class RleMatrixR extends MatriR with Error with Serializable
The RleMatrixR class stores and operates on Numeric Matrices of type Real.
Rather than storing the matrix as a 2 dimensional array, it is stored as an array
of RleVectorR's.
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- RleMatrixR
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- MatriR
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Instance Constructors
-
new
RleMatrixR(dim1: Int)
Construct a 'dim1' by 'dim1' square matrix.
Construct a 'dim1' by 'dim1' square matrix.
- dim1
the row and column dimension
-
new
RleMatrixR(d1: Int, d2: Int, v: Array[RleVectorR] = null, deferred: Boolean = false)
- d1
the first/row dimension
- d2
the second/column dimension
- v
the 1D array used to store matrix elements
Value Members
-
def
*(b: MatriR): MatriR
Multiply 'this' matrix by matrix 'b'.
Multiply 'this' matrix by matrix 'b'.
- b
the matrix to multiply by (requires 'sameCrossDimensions')
- Definition Classes
- RleMatrixR → MatriR
-
def
*(x: Real): RleMatrixR
Multiply 'this' matrix by scalar 'x'.
Multiply 'this' matrix by scalar 'x'.
- x
the scalar to multiply by
- Definition Classes
- RleMatrixR → MatriR
-
def
*(u: VectoR): VectoR
Multiply 'this' matrix by (column) vector 'u'
Multiply 'this' matrix by (column) vector 'u'
- u
the vector to multiply by
- Definition Classes
- RleMatrixR → MatriR
-
def
**(u: VectoR): MatriR
Multiply 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
Multiply 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'. E.g., multiply a matrix by a diagonal matrix represented as a vector.
- u
the vector to multiply by
- Definition Classes
- RleMatrixR → MatriR
-
def
**(b: MatriR): MatriR
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
- MatriR
- See also
en.wikipedia.org/wiki/Hadamard_product_(matrices) FIX - remove ??? and implement in all implementing classes
-
def
**:(u: VectoR): MatriR
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
- RleMatrixR → MatriR
-
def
**=(u: VectoR): MatriR
Multiply in-place 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
Multiply in-place 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'.
- u
the vector to multiply by
- Definition Classes
- RleMatrixR → MatriR
-
def
*:(u: VectoR): VectoR
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
- MatriR
-
def
*=(b: MatriR): MatriR
Multiply in-place 'this' matrix by matrix 'b'
Multiply in-place 'this' matrix by matrix 'b'
- b
the matrix to multiply by (requires square and 'sameCrossDimensions')
- Definition Classes
- RleMatrixR → MatriR
-
def
*=(x: Real): RleMatrixR
Multiply in-place 'this' matrix by matrix 'x'
Multiply in-place 'this' matrix by matrix 'x'
- x
the matrix to multiply by
- Definition Classes
- RleMatrixR → MatriR
-
def
+(u: VectoR): MatriR
Add 'this' matrix and vector 'u'.
Add 'this' matrix and vector 'u'.
- u
the matrix to add (requires leDimensions)
- Definition Classes
- RleMatrixR → MatriR
-
def
+(x: Real): RleMatrixR
Add 'this' matrix and scalar 'x'.
-
def
+(b: MatriR): RleMatrixR
Add 'this' matrix and matrix 'b'.
Add 'this' matrix and matrix 'b'.
- b
the matrix to add (requires leDimensions)
- Definition Classes
- RleMatrixR → MatriR
-
def
++(b: MatriR): RleMatrixR
Concatenate (row-wise) 'this' matrix and matrix 'b'.
Concatenate (row-wise) 'this' matrix and matrix 'b'. FIX
- b
the matrix to be concatenated as the new last rows in new matrix
- Definition Classes
- RleMatrixR → MatriR
-
def
++^(b: MatriR): RleMatrixR
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
- RleMatrixR → MatriR
-
def
+:(u: VectoR): RleMatrixR
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
- RleMatrixR → MatriR
-
def
+=(b: MatriR): MatriR
Add in-place 'this' matrix and matrix 'b'.
Add in-place 'this' matrix and matrix 'b'.
- b
the matrix to add (requires 'leDimensions')
- Definition Classes
- RleMatrixR → MatriR
-
def
+=(u: VectoR): MatriR
Add in-place 'this' matrix and vector 'u'.
-
def
+=(x: Real): MatriR
Add in-place 'this' matrix and scalar 'x'.
-
def
+^:(u: VectoR): RleMatrixR
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
- RleMatrixR → MatriR
-
def
-(b: MatriR): MatriR
From 'this' matrix subtract matrix 'b'.
From 'this' matrix subtract matrix 'b'.
- b
the matrix to subtract
- Definition Classes
- RleMatrixR → MatriR
-
def
-(u: VectoR): RleMatrixR
From 'this' matrix subtract vector 'u'.
From 'this' matrix subtract vector 'u'.
- u
the vector to subtract
- Definition Classes
- RleMatrixR → MatriR
-
def
-(x: Real): MatriR
From 'this' matrix subtract scalar 'x'.
From 'this' matrix subtract scalar 'x'.
- x
the scalar to subtract
- Definition Classes
- RleMatrixR → MatriR
-
def
-=(b: MatriR): MatriR
From 'this' matrix subtract in-place matrix 'b'.
From 'this' matrix subtract in-place matrix 'b'.
- b
the matrix to subtract (requires 'leDimensions')
- Definition Classes
- RleMatrixR → MatriR
-
def
-=(u: VectoR): MatriR
From 'this' matrix subtract in-place vector 'u'.
From 'this' matrix subtract in-place vector 'u'.
- u
the vector to subtract
- Definition Classes
- RleMatrixR → MatriR
-
def
-=(x: Real): MatriR
From 'this' matrix subtract in-place scalar 'x'.
From 'this' matrix subtract in-place scalar 'x'.
- x
the scalar to subtract
- Definition Classes
- RleMatrixR → MatriR
-
def
/(x: Real): MatriR
Divide 'this' matrix by scalar 'x'.
-
def
/=(x: Real): MatriR
Divide in-place 'this' matrix by scalar 'x'.
Divide in-place 'this' matrix by scalar 'x'.
- x
the scalar to divide by
- Definition Classes
- RleMatrixR → MatriR
-
def
:+(u: VectoR): RleMatrixR
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
- RleMatrixR → MatriR
-
def
:^+(u: VectoR): RleMatrixR
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
- RleMatrixR → MatriR
-
def
apply(): Array[RleVectorR]
Get the underlying 1D array for 'this' matrix.
-
def
apply(ir: Range, jr: Range): MatriR
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
- RleMatrixR → MatriR
-
def
apply(i: Int): RleVectorR
Get 'this' matrix's vector at the 'i'-th index position ('i'-th row).
Get 'this' matrix's vector at the 'i'-th index position ('i'-th row).
- i
the row index
- Definition Classes
- RleMatrixR → MatriR
-
def
apply(i: Int, j: Int): Real
Get 'this' matrix's element at the 'i, j'-th index position.
Get 'this' matrix's element at the 'i, j'-th index position.
- i
the row index
- j
the column index
- Definition Classes
- RleMatrixR → MatriR
-
def
apply(iv: VectoI): MatriR
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
- MatriR
-
def
apply(i: Int, jr: Range): VectoR
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
- MatriR
-
def
apply(ir: Range, j: Int): VectoR
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
- MatriR
-
def
bsolve(y: VectoR): RleVectorR
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
- RleMatrixR → MatriR
-
def
clean(thres: Double = TOL, relative: Boolean = true): MatriR
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
- Definition Classes
- RleMatrixR → MatriR
-
def
col(col: Int, from: Int = 0): VectorR
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
- RleMatrixR → MatriR
-
def
col(col: Int): RleVectorR
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
-
def
copy(): RleMatrixR
Create an exact copy of 'this' m-by-n matrix.
Create an exact copy of 'this' m-by-n matrix.
- Definition Classes
- RleMatrixR → MatriR
-
def
csize: VectorI
Get size of each column of 'this' RleMatrix
- val d1: Int
- val d2: Int
- val deferred: Boolean
-
def
det: Real
Compute the determinant of 'this' matrix.
Compute the determinant of 'this' matrix. The value of the determinant indicates, among other things, whether there is a unique solution to a system of linear equations (a nonzero determinant).
- Definition Classes
- RleMatrixR → MatriR
-
def
diag(b: MatriR): RleMatrixR
Combine 'this' matrix with matrix 'b', placing them along the diagonal and filling in the bottom left and top right regions with zeros; '[this, b]'.
Combine 'this' matrix with matrix 'b', placing them along the diagonal and filling in the bottom left and top right regions with zeros; '[this, b]'.
- b
the matrix to combine with 'this' matrix
- Definition Classes
- RleMatrixR → MatriR
-
def
diag(p: Int, q: Int = 0): MatriR
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
- RleMatrixR → MatriR
-
lazy val
dim1: Int
Dimension 1
Dimension 1
- Definition Classes
- RleMatrixR → MatriR
-
lazy val
dim2: Int
Dimension 2
Dimension 2
- Definition Classes
- RleMatrixR → MatriR
-
def
dot(b: RleMatrixR): RleVectorR
Compute the dot product of 'this' matrix and matrix 'b'.
Compute the dot product of 'this' matrix and matrix 'b'. Results in a Vector.
- b
the matrix to multiply by (requires same first dimensions)
-
def
dot(b: MatriR): RleVectorR
Compute the dot product of 'this' matrix and matrix 'b'.
Compute the dot product of 'this' matrix and matrix 'b'. Results in a Vector.
- b
the matrix to multiply by (requires same first dimensions)
- Definition Classes
- RleMatrixR → MatriR
-
def
dot(b: VectoR): VectoR
Compute the dot product of 'this' matrix and vector 'b', by first transposing 'this' matrix and then multiplying by 'b' (i.e., 'a dot u = a.t * b').
Compute the dot product of 'this' matrix and vector 'b', by first transposing 'this' matrix and then multiplying by 'b' (i.e., 'a dot u = a.t * b').
- b
the vector to multiply by (requires same first dimensions)
- Definition Classes
- RleMatrixR → MatriR
-
def
equals(b: Any): Boolean
Override equals to determine whether 'this' vector equals vector 'b'.
Override equals to determine whether 'this' vector equals vector 'b'.
- b
the vector to compare with this
- Definition Classes
- RleMatrixR → AnyRef → Any
-
final
def
flaw(method: String, message: String): Unit
Show the flaw by printing the error message.
Show the flaw by printing the error message.
- method
the method where the error occurred
- message
the error message
- Definition Classes
- Error
-
def
foreach[U](f: (Array[Real]) ⇒ 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
- MatriR
-
def
getDiag(k: Int = 0): RleVectorR
Get the 'k'th diagonal of 'this' matrix.
Get the 'k'th diagonal of 'this' matrix.
- k
how far above the main diagonal, e.g., (-1, 0, 1) for (sub, main, super)
- Definition Classes
- RleMatrixR → MatriR
-
def
hashCode(): Int
Must also override hashCode for 'this' vector to be compatible with equals.
Must also override hashCode for 'this' vector to be compatible with equals.
- Definition Classes
- RleMatrixR → AnyRef → Any
-
def
inverse: MatriR
Invert 'this' matrix (requires a square matrix) and use partial pivoting.
Invert 'this' matrix (requires a square matrix) and use partial pivoting.
- Definition Classes
- RleMatrixR → MatriR
-
def
inverse_ip(): MatriR
Invert in-place 'this' matrix (requires a square matrix) and uses partial pivoting.
Invert in-place 'this' matrix (requires a square matrix) and uses partial pivoting. Note: this method turns the original matrix into the identity matrix. The inverse is returned and is captured by assignment.
- Definition Classes
- RleMatrixR → MatriR
-
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
- MatriR
-
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
- MatriR
-
def
isRectangular: Boolean
Check whether 'this' matrix is rectangular (all rows have the same number of columns).
Check whether 'this' matrix is rectangular (all rows have the same number of columns).
- Definition Classes
- RleMatrixR → MatriR
-
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
- MatriR
-
def
isSymmetric: Boolean
Check whether 'this' matrix is symmetric.
Check whether 'this' matrix is symmetric.
- Definition Classes
- MatriR
-
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
- MatriR
-
def
leDimensions(b: MatriR): 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
- MatriR
-
def
lowerT: RleMatrixR
Return the lower triangular of 'this' matrix (rest are zero).
Return the lower triangular of 'this' matrix (rest are zero).
- Definition Classes
- RleMatrixR → MatriR
-
def
lud_ip(): (RleMatrixR, RleMatrixR)
Factor in-place 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using an 'LU' Factorization algorithm.
Factor in-place 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using an 'LU' Factorization algorithm. FIX - check for 0 pivots (divide by zero).
- Definition Classes
- RleMatrixR → MatriR
-
def
lud_npp: (RleMatrixR, RleMatrixR)
Factor 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using an 'LU' Factorization algorithm.
Factor 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using an 'LU' Factorization algorithm. FIX - check for 0 pivots (divide by zero).
- Definition Classes
- RleMatrixR → MatriR
-
def
mag: Real
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
- MatriR
-
def
map(f: (VectoR) ⇒ VectoR): MatriR
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
- MatriR
-
def
max(e: Int = dim1): Real
Find the maximum element in 'this' matrix.
Find the maximum element in 'this' matrix.
- e
the ending row index (exclusive) for the search
- Definition Classes
- RleMatrixR → MatriR
-
def
mdot(b: RleMatrixR): RleMatrixR
Compute the matrix dot product of 'this' matrix and matrix 'b'.
Compute the matrix dot product of 'this' matrix and matrix 'b'.
- b
the matrix to multiply by (requires same first dimensions)
-
def
mdot(b: MatriR): RleMatrixR
Compute the matrix dot product of 'this' matrix and matrix 'b'.
Compute the matrix dot product of 'this' matrix and matrix 'b'.
- b
the matrix to multiply by (requires same first dimensions)
- Definition Classes
- RleMatrixR → MatriR
-
def
mean: VectoR
Compute the column means of 'this' matrix.
Compute the column means of 'this' matrix.
- Definition Classes
- MatriR
-
def
meanNZ: VectoR
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
- MatriR
-
def
meanR: VectoR
Compute the row means of 'this' matrix.
Compute the row means of 'this' matrix.
- Definition Classes
- MatriR
-
def
meanRNZ: VectoR
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
- MatriR
-
def
min(e: Int = dim1): Real
Find the minimum element in 'this' matrix.
Find the minimum element in 'this' matrix.
- e
the ending row index (exclusive) for the search
- Definition Classes
- RleMatrixR → MatriR
-
def
mul2(u: RleVectorR): RleVectorR
Multiply 'this' matrix by (column) vector 'u'
Multiply 'this' matrix by (column) vector 'u'
- u
the vector to multiply by
-
def
norm1: Real
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
- MatriR
- See also
en.wikipedia.org/wiki/Matrix_norm
-
def
normF: Real
Compute the Frobenius-norm of 'this' matrix, i.e., the sum of the absolute values squared of all the elements.
Compute the Frobenius-norm of 'this' matrix, i.e., the sum of the absolute values squared of all the elements.
- Definition Classes
- MatriR
- See also
en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
-
def
normINF: Real
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
- MatriR
- See also
en.wikipedia.org/wiki/Matrix_norm
-
def
nullspace: VectoR
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
- RleMatrixR → MatriR
- See also
/solving-ax-0-pivot-variables-special-solutions/MIT18_06SCF11_Ses1.7sum.pdf
http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces
-
def
nullspace_ip(): VectoR
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
- RleMatrixR → MatriR
- See also
/solving-ax-0-pivot-variables-special-solutions/MIT18_06SCF11_Ses1.7sum.pdf
http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces
-
val
range1: Range
Range for the storage array on dimension 1 (rows)
Range for the storage array on dimension 1 (rows)
- Definition Classes
- MatriR
-
val
range2: Range
Range for the storage array on dimension 2 (columns)
Range for the storage array on dimension 2 (columns)
- Definition Classes
- MatriR
-
def
reduce: RleMatrixR
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'. It can be used to solve 'a * x = b': augment 'a' with 'b' and call reduce. Takes '[a | b]' to '[I | x]'.
- Definition Classes
- RleMatrixR → MatriR
-
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'. It can be used to solve 'a * x = b': augment 'a' with 'b' and call reduce. Takes '[a | b]' to '[I | x]'.
- Definition Classes
- RleMatrixR → MatriR
-
def
sameCrossDimensions(b: MatriR): 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
- MatriR
-
def
sameDimensions(b: MatriR): 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
- MatriR
-
def
selectCols(colIndex: Array[Int]): RleMatrixR
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
- RleMatrixR → MatriR
-
def
selectRows(rowIndex: Array[Int]): RleMatrixR
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
- RleMatrixR → MatriR
-
def
selectRowsEx(rowIndex: Array[Int]): MatriR
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
- MatriR
-
def
set(u: Array[Array[Real]]): 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
- RleMatrixR → MatriR
-
def
set(i: Int, u: VectoR, 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
- RleMatrixR → MatriR
-
def
set(x: Real): 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
- RleMatrixR → MatriR
-
def
setCol(col: Int, u: VectoR): 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
- RleMatrixR → MatriR
-
def
setDiag(u: VectoR, 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
- RleMatrixR → MatriR
-
def
setDiag(x: Real): Unit
Set the main diagonal of 'this' matrix to the scalar 'x'.
Set the main diagonal of 'this' matrix to the scalar 'x'.
- x
the scalar to set the diagonal to
- Definition Classes
- RleMatrixR → MatriR
-
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): RleMatrixR
Slice 'this' matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.
Slice 'this' 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
- RleMatrixR → MatriR
-
def
slice(from: Int, end: Int): RleMatrixR
Slice 'this' matrix row-wise 'from' to 'end'.
Slice 'this' matrix row-wise 'from' to 'end'.
- from
the start row of the slice (inclusive)
- end
the end row of the slice (exclusive)
- Definition Classes
- RleMatrixR → MatriR
-
def
slice(rg: Range): MatriR
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
- MatriR
-
def
sliceCol(from: Int, end: Int): RleMatrixR
Slice 'this' matrix column-wise 'from' to 'end'.
Slice 'this' matrix column-wise 'from' to 'end'.
- from
the start column of the slice (inclusive)
- end
the end column of the slice (exclusive)
- Definition Classes
- RleMatrixR → MatriR
-
def
sliceEx(row: Int, col: Int): RleMatrixR
Slice 'this' matrix excluding the given row and/or column.
Slice 'this' matrix excluding the given row and/or column.
- row
the row to exclude
- col
the column to exclude
- Definition Classes
- RleMatrixR → MatriR
-
def
sliceEx(rg: Range): MatriR
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
- MatriR
-
def
solve(b: VectoR): VectoR
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
- RleMatrixR → MatriR
-
def
solve(l: MatriR, u: MatriR, b: VectoR): VectoR
Solve for 'x' in the equation 'l*u*x = b'
Solve for 'x' in the equation 'l*u*x = b'
- l
the lower triangular matrix
- u
the upper triangular matrix
- b
the constant vector
- Definition Classes
- RleMatrixR → MatriR
-
def
solve(lu: (MatriR, MatriR), b: VectoR): VectoR
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
- MatriR
-
def
sum: Real
Compute the sum of 'this' matrix, i.e., the sum of its elements.
Compute the sum of 'this' matrix, i.e., the sum of its elements.
- Definition Classes
- RleMatrixR → MatriR
-
def
sumAbs: Real
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
- RleMatrixR → MatriR
-
def
sumLower: Real
Compute the sum of the lower triangular region of 'this' matrix.
Compute the sum of the lower triangular region of 'this' matrix.
- Definition Classes
- RleMatrixR → MatriR
-
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
- MatriR
-
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
- MatriR
-
def
t: RleMatrixR
Transpose 'this' matrix (columns => rows).
Transpose 'this' matrix (columns => rows).
- Definition Classes
- RleMatrixR → MatriR
-
def
toDense: MatrixR
Convert 'this' matrix to a dense matrix.
Convert 'this' matrix to a dense matrix.
- Definition Classes
- RleMatrixR → MatriR
-
def
toInt: MatrixI
Convert 'this'
RleMatrixRinto aMatrixI.Convert 'this'
RleMatrixRinto aMatrixI.- Definition Classes
- RleMatrixR → MatriR
-
def
toString(): String
Convert 'this' real (Real precision) matrix to a string.
Convert 'this' real (Real precision) matrix to a string.
- Definition Classes
- RleMatrixR → AnyRef → Any
-
def
trace: Real
Compute the trace of 'this' matrix, i.e., the sum of the elements on the main diagonal.
Compute the trace of 'this' matrix, i.e., the sum of the elements on the main diagonal. Should also equal the sum of the eigenvalues.
- Definition Classes
- RleMatrixR → MatriR
- See also
Eigen.scala
-
def
update(ir: Range, jr: Range, b: MatriR): Unit
Set a slice 'this' matrix row-wise on range ir and column-wise on range 'jr'.
Set a slice 'this' matrix row-wise on range ir and column-wise on range 'jr'. Ex: a(2..4, 3..5) = b
- ir
the row range
- jr
the column range
- b
the matrix to assign
- Definition Classes
- RleMatrixR → MatriR
-
def
update(i: Int, u: VectoR): Unit
Set 'this' matrix's row at the 'i'-th index position to the vector 'u'.
Set 'this' 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
- RleMatrixR → MatriR
-
def
update(i: Int, j: Int, x: Real): Unit
Set 'this' matrix's element at the 'i, j'-th index position to the scalar 'x'.
Set 'this' 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
- RleMatrixR → MatriR
-
def
update(i: Int, jr: Range, u: VectoR): 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
- MatriR
-
def
update(ir: Range, j: Int, u: VectoR): 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
- MatriR
-
def
upperT: RleMatrixR
Return the upper triangular of 'this' matrix (rest are zero).
Return the upper triangular of 'this' matrix (rest are zero).
- Definition Classes
- RleMatrixR → MatriR
-
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
- RleMatrixR → MatriR
-
def
zero(mm: Int, nn: Int): RleMatrixR
Create an m-by-n matrix with all elements intialized to zero.
Create an m-by-n matrix with all elements intialized to zero.
- Definition Classes
- RleMatrixR → MatriR
-
def
~^(p: Int): RleMatrixR
Raise 'this' matrix to the 'p'th power (for some integer 'p' >= 2).
Raise 'this' matrix to the 'p'th power (for some integer 'p' >= 2). FIX - make compatible with imple in BldMatrix
- p
the power to raise 'this' matrix to
- Definition Classes
- RleMatrixR → MatriR