class MatrixD extends MatriD with Error with Serializable
The MatrixD class stores and operates parallel on Numeric Matrices of type
Double. This class follows the MatrixN framework and is provided for efficiency.
This class is only efficient when the dimension is large.
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Instance Constructors
-
new
MatrixD(u: MatrixD)
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
MatrixD(u: Array[VectorD])
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
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 dimesion
- 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 vector u.
-
def
*(b: MatriD): MatrixD
Multiply this matrix by matrix b, transposing b to improve performance.
-
def
*(b: MatrixD): MatrixD
Multiply this matrix by matrix b, transposing b to improve performance.
Multiply this matrix by matrix b, transposing b to improve performance. Use 'times' method to skip the transpose.
- b
the matrix to multiply by (requires sameCrossDimensions)
-
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 subtype of
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 subtype of
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 subtype of
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 for any subtype of
MatriD. -
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(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, relative: Boolean = true): MatrixD
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[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
def
col(col: Int, from: Int = 0): VectorD
Get column 'col' from the matrix, returning it as a vector.
-
def
copy(): MatriD
Create an exact copy of 'this' m-by-n matrix.
- val d1: Int
- val d2: Int
-
def
det: Double
Compute the determinant of this matrix.
-
def
diag(p: Int, q: Int): 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(p: Int): MatrixD
Form a matrix [Ip, this] where Ip is a p by p identity matrix, by positioning the two matrices Ip and this along the diagonal.
Form a matrix [Ip, this] where Ip is a p by p identity matrix, by positioning the two matrices Ip and this along the diagonal. Fill the rest of matrix with zeros.
- p
the size of identity matrix Ip
-
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(u: VectoD): VectorD
Compute the dot product of 'this' matrix and vector 'u', by first transposing 'this' matrix and then multiplying by 'u' (ie., 'a dot u = a.t * u').
-
def
dot(b: MatrixD): MatrixD
Compute the dot product of 'this' matrix and matrix 'b', by first transposing 'this' matrix and then multiplying by 'b' (ie., 'a dot b = a.t * b').
Compute the dot product of 'this' matrix and matrix 'b', by first transposing 'this' matrix and then multiplying by 'b' (ie., 'a dot b = a.t * b').
- b
the matrix to multiply by (requires same first dimensions)
-
def
dot(b: MatriD): VectoD
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.
-
final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
equals(arg0: Any): Boolean
- Definition Classes
- 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
finalize(): Unit
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] )
-
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[_]
- Definition Classes
- AnyRef → Any
-
def
getDiag(k: Int = 0): VectorD
Get the kth diagonal of this matrix.
- val granularity: Int
-
def
hashCode(): Int
- Definition Classes
- AnyRef → Any
-
def
inverse: MatrixD
Invert this matrix (requires a squareMatrix) and use partial pivoting.
-
def
inverse_ip(): MatrixD
Invert in-place this matrix (requires a squareMatrix) and uses partial pivoting.
-
def
inverse_npp: MatrixD
Invert this matrix (requires a squareMatrix) 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: MatriD
Return the lower triangular of 'this' matrix (rest are zero).
-
def
lud_ip(): (MatrixD, MatrixD)
Decompose in-place this matrix into the product of lower and upper triangular matrices (l, u) using an LU Decomposition algorithm.
-
def
lud_npp: (MatrixD, MatrixD)
Decompose this matrix into the product of upper and lower triangular matrices (l, u) using an LU Decomposition 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
max(e: Int = dim1): Double
Find the maximum element in this matrix.
-
def
mdot(b: MatriD): MatriD
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
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
-
final
def
notify(): Unit
- Definition Classes
- AnyRef
-
final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
-
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. 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(): VectorD
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)
- 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(): Unit
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
set(i: Int, u: VectoD, j: Int = 0): Unit
Set this matrix's ith row starting at column j to the vector u.
-
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 kth 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
sliceCol(from: Int, end: Int): MatrixD
Slice this matrix column-wise 'from' to 'end'.
-
def
sliceExclude(row: Int, col: Int): MatrixD
Slice this matrix excluding the given row and column.
-
def
solve(b: VectoD): VectorD
Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' matrix.
-
def
solve(lu: (MatriD, MatriD), b: VectoD): VectorD
Solve for 'x' in the equation 'l*u*x = b' (see lud_npp above).
-
def
solve(l: MatriD, u: MatriD, b: VectoD): VectorD
Solve for x in the equation l*u*x = b (see lud_npp above).
-
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 (rows => columns).
-
def
times(b: MatrixD): MatrixD
Multiply this matrix by matrix b without transposing b.
Multiply this matrix by matrix b without transposing b.
- b
the matrix to multiply by (requires sameCrossDimensions)
-
def
times_ip(b: MatrixD): Unit
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
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
toDense: MatriD
Convert 'this' matrix to a dense matrix.
-
def
toInt: MatrixI
Convert 'this'
MatriDinto aMatriI. -
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: MatriD
Return the upper triangular of 'this' matrix (rest are zero).
-
final
def
wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
def
write(fileName: String): Unit
Write this matrix to a CSV-formatted text file.
-
def
zero(m: Int, n: Int): MatriD
Create an m-by-n matrix with all elements initialized to zero.
-
def
~^(p: Int): MatrixD
Raise this matrix to the pth power (for some integer p >= 2).