final def !=(arg0: Any): Boolean

Definition Classes: AnyRef → Any

final def ##(): Int

Definition Classes: AnyRef → Any

def *(b: MatriQ): MatriQ

Multiply 'this' matrix by matrix 'b'.

b: the matrix to multiply by (requires 'sameCrossDimensions')

Definition Classes: RleMatrixQ → MatriQ

def *(x: Rational): RleMatrixQ

Multiply 'this' matrix by scalar 'x'.

x: the scalar to multiply by

Definition Classes: RleMatrixQ → MatriQ

def *(u: VectoQ): VectoQ

Multiply 'this' matrix by (column) vector 'u'

u: the vector to multiply by

Definition Classes: RleMatrixQ → MatriQ

def **(u: VectoQ): MatriQ

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: RleMatrixQ → MatriQ

def **(b: MatriQ): MatriQ

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): MatriQ

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: RleMatrixQ → MatriQ

def **=(u: VectoQ): MatriQ

Multiply in-place 'this' matrix by vector 'u' to produce another matrix 'a_ij * u_j'.

u: the vector to multiply by

Definition Classes: RleMatrixQ → 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 *=(b: MatriQ): MatriQ

Multiply in-place 'this' matrix by matrix 'b'

b: the matrix to multiply by (requires square and 'sameCrossDimensions')

Definition Classes: RleMatrixQ → MatriQ

def *=(x: Rational): RleMatrixQ

Multiply in-place 'this' matrix by matrix 'x'

x: the matrix to multiply by

Definition Classes: RleMatrixQ → MatriQ

def +(u: VectoQ): MatriQ

Add 'this' matrix and vector 'u'.

u: the matrix to add (requires leDimensions)

Definition Classes: RleMatrixQ → MatriQ

def +(x: Rational): RleMatrixQ

Add 'this' matrix and scalar 'x'.

x: the scalar to add

Definition Classes: RleMatrixQ → MatriQ

def +(b: MatriQ): RleMatrixQ

Add 'this' matrix and matrix 'b'.

b: the matrix to add (requires leDimensions)

Definition Classes: RleMatrixQ → MatriQ

def ++(b: MatriQ): RleMatrixQ

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: RleMatrixQ → MatriQ

def ++^(b: MatriQ): RleMatrixQ

Concatenate (column-wise) 'this' matrix and matrix 'b'.

b: the matrix to be concatenated as the new last columns in new matrix

Definition Classes: RleMatrixQ → MatriQ

def +:(u: VectoQ): RleMatrixQ

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: RleMatrixQ → MatriQ

def +=(b: MatriQ): MatriQ

Add in-place 'this' matrix and matrix 'b'.

b: the matrix to add (requires 'leDimensions')

Definition Classes: RleMatrixQ → MatriQ

def +=(u: VectoQ): MatriQ

Add in-place 'this' matrix and vector 'u'.

u: the vector to add

Definition Classes: RleMatrixQ → MatriQ

def +=(x: Rational): MatriQ

Add in-place 'this' matrix and scalar 'x'.

x: the scalar to add

Definition Classes: RleMatrixQ → MatriQ

def +^:(u: VectoQ): RleMatrixQ

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: RleMatrixQ → MatriQ

def -(b: MatriQ): MatriQ

From 'this' matrix subtract matrix 'b'.

b: the matrix to subtract

Definition Classes: RleMatrixQ → MatriQ

def -(u: VectoQ): RleMatrixQ

From 'this' matrix subtract vector 'u'.

u: the vector to subtract

Definition Classes: RleMatrixQ → MatriQ

def -(x: Rational): MatriQ

From 'this' matrix subtract scalar 'x'.

x: the scalar to subtract

Definition Classes: RleMatrixQ → MatriQ

def -=(b: MatriQ): MatriQ

From 'this' matrix subtract in-place matrix 'b'.

b: the matrix to subtract (requires 'leDimensions')

Definition Classes: RleMatrixQ → MatriQ

def -=(u: VectoQ): MatriQ

From 'this' matrix subtract in-place vector 'u'.

u: the vector to subtract

Definition Classes: RleMatrixQ → MatriQ

def -=(x: Rational): MatriQ

From 'this' matrix subtract in-place scalar 'x'.

x: the scalar to subtract

Definition Classes: RleMatrixQ → MatriQ

def /(x: Rational): MatriQ

Divide 'this' matrix by scalar 'x'.

x: the scalar to divide by

Definition Classes: RleMatrixQ → MatriQ

def /=(x: Rational): MatriQ

Divide in-place 'this' matrix by scalar 'x'.

x: the scalar to divide by

Definition Classes: RleMatrixQ → MatriQ

def :+(u: VectoQ): RleMatrixQ

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: RleMatrixQ → MatriQ

def :^+(u: VectoQ): RleMatrixQ

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: RleMatrixQ → MatriQ

final def ==(arg0: Any): Boolean

Definition Classes: AnyRef → Any

def apply(): Array[RleVectorQ]

Get the underlying 1D array for 'this' matrix.

def apply(ir: Range, jr: Range): MatriQ

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: RleMatrixQ → MatriQ

def apply(i: Int): RleVectorQ

Get 'this' matrix's vector at the 'i'-th index position ('i'-th row).

i: the row index

Definition Classes: RleMatrixQ → MatriQ

def apply(i: Int, j: Int): Rational

Get 'this' matrix's element at the 'i, j'-th index position.

i: the row index
j: the column index

Definition Classes: RleMatrixQ → MatriQ

def apply(iv: VectoI): MatriQ

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): RleVectorQ

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: RleMatrixQ → MatriQ

def clean(thres: Double = TOL, relative: Boolean = true): MatriQ

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: RleMatrixQ → MatriQ

def clone(): AnyRef

Attributes: protected[java.lang]
Definition Classes: AnyRef
Annotations: @native() @throws( ... )

def col(col: Int, from: Int = 0): VectorQ

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: RleMatrixQ → MatriQ

def col(col: Int): RleVectorQ

Get column 'col' from the matrix, returning it as a vector.

col: the column to extract from the matrix

def copy(): RleMatrixQ

Create an exact copy of 'this' m-by-n matrix.

Definition Classes: RleMatrixQ → MatriQ

def csize: VectorI

Get size of each column of 'this' RleMatrix

val d1: Int

val d2: Int

val deferred: Boolean

def det: Rational

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: RleMatrixQ → MatriQ

def diag(b: MatriQ): RleMatrixQ

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: RleMatrixQ → MatriQ

def diag(p: Int, q: Int = 0): MatriQ

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: RleMatrixQ → MatriQ

lazy val dim1: Int

Dimension 1

Definition Classes: RleMatrixQ → MatriQ

lazy val dim2: Int

Dimension 2

Definition Classes: RleMatrixQ → MatriQ

def dot(b: RleMatrixQ): RleVectorQ

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: MatriQ): RleVectorQ

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: RleMatrixQ → MatriQ

def dot(b: VectoQ): VectoQ

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: RleMatrixQ → MatriQ

final def eq(arg0: AnyRef): Boolean

Definition Classes: AnyRef

def equals(b: Any): Boolean

Override equals to determine whether 'this' vector equals vector 'b'.

b: the vector to compare with this

Definition Classes: RleMatrixQ → AnyRef → Any

val fString: String

Format string used for printing vector values (change using 'setFormat')

Attributes: protected
Definition Classes: MatriQ

def finalize(): Unit

Attributes: protected[java.lang]
Definition Classes: AnyRef
Annotations: @throws( classOf[java.lang.Throwable] )

final def flaw(method: String, message: String): Unit

Show the flaw by printing the error message.

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'.

f: the function to apply

Definition Classes: MatriQ

final def getClass(): Class[_]

Definition Classes: AnyRef → Any
Annotations: @native()

def getDiag(k: Int = 0): RleVectorQ

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: RleMatrixQ → MatriQ

def hashCode(): Int

Must also override hashCode for 'this' vector to be compatible with equals.

Definition Classes: RleMatrixQ → AnyRef → Any

def inverse: MatriQ

Invert 'this' matrix (requires a square matrix) and use partial pivoting.

Definition Classes: RleMatrixQ → MatriQ

def inverse_ip(): MatriQ

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: RleMatrixQ → MatriQ

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' matrix is nonnegative (has no negative elements).

Definition Classes: MatriQ

def isRectangular: Boolean

Check whether 'this' matrix is rectangular (all rows have the same number of columns).

Definition Classes: RleMatrixQ → MatriQ

def isSquare: Boolean

Check whether 'this' matrix is square (same row and column dimensions).

Definition Classes: MatriQ

def isSymmetric: Boolean

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'.

b: the other matrix

Definition Classes: MatriQ

def lowerT: RleMatrixQ

Return the lower triangular of 'this' matrix (rest are zero).

Definition Classes: RleMatrixQ → MatriQ

def lud_ip(): (RleMatrixQ, RleMatrixQ)

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: RleMatrixQ → MatriQ

def lud_npp: (RleMatrixQ, RleMatrixQ)

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: RleMatrixQ → MatriQ

def mag: Rational

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' matrix.

e: the ending row index (exclusive) for the search

Definition Classes: RleMatrixQ → MatriQ

def mdot(b: RleMatrixQ): RleMatrixQ

Compute the matrix dot product of 'this' matrix and matrix 'b'.

b: the matrix to multiply by (requires same first dimensions)

def mdot(b: MatriQ): RleMatrixQ

Compute the matrix dot product of 'this' matrix and matrix 'b'.

b: the matrix to multiply by (requires same first dimensions)

Definition Classes: RleMatrixQ → MatriQ

def mean: VectoQ

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).

Definition Classes: MatriQ

def meanR: VectoQ

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).

Definition Classes: MatriQ

def min(e: Int = dim1): Rational

Find the minimum element in 'this' matrix.

e: the ending row index (exclusive) for the search

Definition Classes: RleMatrixQ → MatriQ

def mul2(u: RleVectorQ): RleVectorQ

Multiply 'this' matrix by (column) vector 'u'

u: the vector to multiply by

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 sum of the absolute values squared of all the elements.

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.

Definition Classes: MatriQ
See also: en.wikipedia.org/wiki/Matrix_norm

final def notify(): Unit

Definition Classes: AnyRef
Annotations: @native()

final def notifyAll(): Unit

Definition Classes: AnyRef
Annotations: @native()

def nullspace: VectoQ

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: RleMatrixQ → MatriQ
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(): VectoQ

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: RleMatrixQ → MatriQ
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)

Definition Classes: MatriQ

val range2: Range

Range for the storage array on dimension 2 (columns)

Definition Classes: MatriQ

def reduce: RleMatrixQ

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: RleMatrixQ → MatriQ

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: RleMatrixQ → MatriQ

def sameCrossDimensions(b: MatriQ): Boolean

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.

b: the other matrix

Definition Classes: MatriQ

def selectCols(colIndex: Array[Int]): RleMatrixQ

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: RleMatrixQ → MatriQ

def selectRows(rowIndex: Array[Int]): RleMatrixQ

Select rows from 'this' matrix according to the given index/basis.

rowIndex: the row index positions (e.g., (0, 2, 5))

Definition Classes: RleMatrixQ → MatriQ

def selectRowsEx(rowIndex: Array[Int]): MatriQ

Select all rows from 'this' matrix excluding the rows from the given 'rowIndex'.

rowIndex: the row indices to exclude

Definition Classes: MatriQ

def set(u: Array[Array[Rational]]): Unit

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: RleMatrixQ → 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'.

i: the row index
u: the vector value to assign
j: the starting column index

Definition Classes: RleMatrixQ → MatriQ

def set(x: Rational): Unit

Set all the elements in 'this' matrix to the scalar 'x'.

x: the scalar value to assign

Definition Classes: RleMatrixQ → MatriQ

def setCol(col: Int, u: VectoQ): Unit

Set column 'col' of the matrix to a vector.

col: the column to set
u: the vector to assign to the column

Definition Classes: RleMatrixQ → 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: RleMatrixQ → MatriQ

def setDiag(x: Rational): Unit

Set the main diagonal of 'this' matrix to the scalar 'x'.

x: the scalar to set the diagonal to

Definition Classes: RleMatrixQ → MatriQ

def setFormat(newFormat: String): Unit

Set the format to the 'newFormat'.

newFormat: the new format string

Definition Classes: MatriQ

def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): RleMatrixQ

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: RleMatrixQ → MatriQ

def slice(from: Int, end: Int): RleMatrixQ

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: RleMatrixQ → MatriQ

def slice(rg: Range): MatriQ

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): RleMatrixQ

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: RleMatrixQ → MatriQ

def sliceEx(row: Int, col: Int): RleMatrixQ

Slice 'this' matrix excluding the given row and/or column.

row: the row to exclude
col: the column to exclude

Definition Classes: RleMatrixQ → MatriQ

def sliceEx(rg: Range): MatriQ

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.

b: the constant vector.

Definition Classes: RleMatrixQ → MatriQ

def solve(l: MatriQ, u: MatriQ, b: VectoQ): VectoQ

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: RleMatrixQ → MatriQ

def solve(lu: (MatriQ, MatriQ), b: VectoQ): VectoQ

Solve for 'x' in the equation 'l*u*x = b' (see 'lud' above).

lu: the lower and upper triangular matrices
b: the constant vector

Definition Classes: MatriQ

def sum: Rational

Compute the sum of 'this' matrix, i.e., the sum of its elements.

Definition Classes: RleMatrixQ → 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: RleMatrixQ → MatriQ

def sumLower: Rational

Compute the sum of the lower triangular region of 'this' matrix.

Definition Classes: RleMatrixQ → MatriQ

def swap(i: Int, k: Int, col: Int = 0): Unit

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'.

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: RleMatrixQ

Transpose 'this' matrix (columns => rows).

Definition Classes: RleMatrixQ → MatriQ

def toDense: MatrixQ

Convert 'this' matrix to a dense matrix.

Definition Classes: RleMatrixQ → MatriQ

def toInt: MatrixI

Convert 'this' RleMatrixQ into a MatrixI.

Definition Classes: RleMatrixQ → MatriQ

def toString(): String

Convert 'this' real (Rational precision) matrix to a string.

Definition Classes: RleMatrixQ → AnyRef → Any

def trace: Rational

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: RleMatrixQ → MatriQ
See also: Eigen.scala

def update(ir: Range, jr: Range, b: MatriQ): Unit

Set a slice 'this' matrix row-wise on range ir and column-wise on range 'jr'.

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: RleMatrixQ → MatriQ

def update(i: Int, u: VectoQ): Unit

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: RleMatrixQ → MatriQ

def update(i: Int, j: Int, x: Rational): Unit

Set 'this' matrix's element at the 'i, j'-th index position to the scalar 'x'.

i: the row index
j: the column index
x: the scalar value to assign

Definition Classes: RleMatrixQ → 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: RleMatrixQ

Return the upper triangular of 'this' matrix (rest are zero).

Definition Classes: RleMatrixQ → MatriQ

final def wait(): Unit

Definition Classes: AnyRef
Annotations: @throws( ... )

final def wait(arg0: Long, arg1: Int): Unit

Definition Classes: AnyRef
Annotations: @throws( ... )

final def wait(arg0: Long): Unit

Definition Classes: AnyRef
Annotations: @native() @throws( ... )

def write(fileName: String): Unit

Write 'this' matrix to a CSV-formatted text file with name 'fileName'.

fileName: the name of file to hold the data

Definition Classes: RleMatrixQ → MatriQ

def zero(mm: Int, nn: Int): RleMatrixQ

Create an m-by-n matrix with all elements intialized to zero.

Definition Classes: RleMatrixQ → MatriQ

def ~^(p: Int): RleMatrixQ

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: RleMatrixQ → MatriQ

Packages

RleMatrixQ

Companion object RleMatrixQ

class RleMatrixQ extends MatriQ with Error with Serializable

Instance Constructors

Value Members

Inherited from Serializable

Inherited from Serializable

Inherited from MatriQ

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped

Packages

RleMatrixQ 

Companion object RleMatrixQ

class RleMatrixQ extends MatriQ with Error with Serializable

Instance Constructors

Value Members

Inherited from Serializable

Inherited from Serializable

Inherited from MatriQ

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped

RleMatrixQ