(b: Any): Boolean
Override equals to determine whether 'this' matrix equals matrix 'b'.
Override equals to determine whether 'this' matrix equals matrix 'b'.
- b
the matrix to compare with this
- Definition Classes
- MatrixD → AnyRef → Any
- val fString: String
Format string used for printing vector values (change using 'setFormat')
Format string used for printing vector values (change using 'setFormat')
- Attributes
- protected
- Definition Classes
- MatriD
- def flatten: VectorD
Flatten 'this' matrix in row-major fashion, returning a vector containing all the elements from the matrix.
- final def flaw(method: String, message: String): Unit
Show the flaw by printing the error message.
Show the flaw by printing the error message.
- method
the method where the error occurred
- message
the error message
- Definition Classes
- Error
- def foreach[U](f: (Array[Double]) => U): Unit
Iterate over 'this' matrix row by row applying method 'f'.
Iterate over 'this' matrix row by row applying method 'f'.
- f
the function to apply
- Definition Classes
- MatriD
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def getDiag(k: Int = 0): VectorD
Get the 'k'th diagonal of 'this' matrix.
- def hashCode(): Int
Must also override hashCode for 'this' matrix to be compatible with equals.
Must also override hashCode for 'this' matrix to be compatible with equals.
- Definition Classes
- MatrixD → AnyRef → Any
- def inverse: MatrixD
Invert 'this' matrix (requires a square matrix) and use partial pivoting.
- def inverse_ip(): MatrixD
Invert in-place 'this' matrix (requires a square matrix) and uses partial pivoting.
- def inverse_npp: MatrixD
Invert 'this' matrix (requires a square matrix) and does not use partial pivoting.
- def isBidiagonal: Boolean
Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal).
Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal). The method may be overriding for efficiency.
- Definition Classes
- MatriD
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- def isNonnegative: Boolean
Check whether 'this' matrix is nonnegative (has no negative elements).
Check whether 'this' matrix is nonnegative (has no negative elements).
- Definition Classes
- MatriD
- def isRectangular: Boolean
Check whether 'this' matrix is rectangular (all rows have the same number of columns).
- def isSquare: Boolean
Check whether 'this' matrix is square (same row and column dimensions).
Check whether 'this' matrix is square (same row and column dimensions).
- Definition Classes
- MatriD
- def isSymmetric: Boolean
Check whether 'this' matrix is symmetric.
Check whether 'this' matrix is symmetric.
- Definition Classes
- MatriD
- def isTridiagonal: Boolean
Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal).
Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal). The method may be overriding for efficiency.
- Definition Classes
- MatriD
- def leDimensions(b: MatriD): Boolean
Check whether 'this' matrix dimensions are less than or equal to 'le' those of the other matrix 'b'.
Check whether 'this' matrix dimensions are less than or equal to 'le' those of the other matrix 'b'.
- b
the other matrix
- Definition Classes
- MatriD
- def lowerT: MatrixD
Return the lower triangular of 'this' matrix (rest are zero).
- def lud_ip(): (MatrixD, MatrixD)
Factor in-place 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Factorization algorithm.
- def lud_npp: (MatrixD, MatrixD)
Factor 'this' matrix into the product of upper and lower triangular matrices '(l, u)' using the 'LU' Factorization algorithm.
- def mag: Double
Find the magnitude of 'this' matrix, the element value farthest from zero.
Find the magnitude of 'this' matrix, the element value farthest from zero.
- Definition Classes
- MatriD
- def map(f: (VectoD) => VectoD): MatrixD
Map the elements of 'this' matrix by applying the mapping function 'f'.
- def max(rg1: Range, rg2: Range): Double
Find the maximum element within the specified ranges of 'this' matrix.
Find the maximum element within the specified ranges of 'this' matrix.
- rg1
the range for the first dimension
- rg2
the range for the second dimension
- def max(e: Int = dim1): Double
Find the maximum element in 'this' matrix.
- def mdot(b: MatrixD): MatrixD
Compute the matrix dot product of 'this' matrix and matrix 'b', by first transposing 'this' matrix and then multiplying by 'b' (i.e., 'a dot b = a.t * b').
Compute the matrix dot product of 'this' matrix and matrix 'b', by first transposing 'this' matrix and then multiplying by 'b' (i.e., 'a dot b = a.t * b').
- b
the matrix to multiply by (requires same first dimensions)
- def mdot(b: MatriD): MatrixD
Compute the matrix dot product of 'this' matrix and matrix 'b', by first transposing 'this' matrix and then multiplying by 'b' (i.e., 'a dot b = a.t * b').
- def mean: VectoD
Compute the column means of 'this' matrix.
Compute the column means of 'this' matrix.
- Definition Classes
- MatriD
- def meanNZ: VectoD
Compute the column means of 'this' matrix ignoring zero elements (e.g., a zero may indicate a missing value as in recommender systems).
Compute the column means of 'this' matrix ignoring zero elements (e.g., a zero may indicate a missing value as in recommender systems).
- Definition Classes
- MatriD
- def meanR: VectoD
Compute the row means of 'this' matrix.
Compute the row means of 'this' matrix.
- Definition Classes
- MatriD
- def meanRNZ: VectoD
Compute the row means of 'this' matrix ignoring zero elements (e.g., a zero may indicate a missing value as in recommender systems).
Compute the row means of 'this' matrix ignoring zero elements (e.g., a zero may indicate a missing value as in recommender systems).
- Definition Classes
- MatriD
- def min(rg1: Range, rg2: Range): Double
Find the minimum element within the specified ranges of 'this' matrix.
Find the minimum element within the specified ranges of 'this' matrix.
- rg1
the range for the first dimension
- rg2
the range for the second dimension
- def min(e: Int = dim1): Double
Find the minimum element in 'this' matrix.
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def norm1: Double
Compute the 1-norm of 'this' matrix, i.e., the maximum 1-norm of the column vectors.
Compute the 1-norm of 'this' matrix, i.e., the maximum 1-norm of the column vectors. This is useful for comparing matrices '(a - b).norm1'.
- Definition Classes
- MatriD
- See also
en.wikipedia.org/wiki/Matrix_norm
- def normF: Double
Compute the Frobenius-norm of 'this' matrix, i.e., the square root of the sum of the squared values over all the elements (sqrt (sse)).
Compute the Frobenius-norm of 'this' matrix, i.e., the square root of the sum of the squared values over all the elements (sqrt (sse)). FIX: for
MatriCshould take absolute values, first.- Definition Classes
- MatriD
- See also
en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
- def normFSq: Double
Compute the sqaure of the Frobenius-norm of 'this' matrix, i.e., the sum of the squared values over all the elements (sse).
Compute the sqaure of the Frobenius-norm of 'this' matrix, i.e., the sum of the squared values over all the elements (sse). FIX: for
MatriCshould take absolute values, first.- Definition Classes
- MatriD
- See also
en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
- def normINF: Double
Compute the (infinity) INF-norm of 'this' matrix, i.e., the maximum 1-norm of the row vectors.
Compute the (infinity) INF-norm of 'this' matrix, i.e., the maximum 1-norm of the row vectors.
- Definition Classes
- MatriD
- See also
en.wikipedia.org/wiki/Matrix_norm
- def normalizeU: MatrixD
Create a normalized version of 'this' matrix.
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def nullspace: VectorD
Compute the (right) nullspace of 'this' 'm-by-n' matrix (requires 'n = m+1') by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.
Compute the (right) nullspace of 'this' 'm-by-n' matrix (requires 'n = m+1') by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.
nullspace (a) = set of orthogonal vectors v s.t. a * v = 0
The left nullspace of matrix 'a' is the same as the right nullspace of 'a.t'. FIX: need a more robust algorithm for computing nullspace (@see Fac_QR.scala). FIX: remove the 'n = m+1' restriction.
- def nullspace_ip(): VectorD
Compute in-place the (right) nullspace of 'this' 'm-by-n' matrix (requires 'n = m+1') by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.
Compute in-place the (right) nullspace of 'this' 'm-by-n' matrix (requires 'n = m+1') by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.
nullspace (a) = set of orthogonal vectors v s.t. a * v = 0
The left nullspace of matrix 'a' is the same as the right nullspace of 'a.t'. FIX: need a more robust algorithm for computing nullspace (@see Fac_QR.scala). FIX: remove the 'n = m+1' restriction.
- val range1: Range
Range for the storage array on dimension 1 (rows)
Range for the storage array on dimension 1 (rows)
- Definition Classes
- MatriD
- val range2: Range
Range for the storage array on dimension 2 (columns)
Range for the storage array on dimension 2 (columns)
- Definition Classes
- MatriD
- def reduce: MatrixD
Use Gauss-Jordan reduction on 'this' matrix to make the left part embed an identity matrix.
- def reduce_ip(): MatrixD
Use Gauss-Jordan reduction in-place on 'this' matrix to make the left part embed an identity matrix.
- def sameCrossDimensions(b: MatriD): Boolean
Check whether 'this' matrix and the other matrix 'b' have the same cross dimensions.
Check whether 'this' matrix and the other matrix 'b' have the same cross dimensions.
- b
the other matrix
- Definition Classes
- MatriD
- def sameDimensions(b: MatriD): Boolean
Check whether 'this' matrix and the other matrix 'b' have the same dimensions.
Check whether 'this' matrix and the other matrix 'b' have the same dimensions.
- b
the other matrix
- Definition Classes
- MatriD
- def selectCols(colIndex: Array[Int]): MatrixD
Select columns from 'this' matrix according to the given index/basis.
- def selectRows(rowIndex: Array[Int]): MatrixD
Select rows from 'this' matrix according to the given index/basis.
- def selectRows(rowIndex: VectoI): MatriD
Select rows from 'this' matrix according to the given index/basis 'rowIndex'.
Select rows from 'this' matrix according to the given index/basis 'rowIndex'.
- rowIndex
the row index positions (e.g., (0, 2, 5))
- Definition Classes
- MatriD
- def selectRowsEx(rowIndex: VectoI): MatriD
Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.
Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.
- rowIndex
the row indices to exclude
- Definition Classes
- MatriD
- def selectRowsEx(rowIndex: Array[Int]): MatriD
Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.
Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.
- rowIndex
the row indices to exclude
- Definition Classes
- MatriD
- def set(i: Int, u: VectoD, j: Int = 0): Unit
Set 'this' matrix's 'i'-th row starting at column 'j' to the vector 'u'.
- def set(b: MatriD): Unit
Set all the values in 'this' matrix as copies of the values in matrix 'b'.
- def set(u: Array[Array[Double]]): Unit
Set all the values in 'this' matrix as copies of the values in 2D array 'u'.
- def set(x: Double): Unit
Set all the elements in 'this' matrix to the scalar 'x'.
- def setCol(col: Int, u: VectoD): Unit
Set column 'col' of the matrix to a vector.
- def setDiag(x: Double): Unit
Set the main diagonal of 'this' matrix to the scalar 'x'.
- def setDiag(u: VectoD, k: Int = 0): Unit
Set the 'k'th diagonal of 'this' matrix to the vector 'u'.
- def setFormat(newFormat: String): Unit
Set the format to the 'newFormat'.
- def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): MatrixD
Slice 'this' matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.
- def slice(from: Int, end: Int): MatrixD
Slice 'this' matrix row-wise 'from' to 'end'.
- def slice(rg: Range): MatriD
Slice 'this' matrix row-wise over the given range 'rg'.
Slice 'this' matrix row-wise over the given range 'rg'.
- rg
the range specifying the slice
- Definition Classes
- MatriD
- def sliceCol(from: Int, end: Int): MatrixD
Slice 'this' matrix column-wise 'from' to 'end'.
- def sliceEx(row: Int, col: Int): MatrixD
Slice 'this' matrix excluding the given row and/or column.
- def sliceEx(rg: Range): MatriD
Slice 'this' matrix row-wise excluding the given range 'rg'.
Slice 'this' matrix row-wise excluding the given range 'rg'.
- rg
the excluded range of the slice
- Definition Classes
- MatriD
- def solve(b: VectoD): VectoD
Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' matrix.
- def solve(l: MatriD, u: MatriD, b: VectoD): VectoD
Solve for 'x' in the equation 'l*u*x = b' (see 'lud_npp' above).
- def solve(lu: (MatriD, MatriD), b: VectoD): VectoD
Solve for 'x' in the equation 'l*u*x = b' (see 'lud' above).
Solve for 'x' in the equation 'l*u*x = b' (see 'lud' above).
- lu
the lower and upper triangular matrices
- b
the constant vector
- Definition Classes
- MatriD
- def splitRows(rowIndex: VectoI): (MatriD, MatriD)
Split the rows from 'this' matrix to form two matrices, one from the rows in 'rowIndex' and the other from rows not in 'rowIndex'.
Split the rows from 'this' matrix to form two matrices, one from the rows in 'rowIndex' and the other from rows not in 'rowIndex'.
- rowIndex
the row indices to include/exclude
- Definition Classes
- MatriD
- def splitRows(rowIndex: Array[Int]): (MatriD, MatriD)
Split the rows from 'this' matrix to form two matrices, one from the rows in 'rowIndex' and the other from rows not in 'rowIndex'.
Split the rows from 'this' matrix to form two matrices, one from the rows in 'rowIndex' and the other from rows not in 'rowIndex'.
- rowIndex
the row indices to include/exclude
- Definition Classes
- MatriD
- def sum: Double
Compute the sum of 'this' matrix, i.e., the sum of its elements.
- def sumAbs: Double
Compute the 'abs' sum of 'this' matrix, i.e., the sum of the absolute value of its elements.
- def sumLower: Double
Compute the sum of the lower triangular region of 'this' matrix.
- def swap(i: Int, k: Int, col: Int = 0): Unit
Swap the elements in rows 'i' and 'k' starting from column 'col'.
Swap the elements in rows 'i' and 'k' starting from column 'col'.
- i
the first row in the swap
- k
the second row in the swap
- col
the starting column for the swap (default 0 => whole row)
- Definition Classes
- MatriD
- def swapCol(j: Int, l: Int, row: Int = 0): Unit
Swap the elements in columns 'j' and 'l' starting from row 'row'.
Swap the elements in columns 'j' and 'l' starting from row 'row'.
- j
the first column in the swap
- l
the second column in the swap
- row
the starting row for the swap (default 0 => whole column)
- Definition Classes
- MatriD
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- def t: MatrixD
Transpose 'this' matrix (columns => rows).
- def times(b: MatrixD): MatrixD
Multiply 'this' matrix by matrix 'b' without first transposing 'b'.
Multiply 'this' matrix by matrix 'b' without first transposing 'b'.
- b
the matrix to multiply by (requires 'sameCrossDimensions')
- def times_d(b: MatriD): MatrixD
Multiply 'this' matrix by matrix 'b' using 'dot' product (concise solution).
Multiply 'this' matrix by matrix 'b' using 'dot' product (concise solution).
- b
the matrix to multiply by (requires 'sameCrossDimensions')
- def times_ip(b: MatrixD): MatrixD
Multiply in-place 'this' matrix by matrix 'b' without first transposing 'b'.
Multiply in-place 'this' matrix by matrix 'b' without first transposing 'b'. If 'b' and 'this' reference the same matrix 'b == this', a copy of the 'this' matrix is made.
- b
the matrix to multiply by (requires square and 'sameCrossDimensions')
- def times_ip_pre(b: MatrixD, d: Int = 0): MatrixD
Pre-multiply in-place 'this' ('a') matrix by matrix 'b', starting with column 'd'.
Pre-multiply in-place 'this' ('a') matrix by matrix 'b', starting with column 'd'.
a(d:m, d:n) = b a(d:m, d:n)
- b
the matrix to pre-multiply by 'this' (requires square and 'sameCrossDimensions')
- d
the column to start with
- def times_s(b: MatrixD): MatrixD
Multiply 'this' matrix by matrix 'b' using the Strassen matrix multiplication algorithm.
Multiply 'this' matrix by matrix 'b' using the Strassen matrix multiplication algorithm. Both matrices ('this' and 'b') must be square. Although the algorithm is faster than the traditional cubic algorithm, its requires more memory and is often less stable (due to round-off errors). FIX: could be make more efficient using a virtual slice 'vslice' method.
- b
the matrix to multiply by (it has to be a square matrix)
- See also
http://en.wikipedia.org/wiki/Strassen_algorithm
- def tip(): MatrixD
Transpose, in-place, 'this' matrix (columns => rows).
Transpose, in-place, 'this' matrix (columns => rows). FIX: may wish to use algorithm with better data locality.
- def toDense: MatrixD
Convert 'this' matrix to a dense matrix.
- def toDouble: MatrixD
Convert 'this'
MatrixDinto a dense double matrixMatrixD. - def toInt: MatrixI
Convert 'this'
MatrixDinto a dense integer matrixMatrixI. - def toString(): String
Convert 'this' matrix to a string.
Convert 'this' matrix to a string.
- Definition Classes
- MatrixD → AnyRef → Any
- def trace: Double
Compute the trace of 'this' matrix, i.e., the sum of the elements on the main diagonal.
- def update(ir: Range, jr: Range, b: MatriD): Unit
Set a slice 'this' matrix row-wise on range 'ir' and column-wise on range 'jr'.
- def update(i: Int, u: VectoD): Unit
Set 'this' matrix's row at the 'i'-th index position to the vector 'u'.
- def update(i: Int, j: Int, x: Double): Unit
Set 'this' matrix's element at the 'i,j'-th index position to the scalar 'x'.
- def update(i: Int, jr: Range, u: VectoD): Unit
Set a slice of 'this' matrix row-wise at index 'i' and column-wise on range 'jr' to vector 'u'.
Set a slice of 'this' matrix row-wise at index 'i' and column-wise on range 'jr' to vector 'u'. Ex: a(2, 3..5) = u
- i
the row index
- jr
the column range
- u
the vector to assign
- Definition Classes
- MatriD
- def update(ir: Range, j: Int, u: VectoD): Unit
Set a slice of 'this' matrix row-wise on range 'ir' and column-wise at index 'j' to vector 'u'.
Set a slice of 'this' matrix row-wise on range 'ir' and column-wise at index 'j' to vector 'u'. Ex: a(2..4, 3) = u
- ir
the row range
- j
the column index
- u
the vector to assign
- Definition Classes
- MatriD
- def upperT: MatrixD
Return the upper triangular of 'this' matrix (rest are zero).
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- def write(fileName: String): Unit
Write 'this' matrix to a CSV-formatted text file with name 'fileName'.
- def zero(m: Int = dim1, n: Int = dim2): MatrixD
Create an m-by-n matrix with all elements initialized to zero.
- def ~^(p: Int): MatrixD
Raise 'this' matrix to the 'p'th power (for some integer 'p' >= 1) using a divide and conquer algorithm.
Deprecated Value Members
- def finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.Throwable]) @Deprecated
- Deprecated