class SparseMatrixQ extends MatriQ with Error with Serializable
The SparseMatrixQ class stores and operates on Matrices of Rationals. Rather
than storing the matrix as a 2 dimensional array, it is stored as an array
of sorted-linked-maps, which record all the non-zero values for each particular
row, along with their j-index as (j, v) pairs.
- Alphabetic
- By Inheritance
- SparseMatrixQ
- Serializable
- Serializable
- MatriQ
- Error
- AnyRef
- Any
- Hide All
- Show All
- Public
- All
Instance Constructors
-
new
SparseMatrixQ(b: MatrixQ)
Construct a sparse matrix and assign values from dense matrix
MatrixQ'b'.Construct a sparse matrix and assign values from dense matrix
MatrixQ'b'.- b
the matrix of values to assign
-
new
SparseMatrixQ(b: SparseMatrixQ)
Construct a sparse matrix and assign values from matrix 'b'.
Construct a sparse matrix and assign values from matrix 'b'.
- b
the matrix of values to assign
-
new
SparseMatrixQ(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
SparseMatrixQ(dim1: Int, dim2: Int, x: Rational)
Construct a 'dim1' by 'dim2' sparse matrix and assign each element the value 'x'.
Construct a 'dim1' by 'dim2' sparse matrix and assign each element the value 'x'.
- dim1
the row dimension
- dim2
the column dimension
- x
the scalar value to assign
-
new
SparseMatrixQ(dim1: Int)
Construct a 'dim1' by 'dim1' square sparse matrix.
Construct a 'dim1' by 'dim1' square sparse matrix.
- dim1
the row and column dimension
-
new
SparseMatrixQ(dim1: Int, dim2: Int, u: Array[RowMap])
Construct a 'dim1' by 'dim2' sparse matrix from an array of sorted-linked-maps.
Construct a 'dim1' by 'dim2' sparse matrix from an array of sorted-linked-maps.
- dim1
the row dimension
- dim2
the column dimension
- u
the array of sorted-linked-maps
-
new
SparseMatrixQ(d1: Int, d2: Int)
- d1
the first/row dimension
- d2
the second/column dimension
Value Members
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
##(): Int
- Definition Classes
- AnyRef → Any
-
def
*(x: Rational): SparseMatrixQ
Multiply 'this' sparse matrix by scalar 'x'.
Multiply 'this' sparse matrix by scalar 'x'.
- x
the scalar to multiply by
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
*(u: VectoQ): VectorQ
Multiply 'this' sparse matrix by vector 'u' (vector elements beyond 'dim2' ignored).
Multiply 'this' sparse matrix by vector 'u' (vector elements beyond 'dim2' ignored).
- u
the vector to multiply by
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
*(b: MatriQ): SparseMatrixQ
Multiply 'this' sparse matrix by dense matrix 'b'.
Multiply 'this' sparse matrix by dense matrix 'b'.
- b
the matrix to multiply by (requires 'sameCrossDimensions')
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
*(b: SparseMatrixQ): SparseMatrixQ
Multiply 'this' sparse matrix by sparse matrix 'b', by performing a merge operation on the rows on 'this' sparse matrix and the transpose of the 'b' matrix.
Multiply 'this' sparse matrix by sparse matrix 'b', by performing a merge operation on the rows on 'this' sparse matrix and the transpose of the 'b' matrix.
- b
the matrix to multiply by (requires 'sameCrossDimensions')
-
def
**(u: VectoQ): SparseMatrixQ
Multiply 'this' sparse matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
Multiply 'this' sparse matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
- u
the vector to multiply by
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
**(b: MatriQ): MatriQ
Multiply 'this' matrix by matrix 'b' elementwise (Hadamard product).
Multiply 'this' matrix by matrix 'b' elementwise (Hadamard product).
- b
the matrix to multiply by
- Definition Classes
- MatriQ
- See also
en.wikipedia.org/wiki/Hadamard_product_(matrices) FIX - remove ??? and implement in all implementing classes
-
def
**:(u: VectoQ): SparseMatrixQ
Multiply vector 'u' by 'this' matrix to produce another matrix 'u_i * a_ij'.
Multiply vector 'u' by 'this' matrix to produce another matrix 'u_i * a_ij'. E.g., multiply a diagonal matrix represented as a vector by a matrix. This operator is right associative.
- u
the vector to multiply by
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
**=(u: VectoQ): SparseMatrixQ
Multiply in-place 'this' sparse matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
Multiply in-place 'this' sparse matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
- u
the vector to multiply by
- Definition Classes
- SparseMatrixQ → MatriQ
-
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): SparseMatrixQ
Multiply in-place 'this' sparse matrix by scalar 'x'.
Multiply in-place 'this' sparse matrix by scalar 'x'.
- x
the scalar to multiply by
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
*=(b: MatriQ): SparseMatrixQ
Multiply in-place 'this' sparse matrix by dense matrix 'b'.
Multiply in-place 'this' sparse matrix by dense matrix 'b'.
- b
the matrix to multiply by (requires square and 'sameCrossDimensions')
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
*=(b: SparseMatrixQ): SparseMatrixQ
Multiply in-place 'this' sparse matrix by sparse matrix 'b', by performing a merge operation on the rows on 'this' sparse matrix and the transpose of the 'b' matrix.
Multiply in-place 'this' sparse matrix by sparse matrix 'b', by performing a merge operation on the rows on 'this' sparse matrix and the transpose of the 'b' matrix.
- b
the matrix to multiply by (requires square and 'sameCrossDimensions')
-
def
+(x: Rational): MatrixQ
Add 'this' sparse matrix and scalar 'x'.
Add 'this' sparse matrix and scalar 'x'. Note: every element will be likely filled, hence the return type is a dense matrix.
- x
the scalar to add
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
+(u: VectoQ): SparseMatrixQ
Add 'this' sparse matrix and (row) vector 'u'.
Add 'this' sparse matrix and (row) vector 'u'.
- u
the vector to add
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
+(b: MatriQ): SparseMatrixQ
Add 'this' sparse matrix and matrix 'b'.
Add 'this' sparse matrix and matrix 'b'. 'b' may be any subtype of
MatriQ. Note, subtypes ofMatriQshould also implement a more efficient version, e.g.,def + (b: SparseMatrixQ): SparseMatrixQ.- b
the matrix to add (requires 'sameCrossDimensions')
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
+(b: SparseMatrixQ): SparseMatrixQ
Add 'this' sparse matrix and sparse matrix 'b'.
Add 'this' sparse matrix and sparse matrix 'b'.
- b
the matrix to add (requires 'sameCrossDimensions')
-
def
++(b: MatriQ): SparseMatrixQ
Concatenate (row-wise) 'this' matrix and matrix 'b'.
Concatenate (row-wise) 'this' matrix and matrix 'b'.
- b
the matrix to be concatenated as the new last rows in new matrix
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
++^(b: MatriQ): SparseMatrixQ
Concatenate (column-wise) 'this' matrix and matrix 'b'.
Concatenate (column-wise) 'this' matrix and matrix 'b'.
- b
the matrix to be concatenated as the new last columns in new matrix
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
+:(u: VectoQ): SparseMatrixQ
Concatenate (row) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.
Concatenate (row) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.
- u
the vector to be prepended as the new first row in new matrix
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
+=(x: Rational): SparseMatrixQ
Add in-place 'this' sparse matrix and scalar 'x'.
Add in-place 'this' sparse matrix and scalar 'x'.
- x
the scalar to add
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
+=(u: VectoQ): SparseMatrixQ
Add in-place this matrix and (row) vector 'u'.
Add in-place this matrix and (row) vector 'u'.
- u
the vector to add
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
+=(b: MatriQ): SparseMatrixQ
Add in-place 'this' sparse matrix and matrix 'b'.
Add in-place 'this' sparse matrix and matrix 'b'.
- b
the matrix to add (requires 'sameCrossDimensions')
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
+=(b: SparseMatrixQ): SparseMatrixQ
Add in-place 'this' sparse matrix and sparse matrix 'b'.
Add in-place 'this' sparse matrix and sparse matrix 'b'.
- b
the matrix to add (requires 'sameCrossDimensions')
-
def
+^:(u: VectoQ): SparseMatrixQ
Concatenate (column) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.
Concatenate (column) vector 'u' and 'this' matrix, i.e., prepend 'u' to 'this'.
- u
the vector to be prepended as the new first column in new matrix
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
-(x: Rational): MatrixQ
From 'this' sparse matrix subtract scalar 'x'.
From 'this' sparse matrix subtract scalar 'x'. Note: every element will be likely filled, hence the return type is a dense matrix.
- x
the scalar to subtract
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
-(u: VectoQ): SparseMatrixQ
From
thissparse matrix subtract (row) vector 'u'.From
thissparse matrix subtract (row) vector 'u'.- u
the vector to subtract
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
-(b: MatriQ): SparseMatrixQ
From 'this' sparse matrix subtract matrix 'b'.
From 'this' sparse matrix subtract matrix 'b'.
- b
the matrix to subtract (requires 'sameCrossDimensions')
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
-(b: SparseMatrixQ): SparseMatrixQ
From 'this' sparse matrix subtract matrix 'b'.
From 'this' sparse matrix subtract matrix 'b'.
- b
the sparse matrix to subtract (requires 'sameCrossDimensions')
-
def
-=(x: Rational): SparseMatrixQ
From 'this' sparse matrix subtract in-place scalar 'x'.
From 'this' sparse matrix subtract in-place scalar 'x'.
- x
the scalar to subtract
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
-=(u: VectoQ): SparseMatrixQ
From
thissparse matrix subtract in-place (row) vector 'u'.From
thissparse matrix subtract in-place (row) vector 'u'.- u
the vector to subtract
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
-=(b: MatriQ): SparseMatrixQ
From 'this' sparse matrix subtract in-place matrix 'b'.
From 'this' sparse matrix subtract in-place matrix 'b'.
- b
the matrix to subtract (requires 'sameCrossDimensions')
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
-=(b: SparseMatrixQ): SparseMatrixQ
From 'this' sparse matrix subtract in-place sparse matrix 'b'.
From 'this' sparse matrix subtract in-place sparse matrix 'b'.
- b
the sparse matrix to subtract (requires 'sameCrossDimensions')
-
def
/(x: Rational): SparseMatrixQ
Divide 'this' sparse matrix by scalar 'x'.
Divide 'this' sparse matrix by scalar 'x'.
- x
the scalar to divide by
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
/=(x: Rational): SparseMatrixQ
Divide in-place 'this' sparse matrix by scalar 'x'.
Divide in-place 'this' sparse matrix by scalar 'x'.
- x
the scalar to divide by
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
:+(u: VectoQ): SparseMatrixQ
Concatenate 'this' matrix and (row) vector 'u', i.e., append 'u' to 'this'.
Concatenate 'this' matrix and (row) vector 'u', i.e., append 'u' to 'this'.
- u
the vector to be appended as the new last row in new matrix
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
:^+(u: VectoQ): SparseMatrixQ
Concatenate 'this' matrix and (column) vector 'u', i.e., append 'u' to 'this'.
Concatenate 'this' matrix and (column) vector 'u', i.e., append 'u' to 'this'.
- u
the vector to be appended as the new last column in new matrix
- Definition Classes
- SparseMatrixQ → MatriQ
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
def
apply(ir: Range, jr: Range): SparseMatrixQ
Get a slice this matrix row-wise on range 'ir' and column-wise on range 'jr'.
Get a slice this matrix row-wise on range 'ir' and column-wise on range 'jr'. Ex: b = a(2..4, 3..5)
- ir
the row range
- jr
the column range
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
apply(i: Int): VectorQ
Get 'this' sparse matrix's vector at the 'i'-th index position ('i'-th row).
Get 'this' sparse matrix's vector at the 'i'-th index position ('i'-th row).
- i
the row index
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
apply(i: Int, j: Int): Rational
Get 'this' sparse matrix's element at the 'i,j'-th index position.
Get 'this' sparse matrix's element at the 'i,j'-th index position.
- i
the row index
- j
the column index
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
apply(iv: VectoI): MatriQ
Get the rows indicated by the index vector 'iv' FIX - implement in all implementing classes
Get the rows indicated by the index vector 'iv' FIX - implement in all implementing classes
- iv
the vector of row indices
- Definition Classes
- MatriQ
-
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).
Solve for 'x' using back substitution in the equation 'u*x = y' where 'this' matrix ('u') is upper triangular (see 'lud_npp' above).
- y
the constant vector
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
clean(thres: Double, relative: Boolean = true): SparseMatrixQ
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
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( ... ) @native() @HotSpotIntrinsicCandidate()
-
def
col(col: Int, from: Int = 0): VectorQ
Get column 'col' from the matrix, returning it as a vector.
Get column 'col' from the matrix, returning it as a vector.
- col
the column to extract from the matrix
- from
the position to start extracting from
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
copy(): SparseMatrixQ
Create a clone of 'this' 'm-by-n' sparse matrix.
Create a clone of 'this' 'm-by-n' sparse matrix.
- Definition Classes
- SparseMatrixQ → MatriQ
- val d1: Int
- val d2: Int
-
def
det: Rational
Compute the determinant of 'this' sparse matrix.
Compute the determinant of 'this' sparse matrix.
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
diag(p: Int, q: Int): SparseMatrixQ
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.
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.
- p
the size of identity matrix Ip
- q
the size of identity matrix Iq
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
diag(b: MatriQ): SparseMatrixQ
Combine 'this' sparse 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' sparse 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
- Definition Classes
- SparseMatrixQ → MatriQ
-
lazy val
dim1: Int
Dimension 1
Dimension 1
- Definition Classes
- SparseMatrixQ → MatriQ
-
lazy val
dim2: Int
Dimension 2
Dimension 2
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
dot(b: MatriQ): VectorQ
Compute the dot product of 'this' matrix with matrix 'b' to produce a vector.
Compute the dot product of 'this' matrix with matrix 'b' to produce a vector.
- b
the second matrix of the dot product
- Definition Classes
- SparseMatrixQ → MatriQ
-
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').
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').
- u
the vector to multiply by (requires same first dimensions)
- Definition Classes
- SparseMatrixQ → MatriQ
-
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
flatten: VectoQ
Flatten 'this' matrix in row-major fashion, returning a vector containing all the elements from the matrix.
Flatten 'this' matrix in row-major fashion, returning a vector containing all the elements from the matrix.
- Definition Classes
- MatriQ
-
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[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
-
def
getDiag(k: Int = 0): VectorQ
Get the 'k'th diagonal of this matrix.
Get the 'k'th diagonal of this matrix. Assumes 'dim2 >= dim1'.
- k
how far above the main diagonal, e.g., (-1, 0, 1) for (sub, main, super)
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
-
def
inverse: SparseMatrixQ
Invert 'this' sparse matrix (requires a 'squareMatrix') using partial pivoting.
Invert 'this' sparse matrix (requires a 'squareMatrix') using partial pivoting.
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
inverse_ip(): SparseMatrixQ
Invert in-place 'this' sparse matrix (requires a 'squareMatrix').
Invert in-place 'this' sparse matrix (requires a 'squareMatrix'). This version uses partial pivoting.
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
inverse_npp: SparseMatrixQ
Invert 'this' sparse matrix (requires a 'squareMatrix') not using 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' sparse matrix is nonnegative (has no negative elements).
Check whether 'this' sparse matrix is nonnegative (has no negative elements).
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
isRectangular: Boolean
Check whether 'this' sparse matrix is rectangular (all rows have the same number of columns).
Check whether 'this' sparse matrix is rectangular (all rows have the same number of columns).
- Definition Classes
- SparseMatrixQ → MatriQ
-
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: SparseMatrixQ
Return the lower triangular of 'this' matrix (rest are zero).
Return the lower triangular of 'this' matrix (rest are zero).
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
lud_ip(): (SparseMatrixQ, SparseMatrixQ)
Factor in-place 'this' sparse matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.
Factor in-place 'this' sparse matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
lud_npp: (SparseMatrixQ, SparseMatrixQ)
Factor 'this' sparse matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.
Factor 'this' sparse matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.
- Definition Classes
- SparseMatrixQ → MatriQ
-
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): MatriQ
Map the elements of 'this' matrix by applying the mapping function 'f'.
Map the elements of 'this' matrix by applying the mapping function 'f'. FIX - remove ??? and implement in all implementing classes
- f
the function to apply
- Definition Classes
- MatriQ
-
def
max(e: Int = dim1): Rational
Find the maximum element in 'this' sparse matrix.
Find the maximum element in 'this' sparse matrix.
- e
the ending row index (exclusive) for the search
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
mdot(b: MatriQ): SparseMatrixQ
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)
- Definition Classes
- SparseMatrixQ → MatriQ
-
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(e: Int = dim1): Rational
Find the minimum element in 'this' sparse matrix.
Find the minimum element in 'this' sparse matrix.
- e
the ending row index (exclusive) for the search
- Definition Classes
- SparseMatrixQ → MatriQ
-
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
-
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.
- Definition Classes
- SparseMatrixQ → MatriQ
- See also
http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces
/solving-ax-0-pivot-variables-special-solutions/MIT18_06SCF11_Ses1.7sum.pdf
-
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.
- Definition Classes
- SparseMatrixQ → MatriQ
- See also
http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces
/solving-ax-0-pivot-variables-special-solutions/MIT18_06SCF11_Ses1.7sum.pdf
-
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: SparseMatrixQ
Use Gauss-Jordan reduction on 'this' sparse matrix to make the left part embed an identity matrix.
Use Gauss-Jordan reduction on 'this' sparse matrix to make the left part embed an identity matrix. A constraint on this m by n matrix is that n >= m. It can be used to solve 'a * x = b': augment 'a' with 'b' and call reduce. Takes '[a | b]' to '[I | x]'.
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
reduce_ip(): Unit
Use Gauss-Jordan reduction in-place on 'this' sparse matrix to make the left part embed an identity matrix.
Use Gauss-Jordan reduction in-place on 'this' sparse matrix to make the left part embed an identity matrix. A constraint on this m by n matrix is that n >= m. It can be used to solve 'a * x = b': augment 'a' with 'b' and call reduce. Takes '[a | b]' to '[I | x]'.
- Definition Classes
- SparseMatrixQ → MatriQ
-
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]): SparseMatrixQ
Select columns from this matrix according to the given index/basis.
Select columns from this matrix according to the given index/basis. Ex: Can be used to divide a matrix into a basis and a non-basis.
- colIndex
the column index positions (e.g., (0, 2, 5))
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
selectRows(rowIndex: Array[Int]): SparseMatrixQ
Select rows from this matrix according to the given index/basis.
Select rows from this matrix according to the given index/basis.
- rowIndex
the row index positions (e.g., (0, 2, 5))
- Definition Classes
- SparseMatrixQ → MatriQ
-
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'.
Set this matrix's 'i'th row starting at column 'j' to the vector 'u'.
- i
the row index
- u
the vector value to assign
- j
the starting column index
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
set(u: MatriQ): Unit
Set the values in 'this' matrix as copies of the values in matrix 'u'.
Set the values in 'this' matrix as copies of the values in matrix 'u'.
- u
the matrix of values to assign
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
set(u: Array[Array[Rational]]): Unit
Set all the values in this matrix as copies of the values in 2D array 'u'.
Set all the values in this matrix as copies of the values in 2D array 'u'.
- u
the 2D array of values to assign
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
set(x: Rational): Unit
Set all the elements in this matrix to the scalar 'x'.
Set all the elements in this matrix to the scalar 'x'.
- x
the scalar value to assign
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
setCol(col: Int, u: VectoQ): Unit
Set column 'col' of the matrix to a vector.
Set column 'col' of the matrix to a vector.
- col
the column to set
- u
the vector to assign to the column
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
setDiag(x: Rational): Unit
Set the main diagonal of this matrix to the scalar 'x'.
Set the main diagonal of this matrix to the scalar 'x'. Assumes 'dim2 >= dim1'.
- x
the scalar to set the diagonal to
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
setDiag(u: VectoQ, k: Int = 0): Unit
Set the 'k'th diagonal of this matrix to the vector 'u'.
Set the 'k'th diagonal of this matrix to the vector 'u'. Assumes 'dim2 >= dim1'.
- u
the vector to set the diagonal to
- k
how far above the main diagonal, e.g., (-1, 0, 1) for (sub, main, super)
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
setFormat(newFormat: String): Unit
Set the format to the 'newFormat'.
-
def
showAll(): Unit
Show all elements in 'this' sparse matrix.
-
def
slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): SparseMatrixQ
Slice 'this' sparse matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.
Slice 'this' sparse matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.
- r_from
the start of the row slice
- r_end
the end of the row slice
- c_from
the start of the column slice
- c_end
the end of the column slice
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
slice(from: Int, end: Int): SparseMatrixQ
Slice 'this' sparse matrix row-wise 'from' to 'end'.
Slice 'this' sparse matrix row-wise 'from' to 'end'.
- from
the start row of the slice
- end
the end row of the slice
- Definition Classes
- SparseMatrixQ → MatriQ
-
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): SparseMatrixQ
Slice 'this' sparse matrix column-wise 'from' to 'end'.
Slice 'this' sparse matrix column-wise 'from' to 'end'.
- from
the start column of the slice (inclusive)
- end
the end column of the slice (exclusive)
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
sliceEx(row: Int, col: Int): SparseMatrixQ
Slice 'this' sparse matrix excluding the given row and column.
Slice 'this' sparse matrix excluding the given row and column.
- row
the row to exclude
- col
the column to exclude
- Definition Classes
- SparseMatrixQ → MatriQ
-
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.
Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' matrix.
- b
the constant vector.
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
solve(l: MatriQ, u: MatriQ, b: VectoQ): VectoQ
Solve for 'x' in the equation 'l*u*x = b' (see 'lud_npp' above).
Solve for 'x' in the equation 'l*u*x = b' (see 'lud_npp' above).
- l
the lower triangular matrix
- u
the upper triangular matrix
- b
the constant vector
- Definition Classes
- SparseMatrixQ → MatriQ
-
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' sparse matrix, i.e., the sum of its elements.
Compute the sum of 'this' sparse matrix, i.e., the sum of its elements.
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
sumAbs: Rational
Compute the 'abs' sum of this matrix, i.e., the sum of the absolute value of its elements.
Compute the 'abs' sum of this matrix, i.e., the sum of the absolute value of its elements. This is useful for comparing matrices '(a - b).sumAbs'.
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
sumLower: Rational
Compute the sum of the lower triangular region of 'this' sparse matrix.
Compute the sum of the lower triangular region of 'this' sparse matrix.
- Definition Classes
- SparseMatrixQ → MatriQ
-
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: SparseMatrixQ
Transpose 'this' sparse matrix (rows => columns).
Transpose 'this' sparse matrix (rows => columns).
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
times_s(b: SparseMatrixQ): SparseMatrixQ
Multiply 'this' sparse matrix by sparse matrix 'b' using the Strassen matrix multiplication algorithm.
Multiply 'this' sparse matrix by sparse 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: MatrixQ
Convert this sparse matrix to a dense matrix.
Convert this sparse matrix to a dense matrix. FIX - new builder
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
toDouble: MatrixD
Convert 'this'
SparseMatrixQinto a dense double matrixMatrixD.Convert 'this'
SparseMatrixQinto a dense double matrixMatrixD.- Definition Classes
- SparseMatrixQ → MatriQ
-
def
toInt: MatrixI
Convert 'this'
SparseMatrixQinto a dense integer matrixMatrixI.Convert 'this'
SparseMatrixQinto a dense integer matrixMatrixI.- Definition Classes
- SparseMatrixQ → MatriQ
-
def
toString(): String
Show the non-zero elements in 'this' sparse matrix.
Show the non-zero elements in 'this' sparse matrix.
- Definition Classes
- SparseMatrixQ → AnyRef → Any
-
def
trace: Rational
Compute the trace of 'this' sparse matrix, i.e., the sum of the elements on the main diagonal.
Compute the trace of 'this' sparse matrix, i.e., the sum of the elements on the main diagonal. Should also equal the sum of the eigenvalues.
- Definition Classes
- SparseMatrixQ → MatriQ
- See also
Eigen.scala
-
def
update(ir: Range, jr: Range, b: MatriQ): Unit
Set a slice 'this' sparse matrix row-wise on range 'ir' and column-wise on range 'jr'.
Set a slice 'this' sparse 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
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
update(i: Int, u: RowMap): Unit
Set 'this' sparse matrix's row at the 'i'-th index position to the sorted-linked-map 'u'.
Set 'this' sparse matrix's row at the 'i'-th index position to the sorted-linked-map 'u'.
- i
the row index
- u
the sorted-linked-map of non-zero values to assign
-
def
update(i: Int, u: VectoQ): Unit
Set 'this' sparse matrix's row at the i-th index position to the vector 'u'.
Set 'this' sparse matrix's row at the i-th index position to the vector 'u'.
- i
the row index
- u
the vector value to assign
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
update(i: Int, j: Int, x: Rational): Unit
Set 'this' sparse matrix's element at the 'i,j'-th index position to the scalar 'x'.
Set 'this' sparse matrix's element at the 'i,j'-th index position to the scalar 'x'. Only store 'x' if it is non-zero.
- i
the row index
- j
the column index
- x
the scalar value to assign
- Definition Classes
- SparseMatrixQ → MatriQ
-
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: SparseMatrixQ
Return the upper triangular of 'this' matrix (rest are zero).
Return the upper triangular of 'this' matrix (rest are zero).
- Definition Classes
- SparseMatrixQ → MatriQ
-
final
def
wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... ) @native()
-
final
def
wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
def
write(fileName: String): Unit
Write 'this' matrix to a CSV-formatted text file with name 'fileName'.
Write 'this' matrix to a CSV-formatted text file with name 'fileName'.
- fileName
the name of file to hold the data
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
zero(m: Int = dim1, n: Int = dim2): SparseMatrixQ
Create an 'm-by-n' sparse matrix with all elements initialized to zero.
Create an 'm-by-n' sparse matrix with all elements initialized to zero.
- m
the number of rows
- n
the number of columns
- Definition Classes
- SparseMatrixQ → MatriQ
-
def
~^(p: Int): SparseMatrixQ
Raise 'this' sparse matrix to the 'p'th power (for some integer 'p' >= 2).
Raise 'this' sparse matrix to the 'p'th power (for some integer 'p' >= 2). Caveat: should be replace by a divide and conquer algorithm.
- p
the power to raise this matrix to
- Definition Classes
- SparseMatrixQ → MatriQ
Deprecated Value Members
-
def
finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] ) @Deprecated
- Deprecated