class MatrixN[T] extends Matrix[T] with Error with Serializable
The MatrixN class stores and operates on Numeric Matrices of various sizes
and types. The element type may be any subtype of Numeric.
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Instance Constructors
- new MatrixN(u: MatrixN[T])(implicit arg0: ClassTag[T], arg1: Numeric[T])
Construct a matrix and assign values from matrix 'u'.
Construct a matrix and assign values from matrix 'u'.
- u
the matrix of values to assign
- new MatrixN(u: Array[VectorN[T]])(implicit arg0: ClassTag[T], arg1: Numeric[T])
Construct a matrix and assign values from array of vectors 'u'.
Construct a matrix and assign values from array of vectors 'u'.
- u
the 2D array of values to assign
- new MatrixN(dim: (Int, Int), u: T*)(implicit arg0: ClassTag[T], arg1: Numeric[T])
Construct a matrix from repeated values.
Construct a matrix from repeated values.
- dim
the (row, column) dimensions
- u
the repeated values
- new MatrixN(u: Array[Array[T]])(implicit arg0: ClassTag[T], arg1: Numeric[T])
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 MatrixN(dim1: Int, x: T, y: T)(implicit arg0: ClassTag[T], arg1: Numeric[T])
Construct a 'dim1-by-dim1' square matrix with 'x' assigned on the diagonal and y assigned off the diagonal.
Construct a 'dim1-by-dim1' square matrix with 'x' assigned on the diagonal and y assigned off the diagonal. To obtain an identity matrix, let 'x = 1' and 'y = 0'.
- dim1
the row and column dimension
- x
the scalar value to assign on the diagonal
- y
the scalar value to assign off the diagonal
- new MatrixN(dim1: Int, dim2: Int, x: T)(implicit arg0: ClassTag[T], arg1: Numeric[T])
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 MatrixN(dim1: Int)(implicit arg0: ClassTag[T], arg1: Numeric[T])
Construct a 'dim1-by-dim1' square matrix.
Construct a 'dim1-by-dim1' square matrix.
- dim1
the row and column dimension
- new MatrixN(d1: Int, d2: Int, v: Array[Array[T]] = null)(implicit arg0: ClassTag[T], arg1: Numeric[T])
- 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: T): MatrixN[T]
Multiply this matrix by scalar 'x'.
- def *(u: VectorD): VectorD
Multiply this matrix by vector 'u' (efficient solution).
Multiply this matrix by vector 'u' (efficient solution).
- u
the vector to multiply by
- def *(u: VectorN[T]): VectorN[T]
Multiply this matrix by vector 'u' (efficient solution).
- def *(b: MatrixN[T]): MatrixN[T]
Multiply this matrix by matrix 'b' (efficient solution).
Multiply this matrix by matrix 'b' (efficient solution).
- b
the matrix to multiply by (requires 'sameCrossDimensions')
- def **(u: VectorN[T]): MatrixN[T]
Multiply this matrix by vector 'u' to produce another matrix 'a_ij * b_j'.
- def **=(u: VectorN[T]): MatrixN[T]
Multiply in-place this matrix by vector 'u' to produce another matrix 'a_ij * b_j'.
- def *=(x: T): MatrixN[T]
Multiply in-place this matrix by scalar 'x'.
- def *=(b: MatrixN[T]): MatrixN[T]
Multiply in-place this matrix by matrix 'b'.
Multiply in-place this matrix by matrix '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 +(x: T): MatrixN[T]
Add this matrix and scalar 'x'.
- def +(u: MatrixN[T]): MatrixN[T]
Add this matrix and matrix 'u'.
Add this matrix and matrix 'u'.
- u
the matrix to add (requires 'leDimensions')
- def ++(u: VectorN[T]): MatrixN[T]
Concatenate this matrix and vector 'u'.
- def +=(x: T): MatrixN[T]
Add in-place this matrix and scalar 'x'.
- def +=(b: MatrixN[T]): MatrixN[T]
Add in-place this matrix and matrix 'b'.
Add in-place this matrix and matrix 'b'.
- b
the matrix to add (requires 'leDimensions')
- def -(x: T): MatrixN[T]
From this matrix subtract scalar 'x'.
- def -(b: MatrixN[T]): MatrixN[T]
From this matrix subtract matrix 'b'.
From this matrix subtract matrix 'b'.
- b
the matrix to subtract (requires 'leDimensions')
- def -=(x: T): MatrixN[T]
From this matrix subtract in-place scalar x.
- def -=(b: MatrixN[T]): MatrixN[T]
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: T)(implicit fr: Fractional[T]): MatrixN[T]
Divide this matrix by scalar 'x'.
- def /=(x: T)(implicit fr: Fractional[T]): MatrixN[T]
Divide in-place this matrix by scalar 'x'.
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- val _0: T
Numeric zero (0)
- val _1: T
Numeric one (1)
- val _1n: T
Numeric minus one (-1)
- def apply(i: Int, jr: Range): VectorN[T]
Get a slice this matrix row-wise at index 'i' and column-wise on range 'jr'.
- def apply(ir: Range, j: Int): VectorN[T]
Get a slice this matrix row-wise on range 'ir' and column-wise at index 'j'.
- def apply(ir: Range, jr: Range): MatrixN[T]
Get a slice this matrix row-wise on range 'ir' and column-wise on range 'jr'.
- def apply(i: Int): VectorN[T]
Get this matrix's vector at the 'i'th index position ('i'th row).
- def apply(i: Int, j: Int): T
Get this matrix's element at the 'i,j'-th index position.
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- def clean(thres: T, relative: Boolean = true)(implicit fr: Fractional[T]): MatrixN[T]
Clean values in matrix at or below the threshold by setting them to zero.
Clean values in matrix at or below the threshold 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): VectorN[T]
Get column 'col' from the matrix, returning it as a vector.
- val d1: Int
- val d2: Int
- def det: T
Compute the determinant of this matrix.
- def diag(p: Int, q: Int): MatrixN[T]
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: MatrixN[T]): MatrixN[T]
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]'.
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]'.
- b
the matrix to combine with this matrix
- lazy val dim1: Int
Dimension 1
- lazy val dim2: Int
Dimension 2
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def equals(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef → Any
- 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[T]) => U): Unit
Iterate over the matrix row by row.
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def getDiag(k: Int = 0): VectorN[T]
Get 'k'th main diagonal of this matrix.
- def hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def inverse(implicit fr: Fractional[T]): MatrixN[T]
Invert this matrix (requires a 'squareMatrix') using partial pivoting.
- def inverse_ip(implicit fr: Fractional[T]): MatrixN[T]
Invert in-place this matrix (requires a 'squareMatrix') using partial pivoting.
- def inverse_npp(implicit fr: Fractional[T]): MatrixN[T]
Invert this matrix (requires a 'squareMatrix') not using partial pivoting.
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- def isNonnegative: Boolean
Check whether this matrix is nonnegative (has no negative elements).
- 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
- Matrix
- def isSymmetric: Boolean
Check whether this matrix is symmetric.
Check whether this matrix is symmetric.
- Definition Classes
- Matrix
- def leDimensions(b: Matrix[T]): Boolean
Check whether this matrix dimensions are less than or equal to 'le' those of the other Matrix.
Check whether this matrix dimensions are less than or equal to 'le' those of the other Matrix.
- b
the other matrix
- Definition Classes
- Matrix
- def lud(implicit fr: Fractional[T]): (MatrixN[T], MatrixN[T])
Decompose this matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.
- def lud_ip(implicit fr: Fractional[T]): (MatrixN[T], MatrixN[T])
Decompose in-place this matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.
- def lud_npp(implicit fr: Fractional[T]): (MatrixN[T], MatrixN[T])
Decompose this matrix into the product of upper and lower triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.
Decompose this matrix into the product of upper and lower triangular matrices '(l, u)' using the 'LU' Decomposition algorithm. This version uses no partial pivoting.
- def mag: T
Find the magnitude of this matrix, the element value farthest from zero.
- def max(e: Int = dim1): T
Find the maximum element in this matrix.
- def min(e: Int = dim1): T
Find the minimum element in this matrix.
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def norm1: T
Compute the 1-norm of this matrix, i.e., the maximum 1-norm of the column vectors.
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- val nu: Numeric[T]
Import Numeric evidence (gets nu val from superclass)
- def nullspace(implicit fr: Fractional[T]): VectorN[T]
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. The nullspace of matrix 'a' is "this vector 'v' times any scalar 's'", i.e., 'a*(v*s) = 0'. The left nullspace of matrix 'a' is the same as the right nullspace of 'a.t' ('a' transpose).
- def nullspace_ip(implicit fr: Fractional[T]): VectorN[T]
Compute the (right) nullspace in-place 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 in-place 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. The nullspace of matrix 'a' is "this vector 'v' times any scalar 's'", i.e., 'a*(v*s) = 0'. The left nullspace of matrix 'a' is the same as the right nullspace of 'a.t' ('a' transpose).
- val range1: Range
Range for the storage array on dimension 1 (rows)
Range for the storage array on dimension 1 (rows)
- Attributes
- protected
- Definition Classes
- Matrix
- val range2: Range
Range for the storage array on dimension 2 (columns)
Range for the storage array on dimension 2 (columns)
- Attributes
- protected
- Definition Classes
- Matrix
- def rank(implicit fr: Fractional[T]): Int
Determine the rank of this 'm-by-n' matrix by taking the upper triangular matrix from the 'LU' Decomposition and counting the number of non-zero diagonal elements.
Determine the rank of this 'm-by-n' matrix by taking the upper triangular matrix from the 'LU' Decomposition and counting the number of non-zero diagonal elements. FIX: should implement in implementing classes.
- Definition Classes
- Matrix
- def reduce(implicit fr: Fractional[T]): MatrixN[T]
Use Gauss-Jordan reduction on this matrix to make the left part embed an identity matrix.
- def reduce_ip(implicit fr: Fractional[T]): MatrixN[T]
Use Gauss-Jordan reduction in-place on this matrix to make the left part embed an identity matrix.
- def sameCrossDimensions(b: Matrix[T]): Boolean
Check whether this matrix and the other matrix have the same cross dimensions.
Check whether this matrix and the other matrix have the same cross dimensions.
- b
the other matrix
- Definition Classes
- Matrix
- def sameDimensions(b: Matrix[T]): Boolean
Check whether this matrix and the other Matrix have the same dimensions.
Check whether this matrix and the other Matrix have the same dimensions.
- b
the other matrix
- Definition Classes
- Matrix
- def selectCols(colIndex: Array[Int]): MatrixN[T]
Select columns from this matrix according to the given index/basis.
- def selectRows(rowIndex: Array[Int]): MatrixN[T]
Select rows from this matrix according to the given index/basis.
- def set(i: Int, u: VectorN[T], j: Int = 0): Unit
Set this matrix's 'i'th row starting at column 'j' to the vector 'u'.
- def set(u: Array[Array[T]]): Unit
Set all the values in this matrix as copies of the values in 2D array 'u'.
- def set(x: T): Unit
Set all the elements in this matrix to the scalar 'x'.
- def setCol(col: Int, u: VectorN[T]): Unit
Set column 'col' of the matrix to a vector.
- def setDiag(x: T): Unit
Set the main diagonal of this matrix to the scalar 'x'.
- def setDiag(u: VectorN[T], k: Int = 0): Unit
Set the 'k'th diagonal of this matrix to the vector 'u'.
- def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): MatrixN[T]
Slice this matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.
- def slice(from: Int, end: Int): MatrixN[T]
Slice this matrix row-wise 'from' to 'end'.
- def sliceExclude(row: Int, col: Int): MatrixN[T]
Slice this matrix excluding the given row and column.
- def solve(b: VectorN[T])(implicit fr: Fractional[T]): VectorN[T]
Solve for 'x' in the equation 'a*x = b' where 'a' is this matrix (see 'lud' above).
- def solve(lu: (Matrix[T], Matrix[T]), b: VectorN[T])(implicit fr: Fractional[T]): VectorN[T]
Solve for 'x' in the equation 'l*u*x = b' (see 'lud' above).
- def solve(l: Matrix[T], u: Matrix[T], b: VectorN[T])(implicit fr: Fractional[T]): VectorN[T]
Solve for 'x' in the equation 'l*u*x = b' (see 'lud' above).
- def sum: T
Compute the sum of this matrix, i.e., the sum of its elements.
- def sumAbs: T
Compute the 'abs' sum of this matrix, i.e., the sum of the absolute value of its elements.
- def sumLower: T
Compute the sum of the lower triangular region of this matrix.
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- def t: MatrixN[T]
Transpose this matrix (rows => columns).
- def toString(): String
Convert this matrix to a string.
Convert this matrix to a string.
- Definition Classes
- MatrixN → AnyRef → Any
- def trace: T
Compute the trace of this matrix, i.e., the sum of the elements on the main diagonal.
- def update(i: Int, jr: Range, u: VectorN[T]): Unit
Set a slice this matrix row-wise at index 'i' and column-wise on range 'jr'.
- def update(ir: Range, j: Int, u: VectorN[T]): Unit
Set a slice this matrix row-wise on range 'ir' and column-wise at index 'j'.
- def update(ir: Range, jr: Range, b: MatrixN[T]): Unit
Set a slice this matrix row-wise on range 'ir' and column-wise on range 'jr'.
Set a slice this matrix row-wise on range 'ir' and column-wise on range 'jr'. Ex: a(2..4, 3..5) = b
- ir
the row range
- jr
the column range
- b
the matrix to assign
- def update(i: Int, u: VectorN[T]): Unit
Set this matrix's row at the 'i'th index position to the vector 'u'.
- def update(i: Int, j: Int, x: T): Unit
Set this matrix's element at the 'i,j'-th index position to the scalar 'x'.
- 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 ~^(p: Int): MatrixN[T]
Raise this matrix to the 'p'th power (for some integer 'p >= 2').
Deprecated Value Members
- def finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.Throwable]) @Deprecated
- Deprecated