class BidMatrixL extends MatriL with Error with Serializable
The BidMatrixL class stores and operates on square (upper) bidiagonal matrices.
The elements are of type of Long. A matrix is stored as two vectors:
the diagonal vector and the sup-diagonal vector.
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- BidMatrixL
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- Serializable
- MatriL
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Instance Constructors
-
new
BidMatrixL(b: MatriL)
Construct a bidiagonal matrix from the given matrix.
Construct a bidiagonal matrix from the given matrix.
- b
the matrix of values to assign
-
new
BidMatrixL(v1: VectoL, v2: VectoL)
Construct a bidiagonal matrix with the given diagonal and sup-diagonal.
Construct a bidiagonal matrix with the given diagonal and sup-diagonal.
- v1
the diagonal vector
- v2
the sup-diagonal vector
-
new
BidMatrixL(d1: Int)
- d1
the first/row dimension (square => d2 = d1)
Value Members
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
##(): Int
- Definition Classes
- AnyRef → Any
-
def
*(x: Long): BidMatrixL
Multiply 'this' bidiagonal matrix by scalar 'x'.
Multiply 'this' bidiagonal matrix by scalar 'x'.
- x
the scalar to multiply by
- Definition Classes
- BidMatrixL → MatriL
-
def
*(u: VectoL): VectorL
Multiply 'this' bidiagonal matrix by vector 'u'.
Multiply 'this' bidiagonal matrix by vector 'u'.
- u
the vector to multiply by
- Definition Classes
- BidMatrixL → MatriL
-
def
*(b: BidMatrixL): MatrixL
Multiply 'this' bidiagonal matrix by matrix 'b'.
Multiply 'this' bidiagonal matrix by matrix 'b'. Requires 'b' to have type
BidMatrixL, but returns a more general type of matrix.- b
the matrix to multiply by
-
def
*(b: MatriL): BidMatrixL
Multiply 'this' bidiagonal matrix by matrix 'b'.
Multiply 'this' bidiagonal matrix by matrix 'b'.
- b
the matrix to multiply by
- Definition Classes
- BidMatrixL → MatriL
-
def
**(u: VectoL): MatrixL
Multiply 'this' bidiagonal matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
Multiply 'this' bidiagonal matrix by vector 'u' to produce another matrix 'a_ij * u_j'. E.g., multiply a diagonal matrix represented as a vector by a matrix.
- u
the vector to multiply by
- Definition Classes
- BidMatrixL → MatriL
-
def
**(b: MatriL): MatriL
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
- MatriL
- See also
en.wikipedia.org/wiki/Hadamard_product_(matrices) FIX - remove ??? and implement in all implementing classes
-
def
**:(u: VectoL): MatrixL
Multiply vector 'u' by 'this' bidiagonal matrix to produce another matrix 'u_i * a_ij'.
Multiply vector 'u' by 'this' bidiagonal 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
- BidMatrixL → MatriL
-
def
**=(u: VectoL): MatrixL
Multiply in-place 'this' bidiagonal matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
Multiply in-place 'this' bidiagonal matrix by vector 'u' to produce another matrix 'a_ij * u_j'. E.g., multiply a diagonal matrix represented as a vector by a matrix.
- u
the vector to multiply by
- Definition Classes
- BidMatrixL → MatriL
-
def
*:(u: VectoL): VectoL
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
- MatriL
-
def
*=(x: Long): BidMatrixL
Multiply in-place 'this' bidiagonal matrix by scalar 'x'.
Multiply in-place 'this' bidiagonal matrix by scalar 'x'.
- x
the scalar to multiply by
- Definition Classes
- BidMatrixL → MatriL
-
def
*=(b: MatriL): BidMatrixL
Multiply in-place 'this' bidiagonal matrix by matrix 'b'.
Multiply in-place 'this' bidiagonal matrix by matrix 'b'.
- b
the matrix to multiply by
- Definition Classes
- BidMatrixL → MatriL
-
def
+(x: Long): BidMatrixL
Add 'this' bidiagonal matrix and scalar 'x'.
Add 'this' bidiagonal matrix and scalar 'x'.
- x
the scalar to add
- Definition Classes
- BidMatrixL → MatriL
-
def
+(u: VectoL): BidMatrixL
Add 'this' bidiagonal matrix and (row) vector u.
Add 'this' bidiagonal matrix and (row) vector u.
- u
the vector to add
- Definition Classes
- BidMatrixL → MatriL
-
def
+(b: MatriL): BidMatrixL
Add 'this' bidiagonal matrix and matrix 'b'.
Add 'this' bidiagonal matrix and matrix 'b'.
- b
the matrix to add (requires 'leDimensions')
- Definition Classes
- BidMatrixL → MatriL
-
def
++(b: MatriL): BidMatrixL
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
- BidMatrixL → MatriL
-
def
++^(b: MatriL): BidMatrixL
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
- BidMatrixL → MatriL
-
def
+:(u: VectoL): BidMatrixL
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
- BidMatrixL → MatriL
-
def
+=(x: Long): BidMatrixL
Add in-place 'this' bidiagonal matrix and scalar 'x'.
Add in-place 'this' bidiagonal matrix and scalar 'x'.
- x
the scalar to add
- Definition Classes
- BidMatrixL → MatriL
-
def
+=(u: VectoL): MatrixL
Add in-place 'this' bidiagonal matrix and (row) vector 'u'.
Add in-place 'this' bidiagonal matrix and (row) vector 'u'.
- u
the vector to add
- Definition Classes
- BidMatrixL → MatriL
-
def
+=(b: MatriL): BidMatrixL
Add in-place 'this' bidiagonal matrix and matrix 'b'.
Add in-place 'this' bidiagonal matrix and matrix 'b'.
- b
the matrix to add (requires 'leDimensions')
- Definition Classes
- BidMatrixL → MatriL
-
def
+^:(u: VectoL): BidMatrixL
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
- BidMatrixL → MatriL
-
def
-(x: Long): BidMatrixL
From 'this' bidiagonal matrix subtract scalar 'x'.
From 'this' bidiagonal matrix subtract scalar 'x'.
- x
the scalar to subtract
- Definition Classes
- BidMatrixL → MatriL
-
def
-(u: VectoL): BidMatrixL
From 'this' bidiagonal matrix subtract (row) vector 'u'.
From 'this' bidiagonal matrix subtract (row) vector 'u'.
- u
the vector to subtract
- Definition Classes
- BidMatrixL → MatriL
-
def
-(b: MatriL): BidMatrixL
From 'this' bidiagonal matrix subtract matrix 'b'.
From 'this' bidiagonal matrix subtract matrix 'b'.
- b
the matrix to subtract (requires 'leDimensions')
- Definition Classes
- BidMatrixL → MatriL
-
def
-=(x: Long): BidMatrixL
From 'this' bidiagonal matrix subtract in-place scalar 'x'.
From 'this' bidiagonal matrix subtract in-place scalar 'x'.
- x
the scalar to subtract
- Definition Classes
- BidMatrixL → MatriL
-
def
-=(u: VectoL): BidMatrixL
From 'this' bidiagonal matrix subtract in-place (row) vector 'u'.
From 'this' bidiagonal matrix subtract in-place (row) vector 'u'.
- u
the vector to subtract
- Definition Classes
- BidMatrixL → MatriL
-
def
-=(b: MatriL): BidMatrixL
From 'this' bidiagonal bidiagonal matrix subtract in-place matrix 'b'.
From 'this' bidiagonal bidiagonal matrix subtract in-place matrix 'b'.
- b
the matrix to subtract (requires 'leDimensions')
- Definition Classes
- BidMatrixL → MatriL
-
def
/(x: Long): BidMatrixL
Divide 'this' bidiagonal matrix by scalar 'x'.
Divide 'this' bidiagonal matrix by scalar 'x'.
- x
the scalar to divide by
- Definition Classes
- BidMatrixL → MatriL
-
def
/=(x: Long): BidMatrixL
Divide in-place 'this' bidiagonal matrix by scalar 'x'.
Divide in-place 'this' bidiagonal matrix by scalar 'x'.
- x
the scalar to divide by
- Definition Classes
- BidMatrixL → MatriL
-
def
:+(u: VectoL): BidMatrixL
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
- BidMatrixL → MatriL
-
def
:^+(u: VectoL): BidMatrixL
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
- BidMatrixL → MatriL
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
def
apply(ir: Range, jr: Range): BidMatrixL
Get a slice 'this' bidiagonal matrix row-wise on range 'ir' and column-wise on range 'jr'.
Get a slice 'this' bidiagonal 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
- BidMatrixL → MatriL
-
def
apply(i: Int): VectorL
Get 'this' bidiagonal matrix's vector at the 'i'-th index position ('i'-th row).
Get 'this' bidiagonal matrix's vector at the 'i'-th index position ('i'-th row).
- i
the row index
- Definition Classes
- BidMatrixL → MatriL
-
def
apply(i: Int, j: Int): Long
Get 'this' bidiagonal matrix's element at the 'i,j'-th index position.
Get 'this' bidiagonal matrix's element at the 'i,j'-th index position.
- i
the row index
- j
the column index
- Definition Classes
- BidMatrixL → MatriL
-
def
apply(iv: VectoI): MatriL
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
- MatriL
-
def
apply(i: Int, jr: Range): VectoL
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
- MatriL
-
def
apply(ir: Range, j: Int): VectoL
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
- MatriL
-
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
def
at(i: Int, j: Int): Long
Get 'this' bidiagonal matrix's element at the 'i,j'-th index position, returning 0, if off bidiagonal.
Get 'this' bidiagonal matrix's element at the 'i,j'-th index position, returning 0, if off bidiagonal.
- i
the row index
- j
the column index
-
def
bsolve(y: VectoL): VectorL
Solve for 'x' using back substitution in the equation 'u*x = y' where 'this' matrix ('u') is upper triangular (see 'lud' above).
Solve for 'x' using back substitution in the equation 'u*x = y' where 'this' matrix ('u') is upper triangular (see 'lud' above).
- y
the constant vector
- Definition Classes
- BidMatrixL → MatriL
-
def
clean(thres: Double, relative: Boolean = true): BidMatrixL
Clean values in 'this' bidiagonal matrix at or below the threshold by setting them to zero.
Clean values in 'this' bidiagonal 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
- BidMatrixL → MatriL
-
def
clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( ... ) @native() @HotSpotIntrinsicCandidate()
-
def
col(col: Int, from: Int = 0): VectorL
Get column 'col' from 'this' bidiagonal matrix, returning it as a vector.
Get column 'col' from 'this' bidiagonal matrix, returning it as a vector.
- col
the column to extract from the matrix
- from
the position to start extracting from
- Definition Classes
- BidMatrixL → MatriL
-
def
copy(): BidMatrixL
Create a clone of 'this' m-by-n matrix.
Create a clone of 'this' m-by-n matrix.
- Definition Classes
- BidMatrixL → MatriL
- val d1: Int
-
def
det: Long
Compute the determinant of 'this' bidiagonal matrix.
Compute the determinant of 'this' bidiagonal matrix.
- Definition Classes
- BidMatrixL → MatriL
-
def
dg: VectorL
Get the diagonal of 'this' bidiagonal matrix.
-
def
dg_(v: VectorL): Unit
Set the diagonal of 'this' bidiagonal matrix.
Set the diagonal of 'this' bidiagonal matrix.
- v
the vector to assign to the diagonal
-
def
diag(p: Int, q: Int): SymTriMatrixL
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. Fill the rest of matrix with zeros.
- p
the size of identity matrix Ip
- q
the size of identity matrix Iq
- Definition Classes
- BidMatrixL → MatriL
-
def
diag(b: MatriL): MatriL
Combine 'this' bidiagonal 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' bidiagonal 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' bidiagonal matrix
- Definition Classes
- BidMatrixL → MatriL
-
lazy val
dim1: Int
Dimension 1
Dimension 1
- Definition Classes
- BidMatrixL → MatriL
-
lazy val
dim2: Int
Dimension 2
Dimension 2
- Definition Classes
- BidMatrixL → MatriL
-
def
dot(b: MatriL): VectorL
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
- BidMatrixL → MatriL
-
def
dot(u: VectoL): VectorL
Compute the dot product of 'this' matrix and vector 'u', by conceptually 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 conceptually 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
- BidMatrixL → MatriL
-
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
- MatriL
-
def
flatten: VectoL
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
- MatriL
-
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[Long]) ⇒ 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
- MatriL
-
final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
-
def
getDiag(k: Int = 0): VectorL
Get the 'k'th diagonal of 'this' bidiagonal matrix.
Get the 'k'th diagonal of 'this' bidiagonal matrix. Assumes 'dim2 >= dim1'.
- k
how far above the main diagonal, e.g., (0, 1) for (main, super)
- Definition Classes
- BidMatrixL → MatriL
-
def
hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
-
def
inverse: MatriL
Invert 'this' bidiagonal matrix.
Invert 'this' bidiagonal matrix.
- Definition Classes
- BidMatrixL → MatriL
-
def
inverse_ip(): BidMatrixL
Invert in-place 'this' matrix (requires a 'squareMatrix') and use partial pivoting.
Invert in-place 'this' matrix (requires a 'squareMatrix') and use partial pivoting.
- Definition Classes
- BidMatrixL → MatriL
-
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).
- Definition Classes
- BidMatrixL → MatriL
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
def
isNonnegative: Boolean
Check whether 'this' bidiagonal matrix is nonnegative (has no negative elements).
Check whether 'this' bidiagonal matrix is nonnegative (has no negative elements).
- Definition Classes
- BidMatrixL → MatriL
-
def
isRectangular: Boolean
Check whether 'this' bidiagonal matrix is rectangular (all rows have the same number of columns).
Check whether 'this' bidiagonal matrix is rectangular (all rows have the same number of columns).
- Definition Classes
- BidMatrixL → MatriL
-
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
- MatriL
-
def
isSymmetric: Boolean
Check whether 'this' matrix is symmetric.
Check whether 'this' matrix is symmetric.
- Definition Classes
- MatriL
-
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).
- Definition Classes
- BidMatrixL → MatriL
-
def
leDimensions(b: MatriL): 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
- MatriL
-
def
lowerT: MatrixL
Return the lower triangular of 'this' matrix (rest are zero).
Return the lower triangular of 'this' matrix (rest are zero).
- Definition Classes
- BidMatrixL → MatriL
-
def
lud_ip(): (MatriL, MatriL)
Factor in-place 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.
Factor in-place 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.
- Definition Classes
- BidMatrixL → MatriL
-
def
lud_npp: (MatriL, MatriL)
Factor 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.
Factor 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.
- Definition Classes
- BidMatrixL → MatriL
-
def
mag: Long
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
- MatriL
-
def
map(f: (VectoL) ⇒ VectoL): MatriL
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
- MatriL
-
def
max(e: Int = dim1): Long
Find the maximum element in 'this' bidiagonal matrix.
Find the maximum element in 'this' bidiagonal matrix.
- e
the ending row index (exclusive) for the search
- Definition Classes
- BidMatrixL → MatriL
-
def
mdot(b: MatriL): MatrixL
Compute the matrix dot product of 'this' matrix with matrix 'b' to produce a matrix.
Compute the matrix dot product of 'this' matrix with matrix 'b' to produce a matrix.
- b
the second matrix of the dot product
- Definition Classes
- BidMatrixL → MatriL
-
def
mdot(b: BidMatrixL): MatrixL
Compute the matrix dot product of 'this' matrix with matrix 'b' to produce a matrix.
Compute the matrix dot product of 'this' matrix with matrix 'b' to produce a matrix.
- b
the second matrix of the dot product
-
def
mean: VectoL
Compute the column means of 'this' matrix.
Compute the column means of 'this' matrix.
- Definition Classes
- MatriL
-
def
meanNZ: VectoL
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
- MatriL
-
def
meanR: VectoL
Compute the row means of 'this' matrix.
Compute the row means of 'this' matrix.
- Definition Classes
- MatriL
-
def
meanRNZ: VectoL
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
- MatriL
-
def
min(e: Int = dim1): Long
Find the minimum element in 'this' bidiagonal matrix.
Find the minimum element in 'this' bidiagonal matrix.
- e
the ending row index (exclusive) for the search
- Definition Classes
- BidMatrixL → MatriL
-
final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
norm1: Long
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
- MatriL
- See also
en.wikipedia.org/wiki/Matrix_norm
-
def
normF: Long
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
- MatriL
- See also
en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
-
def
normFSq: Long
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
- MatriL
- See also
en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
-
def
normINF: Long
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
- MatriL
- 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: VectorL
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
- BidMatrixL → MatriL
- 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(): VectorL
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
- BidMatrixL → MatriL
- 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
- MatriL
-
val
range2: Range
Range for the storage array on dimension 2 (columns)
Range for the storage array on dimension 2 (columns)
- Definition Classes
- MatriL
-
def
reduce: BidMatrixL
Use Gauss-Jordan reduction on 'this' matrix to make the left part embed an identity matrix.
Use Gauss-Jordan reduction on 'this' matrix to make the left part embed an identity matrix. A constraint on 'this' m by n matrix is that n >= m.
- Definition Classes
- BidMatrixL → MatriL
-
def
reduce_ip(): Unit
Use Gauss-Jordan reduction in-place on 'this' matrix to make the left part embed an identity matrix.
Use Gauss-Jordan reduction in-place on 'this' matrix to make the left part embed an identity matrix. A constraint on 'this' m by n matrix is that n >= m.
- Definition Classes
- BidMatrixL → MatriL
-
def
sameCrossDimensions(b: MatriL): 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
- MatriL
-
def
sameDimensions(b: MatriL): 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
- MatriL
-
def
sd: VectorL
Get the sup-diagonal of this bidiagonal matrix.
-
def
sd_(v: VectorL): Unit
Set the sup-diagonal of 'this' bidiagonal matrix.
Set the sup-diagonal of 'this' bidiagonal matrix.
- v
the vector to assign to the sup-diagonal
-
def
selectCols(colIndex: Array[Int]): BidMatrixL
Select columns from 'this' bidiagonal matrix according to the given index/basis.
Select columns from 'this' bidiagonal 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
- BidMatrixL → MatriL
-
def
selectRows(rowIndex: Array[Int]): BidMatrixL
Select rows from 'this' bidiagonal matrix according to the given index/basis.
Select rows from 'this' bidiagonal matrix according to the given index/basis.
- rowIndex
the row index positions (e.g., (0, 2, 5))
- Definition Classes
- BidMatrixL → MatriL
-
def
selectRows(rowIndex: VectoI): MatriL
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
- MatriL
-
def
selectRowsEx(rowIndex: VectoI): MatriL
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
- MatriL
-
def
selectRowsEx(rowIndex: Array[Int]): MatriL
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
- MatriL
-
def
set(i: Int, u: VectoL, j: Int = 0): Unit
Set 'this' bidiagonal matrix's 'i'th row starting at column 'j' to the vector 'u'.
Set 'this' bidiagonal 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
- BidMatrixL → MatriL
-
def
set(u: MatriL): 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
- BidMatrixL → MatriL
-
def
set(u: Array[Array[Long]]): Unit
Set all the values in 'this' bidiagonal matrix as copies of the values in 2D array u.
Set all the values in 'this' bidiagonal matrix as copies of the values in 2D array u.
- u
the 2D array of values to assign
- Definition Classes
- BidMatrixL → MatriL
-
def
set(x: Long): Unit
Set all the elements in 'this' bidiagonal matrix to the scalar 'x'.
Set all the elements in 'this' bidiagonal matrix to the scalar 'x'.
- x
the scalar value to assign
- Definition Classes
- BidMatrixL → MatriL
-
def
setCol(col: Int, u: VectoL): Unit
Set column 'col' of 'this' bidiagonal matrix to a vector.
Set column 'col' of 'this' bidiagonal matrix to a vector.
- col
the column to set
- u
the vector to assign to the column
- Definition Classes
- BidMatrixL → MatriL
-
def
setDiag(x: Long): Unit
Set the main diagonal of 'this' bidiagonal matrix to the scalar 'x'.
Set the main diagonal of 'this' bidiagonal matrix to the scalar 'x'. Assumes 'dim2 >= dim1'.
- x
the scalar to set the diagonal to
- Definition Classes
- BidMatrixL → MatriL
-
def
setDiag(u: VectoL, k: Int = 0): Unit
Set the 'k'th diagonal of 'this' bidiagonal matrix to the vector 'u'.
Set the 'k'th diagonal of 'this' bidiagonal 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
- BidMatrixL → MatriL
-
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): BidMatrixL
Slice 'this' bidiagonal matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.
Slice 'this' bidiagonal 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
- BidMatrixL → MatriL
-
def
slice(from: Int, end: Int): BidMatrixL
Slice 'this' bidiagonal matrix row-wise 'from' to 'end'.
Slice 'this' bidiagonal matrix row-wise 'from' to 'end'.
- from
the start row of the slice (inclusive)
- end
the end row of the slice (exclusive)
- Definition Classes
- BidMatrixL → MatriL
-
def
slice(rg: Range): MatriL
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
- MatriL
-
def
sliceCol(from: Int, end: Int): BidMatrixL
Slice 'this' bidiagonal matrix column-wise 'from' to 'end'.
Slice 'this' bidiagonal matrix column-wise 'from' to 'end'.
- from
the start column of the slice (inclusive)
- end
the end column of the slice (exclusive)
- Definition Classes
- BidMatrixL → MatriL
-
def
sliceEx(row: Int, col: Int): BidMatrixL
Slice 'this' bidiagonal matrix excluding the given 'row' and 'col'umn.
Slice 'this' bidiagonal matrix excluding the given 'row' and 'col'umn.
- row
the row to exclude
- col
the column to exclude
- Definition Classes
- BidMatrixL → MatriL
-
def
sliceEx(rg: Range): MatriL
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
- MatriL
-
def
solve(l: MatriL, u: MatriL, b: VectoL): VectorL
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).
- l
the lower triangular matrix
- u
the upper triangular matrix
- b
the constant vector
- Definition Classes
- BidMatrixL → MatriL
-
def
solve(b: VectoL): VectorL
Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' bidiagonal matrix.
Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' bidiagonal matrix.
- b
the constant vector
- Definition Classes
- BidMatrixL → MatriL
-
def
solve(lu: (MatriL, MatriL), b: VectoL): VectoL
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
- MatriL
-
def
splitRows(rowIndex: VectoI): (MatriL, MatriL)
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
- MatriL
-
def
splitRows(rowIndex: Array[Int]): (MatriL, MatriL)
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
- MatriL
-
def
sum: Long
Compute the sum of 'this' bidiagonal matrix, i.e., the sum of its elements.
Compute the sum of 'this' bidiagonal matrix, i.e., the sum of its elements.
- Definition Classes
- BidMatrixL → MatriL
-
def
sumAbs: Long
Compute the 'abs' sum of 'this' bidiagonal matrix, i.e., the sum of the absolute value of its elements.
Compute the 'abs' sum of 'this' bidiagonal matrix, i.e., the sum of the absolute value of its elements. This is useful for comparing matrices '(a - b).sumAbs'.
- Definition Classes
- BidMatrixL → MatriL
-
def
sumLower: Long
Compute the sum of the lower triangular region of 'this' bidiagonal matrix.
Compute the sum of the lower triangular region of 'this' bidiagonal matrix.
- Definition Classes
- BidMatrixL → MatriL
-
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
- MatriL
-
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
- MatriL
-
final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
-
def
t: BidMatrixL
Transpose 'this' bidiagonal matrix (rows => columns).
Transpose 'this' bidiagonal matrix (rows => columns).
- Definition Classes
- BidMatrixL → MatriL
-
def
toDense: MatrixL
Convert 'this' tridiagonal matrix to a dense matrix.
Convert 'this' tridiagonal matrix to a dense matrix.
- Definition Classes
- BidMatrixL → MatriL
-
def
toDouble: BidMatrixD
Convert 'this'
BidMatrixLinto a double matrixBidMatrixD.Convert 'this'
BidMatrixLinto a double matrixBidMatrixD.- Definition Classes
- BidMatrixL → MatriL
-
def
toInt: BidMatrixI
Convert 'this'
BidMatrixLinto an integer matrixBidMatrixI.Convert 'this'
BidMatrixLinto an integer matrixBidMatrixI.- Definition Classes
- BidMatrixL → MatriL
-
def
toString(): String
Convert 'this' bidiagonal matrix to a string showing the diagonal vector followed by the sup-diagonal vector.
Convert 'this' bidiagonal matrix to a string showing the diagonal vector followed by the sup-diagonal vector.
- Definition Classes
- BidMatrixL → AnyRef → Any
-
def
trace: Long
Compute the trace of 'this' bidiagonal matrix, i.e., the sum of the elements on the main diagonal.
Compute the trace of 'this' bidiagonal matrix, i.e., the sum of the elements on the main diagonal. Should also equal the sum of the eigenvalues.
- Definition Classes
- BidMatrixL → MatriL
- See also
Eigen.scala
-
def
update(ir: Range, jr: Range, b: MatriL): Unit
Set a slice 'this' bidiagonal matrix row-wise on range 'ir' and column-wise on range 'jr'.
Set a slice 'this' bidiagonal 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
- BidMatrixL → MatriL
-
def
update(i: Int, u: VectoL): Unit
Set 'this' bidiagonal matrix's row at the 'i'-th index position to the vector 'u'.
Set 'this' bidiagonal 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
- BidMatrixL → MatriL
-
def
update(i: Int, j: Int, x: Long): Unit
Set 'this' bidiagonal matrix's element at the 'i,j'-th index position to the scalar 'x'.
Set 'this' bidiagonal matrix's element at the 'i,j'-th index position to the scalar 'x'.
- i
the row index
- j
the column index
- x
the scalar value to assign
- Definition Classes
- BidMatrixL → MatriL
-
def
update(i: Int, jr: Range, u: VectoL): 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
- MatriL
-
def
update(ir: Range, j: Int, u: VectoL): 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
- MatriL
-
def
upperT: MatrixL
Return the upper triangular of 'this' matrix (rest are zero).
Return the upper triangular of 'this' matrix (rest are zero).
- Definition Classes
- BidMatrixL → MatriL
-
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
- BidMatrixL → MatriL
-
def
zero(m: Int = dim1, n: Int = dim2): BidMatrixL
Create an m-by-n matrix with all elements initialized to zero.
Create an m-by-n matrix with all elements initialized to zero.
- m
the number of rows
- n
the number of columns
- Definition Classes
- BidMatrixL → MatriL
-
def
~^(p: Int): BidMatrixL
Raise 'this' bidiagonal matrix to the 'p'th power (for some integer 'p' >= 2).
Raise 'this' bidiagonal matrix to the 'p'th power (for some integer 'p' >= 2).
- p
the power to raise 'this' matrix to
- Definition Classes
- BidMatrixL → MatriL
Deprecated Value Members
-
def
finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] ) @Deprecated
- Deprecated