class MatrixQ extends MatriQ with Error with Serializable
The MatrixQ class stores and operates on Numeric Matrices of type Rational.
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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- MatrixQ
- Serializable
- MatriQ
- Error
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Instance Constructors
- new MatrixQ(b: MatriQ)
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 MatrixQ(dim: (Int, Int), u: Rational*)
Construct a matrix from repeated values.
Construct a matrix from repeated values.
- dim
the (row, column) dimensions
- u
the repeated values
- new MatrixQ(u: Array[Array[Rational]])
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 MatrixQ(dim1: Int, dim2: Int, x: Rational)
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 MatrixQ(dim1: Int)
Construct a 'dim1' by 'dim1' square matrix.
Construct a 'dim1' by 'dim1' square matrix.
- dim1
the row and column dimension
- new MatrixQ(d1: Int, d2: Int, v: Array[Array[Rational]] = 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: Rational): MatrixQ
Multiply 'this' matrix by scalar 'x'.
- def *(u: VectoQ): VectorQ
Multiply 'this' matrix by (column) vector 'u' (vector elements beyond 'dim2' ignored).
- def *(b: MatriQ): MatrixQ
Multiply 'this' matrix by matrix 'b', transposing 'b' to improve efficiency.
- def *(b: MatrixQ): MatrixQ
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: MatriQ): MatrixQ
Multiply 'this' matrix by matrix 'b' elementwise (Hadamard product).
- def **(u: VectoQ): MatrixQ
Multiply 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
- def **:(u: VectoQ): MatrixQ
Multiply vector 'u' by 'this' matrix to produce another matrix 'u_i * a_ij'.
- def **=(u: VectoQ): MatrixQ
Multiply in-place 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
- def *:(u: VectoQ): VectoQ
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
- MatriQ
- def *=(x: Rational): MatrixQ
Multiply in-place 'this' matrix by scalar 'x'.
- def *=(b: MatriQ): MatrixQ
Multiply in-place 'this' matrix by matrix 'b', transposing 'b' to improve efficiency.
- def *=(b: MatrixQ): MatrixQ
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: Rational): MatrixQ
Add 'this' matrix and scalar 'x'.
- def +(u: VectoQ): MatrixQ
Add 'this' matrix and (row) vector 'u'.
- def +(b: MatriQ): MatrixQ
Add 'this' matrix and matrix 'b' for any type extending MatriQ.
- def +(b: MatrixQ): MatrixQ
Add 'this' matrix and matrix 'b'.
Add 'this' matrix and matrix 'b'.
- b
the matrix to add (requires 'leDimensions')
- def ++(b: MatriQ): MatrixQ
Concatenate (row-wise) 'this' matrix and matrix 'b'.
- def ++^(b: MatriQ): MatrixQ
Concatenate (column-wise) 'this' matrix and matrix 'b'.
- def +:(u: VectoQ): MatrixQ
Concatenate (row) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.
- def +=(x: Rational): MatrixQ
Add in-place 'this' matrix and scalar 'x'.
- def +=(u: VectoQ): MatrixQ
Add in-place 'this' matrix and (row) vector 'u'.
- def +=(b: MatriQ): MatrixQ
Add in-place 'this' matrix and matrix 'b' for any type extending MatriQ.
- def +=(b: MatrixQ): MatrixQ
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: VectoQ): MatrixQ
Concatenate (column) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.
- def -(x: Rational): MatrixQ
From 'this' matrix subtract scalar 'x'.
- def -(u: VectoQ): MatrixQ
From 'this' matrix subtract (row) vector 'u'.
- def -(b: MatriQ): MatrixQ
From 'this' matrix subtract matrix 'b' for any type extending MatriQ.
- def -(b: MatrixQ): MatrixQ
From 'this' matrix subtract matrix 'b'.
From 'this' matrix subtract matrix 'b'.
- b
the matrix to subtract (requires 'leDimensions')
- def -=(x: Rational): MatrixQ
From 'this' matrix subtract in-place scalar 'x'.
- def -=(u: VectoQ): MatrixQ
From 'this' matrix subtract in-place (row) vector 'u'.
- def -=(b: MatriQ): MatrixQ
From 'this' matrix subtract in-place matrix 'b'.
- def -=(b: MatrixQ): MatrixQ
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: Rational): MatrixQ
Divide 'this' matrix by scalar 'x'.
- def /=(x: Rational): MatrixQ
Divide in-place 'this' matrix by scalar 'x'.
- def :+(u: VectoQ): MatrixQ
Concatenate 'this' matrix and (row) vector 'u', i.e., append 'u' to 'this'.
- def :^+(u: VectoQ): MatrixQ
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): MatrixQ
Get the rows from 'this' matrix according to the given index/basis.
- def apply(): Array[Array[Rational]]
Get the underlying 2D array for 'this' matrix.
- def apply(ir: Range, jr: Range): MatrixQ
Get a slice 'this' matrix row-wise on range 'ir' and column-wise on range 'jr'.
- def apply(i: Int): VectorQ
Get 'this' matrix's vector at the 'i'-th index position ('i'-th row).
- def apply(i: Int, j: Int): Rational
Get 'this' matrix's element at the 'i,j'-th index position.
- def apply(i: Int, jr: Range): VectoQ
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
- MatriQ
- def apply(ir: Range, j: Int): VectoQ
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
- MatriQ
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- def bsolve(y: VectoQ): VectorQ
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): MatrixQ
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): VectorQ
Get column 'col' from the matrix, returning it as a vector.
- def copy: MatrixQ
Create an exact copy of 'this' m-by-n matrix.
- def det: Rational
Compute the determinant of 'this' matrix.
- def diag(p: Int, q: Int = 0): MatrixQ
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: MatriQ): MatrixQ
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: MatrixQ): VectorQ
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: MatriQ): VectorQ
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: VectoQ): VectorQ
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
- MatrixQ → 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
- MatriQ
- def flatten: VectorQ
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[Rational]) => 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
- MatriQ
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def getDiag(k: Int = 0): VectorQ
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
- MatrixQ → AnyRef → Any
- def inverse: MatrixQ
Invert 'this' matrix (requires a square matrix) and use partial pivoting.
- def inverse_ip(): MatrixQ
Invert in-place 'this' matrix (requires a square matrix) and uses partial pivoting.
- def inverse_npp: MatrixQ
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
- MatriQ
- 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
- MatriQ
- 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
- MatriQ
- def isSymmetric: Boolean
Check whether 'this' matrix is symmetric.
Check whether 'this' matrix is symmetric.
- Definition Classes
- MatriQ
- 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
- MatriQ
- def leDimensions(b: MatriQ): 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
- MatriQ
- def lowerT: MatrixQ
Return the lower triangular of 'this' matrix (rest are zero).
- def lud_ip(): (MatrixQ, MatrixQ)
Factor in-place 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Factorization algorithm.
- def lud_npp: (MatrixQ, MatrixQ)
Factor 'this' matrix into the product of upper and lower triangular matrices '(l, u)' using the 'LU' Factorization algorithm.
- def mag: Rational
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
- MatriQ
- def map(f: (VectoQ) => VectoQ): MatrixQ
Map the elements of 'this' matrix by applying the mapping function 'f'.
- def max(rg1: Range, rg2: Range): Rational
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): Rational
Find the maximum element in 'this' matrix.
- def mdot(b: MatrixQ): MatrixQ
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: MatriQ): MatrixQ
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: VectoQ
Compute the column means of 'this' matrix.
Compute the column means of 'this' matrix.
- Definition Classes
- MatriQ
- def meanNZ: VectoQ
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
- MatriQ
- def meanR: VectoQ
Compute the row means of 'this' matrix.
Compute the row means of 'this' matrix.
- Definition Classes
- MatriQ
- def meanRNZ: VectoQ
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
- MatriQ
- def min(rg1: Range, rg2: Range): Rational
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): Rational
Find the minimum element in 'this' matrix.
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def norm1: Rational
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
- MatriQ
- See also
en.wikipedia.org/wiki/Matrix_norm
- def normF: Rational
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
- MatriQ
- See also
en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
- def normFSq: Rational
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
- MatriQ
- See also
en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
- def normINF: Rational
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
- MatriQ
- See also
en.wikipedia.org/wiki/Matrix_norm
- def normalizeU: MatrixQ
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: VectorQ
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(): VectorQ
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
- MatriQ
- val range2: Range
Range for the storage array on dimension 2 (columns)
Range for the storage array on dimension 2 (columns)
- Definition Classes
- MatriQ
- def reduce: MatrixQ
Use Gauss-Jordan reduction on 'this' matrix to make the left part embed an identity matrix.
- def reduce_ip(): MatrixQ
Use Gauss-Jordan reduction in-place on 'this' matrix to make the left part embed an identity matrix.
- def sameCrossDimensions(b: MatriQ): 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
- MatriQ
- def sameDimensions(b: MatriQ): 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
- MatriQ
- def selectCols(colIndex: Array[Int]): MatrixQ
Select columns from 'this' matrix according to the given index/basis.
- def selectRows(rowIndex: Array[Int]): MatrixQ
Select rows from 'this' matrix according to the given index/basis.
- def selectRows(rowIndex: VectoI): MatriQ
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
- MatriQ
- def selectRowsEx(rowIndex: VectoI): MatriQ
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
- MatriQ
- def selectRowsEx(rowIndex: Array[Int]): MatriQ
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
- MatriQ
- def set(i: Int, u: VectoQ, j: Int = 0): Unit
Set 'this' matrix's 'i'-th row starting at column 'j' to the vector 'u'.
- def set(b: MatriQ): Unit
Set all the values in 'this' matrix as copies of the values in matrix 'b'.
- def set(u: Array[Array[Rational]]): Unit
Set all the values in 'this' matrix as copies of the values in 2D array 'u'.
- def set(x: Rational): Unit
Set all the elements in 'this' matrix to the scalar 'x'.
- def setCol(col: Int, u: VectoQ): Unit
Set column 'col' of the matrix to a vector.
- def setDiag(x: Rational): Unit
Set the main diagonal of 'this' matrix to the scalar 'x'.
- def setDiag(u: VectoQ, 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): MatrixQ
Slice 'this' matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.
- def slice(from: Int, end: Int): MatrixQ
Slice 'this' matrix row-wise 'from' to 'end'.
- def slice(rg: Range): MatriQ
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
- MatriQ
- def sliceCol(from: Int, end: Int): MatrixQ
Slice 'this' matrix column-wise 'from' to 'end'.
- def sliceEx(row: Int, col: Int): MatrixQ
Slice 'this' matrix excluding the given row and/or column.
- def sliceEx(rg: Range): MatriQ
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
- MatriQ
- def solve(b: VectoQ): VectoQ
Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' matrix.
- def solve(l: MatriQ, u: MatriQ, b: VectoQ): VectoQ
Solve for 'x' in the equation 'l*u*x = b' (see 'lud_npp' above).
- def solve(lu: (MatriQ, MatriQ), b: VectoQ): VectoQ
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
- MatriQ
- def splitRows(rowIndex: VectoI): (MatriQ, MatriQ)
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
- MatriQ
- def splitRows(rowIndex: Array[Int]): (MatriQ, MatriQ)
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
- MatriQ
- def sum: Rational
Compute the sum of 'this' matrix, i.e., the sum of its elements.
- def sumAbs: Rational
Compute the 'abs' sum of 'this' matrix, i.e., the sum of the absolute value of its elements.
- def sumLower: Rational
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
- MatriQ
- 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
- MatriQ
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- def t: MatrixQ
Transpose 'this' matrix (columns => rows).
- def times(b: MatrixQ): MatrixQ
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: MatriQ): MatrixQ
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: MatrixQ): MatrixQ
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: MatrixQ, d: Int = 0): MatrixQ
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: MatrixQ): MatrixQ
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(): MatrixQ
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: MatrixQ
Convert 'this' matrix to a dense matrix.
- def toDouble: MatrixD
Convert 'this'
MatrixQinto a dense double matrixMatrixD. - def toInt: MatrixI
Convert 'this'
MatrixQinto a dense integer matrixMatrixI. - def toString(): String
Convert 'this' matrix to a string.
Convert 'this' matrix to a string.
- Definition Classes
- MatrixQ → AnyRef → Any
- def trace: Rational
Compute the trace of 'this' matrix, i.e., the sum of the elements on the main diagonal.
- def update(ir: Range, jr: Range, b: MatriQ): Unit
Set a slice 'this' matrix row-wise on range 'ir' and column-wise on range 'jr'.
- def update(i: Int, u: VectoQ): Unit
Set 'this' matrix's row at the 'i'-th index position to the vector 'u'.
- def update(i: Int, j: Int, x: Rational): Unit
Set 'this' matrix's element at the 'i,j'-th index position to the scalar 'x'.
- def update(i: Int, jr: Range, u: VectoQ): 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
- MatriQ
- def update(ir: Range, j: Int, u: VectoQ): 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
- MatriQ
- def upperT: MatrixQ
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): MatrixQ
Create an m-by-n matrix with all elements initialized to zero.
- def ~^(p: Int): MatrixQ
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