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.
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Instance Constructors
-
new
MatrixQ(b: MatrixQ)
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[MM_ArrayQ])
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 dimesion
- 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[MM_ArrayQ] = 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: VectorQ): VectorQ
Multiply 'this' matrix by 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
**(u: VectorQ): MatrixQ
Multiply 'this' matrix by vector 'u' to produce another matrix '(a_ij * u_j)'.
-
def
**=(u: VectorQ): MatrixQ
Multiply in-place 'this' matrix by vector 'u' to produce another matrix '(a_ij * u_j)'.
-
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: VectorQ): 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: VectorQ): 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: VectorQ): 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: VectorQ): 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: VectorQ): 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: VectorQ): 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: VectorQ): MatrixQ
Concatenate 'this' matrix and (row) vector 'u', i.e., append 'u' to 'this'.
-
def
:^+(u: VectorQ): 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(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): VectorQ
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): VectorQ
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
clean(thres: Double, 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[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
def
col(col: Int, from: Int = 0): VectorQ
Get column 'col' from the matrix, returning it as a vector.
- val d1: Int
- val d2: Int
-
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]'.
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lazy val
dim1: Int
Dimension 1
-
lazy val
dim2: Int
Dimension 2
-
def
dot(u: VectorQ): VectorQ
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').
-
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
- MatriQ
-
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: (MM_ArrayQ) ⇒ 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[_]
- Definition Classes
- AnyRef → Any
-
def
getDiag(k: Int = 0): VectorQ
Get the kth diagonal of 'this' matrix.
-
def
hashCode(): Int
- Definition Classes
- 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-zreo elements only in main diagonal and superdiagonal).
Check whether 'this' matrix is bidiagonal (has non-zreo elements only in main diagonal and superdiagonal). 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-zreo elements only in main diagonal and superdiagonal).
Check whether 'this' matrix is bidiagonal (has non-zreo elements only in main diagonal and superdiagonal). 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
lud: (MatrixQ, MatrixQ)
Factor 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using the LU Factorization algorithm.
-
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.
Factor 'this' matrix into the product of upper and lower triangular matrices '(l, u)' using the LU Factorization algorithm. This version uses no partial pivoting.
-
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
max(e: Int = dim1): Rational
Find the maximum element in 'this' matrix.
-
def
mean: VectorQ
Compute the column means of this matrix.
Compute the column means of this matrix.
- Definition Classes
- MatriQ
-
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
-
final
def
notify(): Unit
- Definition Classes
- AnyRef
-
final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
-
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)
- Attributes
- protected
- Definition Classes
- MatriQ
-
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
- MatriQ
-
def
rank: Int
Determine the rank of 'this' m-by-n matrix by taking the upper triangular matrix 'u' 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 'u' from the LU Decomposition and counting the number of non-zero diagonal elements. Implementing classes may override this method with a better one (e.g., SVD or Rank Revealing QR).
- Definition Classes
- MatriQ
- See also
http://en.wikipedia.org/wiki/Rank_%28linear_algebra%29
-
def
reduce: MatrixQ
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: 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
set(i: Int, u: VectorQ, j: Int = 0): Unit
Set 'this' matrix's 'i'-th row starting at column 'j' to the vector 'u'.
-
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: VectorQ): 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: VectorQ, 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): 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
sliceCol(from: Int, end: Int): MatrixQ
Slice 'this' matrix column-wise 'from' to 'end'.
-
def
sliceExclude(row: Int, col: Int): MatrixQ
Slice 'this' matrix excluding the given row and/or column.
-
def
solve(b: VectorQ): VectorQ
Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' matrix.
-
def
solve(u: MatriQ, b: VectorQ): VectorQ
Solve for 'x' in the equation 'l*u*x = b' where 'l = this'.
Solve for 'x' in the equation 'l*u*x = b' where 'l = this'. Requires 'l' to be lower triangular.
- u
the upper triangular matrix
- b
the constant vector
-
def
solve(l: MatriQ, u: MatriQ, b: VectorQ): VectorQ
Solve for 'x' in the equation 'l*u*x = b' (see lud above).
-
def
solve(lu: (MatriQ, MatriQ), b: VectorQ): VectorQ
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
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 (rows => columns).
-
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): Unit
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_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
toString(): String
Convert 'this' real (double precision) matrix to a string.
Convert 'this' real (double precision) 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: VectorQ): 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: VectorQ): 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: VectorQ): 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
-
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 with name 'fileName'.
-
def
~^(p: Int): MatrixQ
Raise 'this' matrix to the 'p'th power (for some integer 'p' >= 2).