final def !=(arg0: Any): Boolean

Definition Classes: AnyRef → Any

final def ##(): Int

Definition Classes: AnyRef → Any

def *(x: Complex): BidMatrixC

Multiply 'this' bidiagonal matrix by scalar 'x'.

x: the scalar to multiply by

Definition Classes: BidMatrixC → MatriC

def *(u: VectoC): VectorC

Multiply 'this' bidiagonal matrix by vector 'u'.

u: the vector to multiply by

Definition Classes: BidMatrixC → MatriC

def *(b: BidMatrixC): MatrixC

Multiply 'this' bidiagonal matrix by matrix 'b'.

Multiply 'this' bidiagonal matrix by matrix 'b'. Requires 'b' to have type BidMatrixC, but returns a more general type of matrix.

b: the matrix to multiply by

def *(b: MatriC): BidMatrixC

Multiply 'this' bidiagonal matrix by matrix 'b'.

b: the matrix to multiply by

Definition Classes: BidMatrixC → MatriC

def **(u: VectoC): MatrixC

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: BidMatrixC → MatriC

def **(b: MatriC): MatriC

Multiply 'this' matrix by matrix 'b' elementwise (Hadamard product).

b: the matrix to multiply by

Definition Classes: MatriC
See also: en.wikipedia.org/wiki/Hadamard_product_(matrices) FIX - remove ??? and implement in all implementing classes

def **:(u: VectoC): MatrixC

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: BidMatrixC → MatriC

def **=(u: VectoC): MatrixC

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: BidMatrixC → MatriC

def *:(u: VectoC): VectoC

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: MatriC

def *=(x: Complex): BidMatrixC

Multiply in-place 'this' bidiagonal matrix by scalar 'x'.

x: the scalar to multiply by

Definition Classes: BidMatrixC → MatriC

def *=(b: MatriC): BidMatrixC

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

b: the matrix to multiply by

Definition Classes: BidMatrixC → MatriC

def +(x: Complex): BidMatrixC

Add 'this' bidiagonal matrix and scalar 'x'.

x: the scalar to add

Definition Classes: BidMatrixC → MatriC

def +(u: VectoC): BidMatrixC

Add 'this' bidiagonal matrix and (row) vector u.

u: the vector to add

Definition Classes: BidMatrixC → MatriC

def +(b: MatriC): BidMatrixC

Add 'this' bidiagonal matrix and matrix 'b'.

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

Definition Classes: BidMatrixC → MatriC

def ++(b: MatriC): BidMatrixC

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

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

Definition Classes: BidMatrixC → MatriC

def ++^(b: MatriC): BidMatrixC

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

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

Definition Classes: BidMatrixC → MatriC

def +:(u: VectoC): BidMatrixC

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: BidMatrixC → MatriC

def +=(x: Complex): BidMatrixC

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

x: the scalar to add

Definition Classes: BidMatrixC → MatriC

def +=(u: VectoC): MatrixC

Add in-place 'this' bidiagonal matrix and (row) vector 'u'.

u: the vector to add

Definition Classes: BidMatrixC → MatriC

def +=(b: MatriC): BidMatrixC

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

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

Definition Classes: BidMatrixC → MatriC

def +^:(u: VectoC): BidMatrixC

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: BidMatrixC → MatriC

def -(x: Complex): BidMatrixC

From 'this' bidiagonal matrix subtract scalar 'x'.

x: the scalar to subtract

Definition Classes: BidMatrixC → MatriC

def -(u: VectoC): BidMatrixC

From 'this' bidiagonal matrix subtract (row) vector 'u'.

u: the vector to subtract

Definition Classes: BidMatrixC → MatriC

def -(b: MatriC): BidMatrixC

From 'this' bidiagonal matrix subtract matrix 'b'.

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

Definition Classes: BidMatrixC → MatriC

def -=(x: Complex): BidMatrixC

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

x: the scalar to subtract

Definition Classes: BidMatrixC → MatriC

def -=(u: VectoC): BidMatrixC

From 'this' bidiagonal matrix subtract in-place (row) vector 'u'.

u: the vector to subtract

Definition Classes: BidMatrixC → MatriC

def -=(b: MatriC): BidMatrixC

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

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

Definition Classes: BidMatrixC → MatriC

def /(x: Complex): BidMatrixC

Divide 'this' bidiagonal matrix by scalar 'x'.

x: the scalar to divide by

Definition Classes: BidMatrixC → MatriC

def /=(x: Complex): BidMatrixC

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

x: the scalar to divide by

Definition Classes: BidMatrixC → MatriC

def :+(u: VectoC): BidMatrixC

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: BidMatrixC → MatriC

def :^+(u: VectoC): BidMatrixC

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: BidMatrixC → MatriC

final def ==(arg0: Any): Boolean

Definition Classes: AnyRef → Any

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

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: BidMatrixC → MatriC

def apply(i: Int): VectorC

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

i: the row index

Definition Classes: BidMatrixC → MatriC

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

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

i: the row index
j: the column index

Definition Classes: BidMatrixC → MatriC

def apply(iv: VectoI): MatriC

Get the rows indicated by the index vector 'iv' FIX - implement in all implementing classes

iv: the vector of row indices

Definition Classes: MatriC

def apply(i: Int, jr: Range): VectoC

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: MatriC

def apply(ir: Range, j: Int): VectoC

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: MatriC

final def asInstanceOf[T0]: T0

Definition Classes: Any

def at(i: Int, j: Int): Complex

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: VectoC): VectorC

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: BidMatrixC → MatriC

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

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: BidMatrixC → MatriC

def clone(): AnyRef

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

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

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: BidMatrixC → MatriC

def copy(): BidMatrixC

Create a clone of 'this' m-by-n matrix.

Definition Classes: BidMatrixC → MatriC

val d1: Int

def det: Complex

Compute the determinant of 'this' bidiagonal matrix.

Definition Classes: BidMatrixC → MatriC

def dg: VectorC

Get the diagonal of 'this' bidiagonal matrix.

def dg_(v: VectorC): Unit

Set the diagonal of 'this' bidiagonal matrix.

v: the vector to assign to the diagonal

def diag(p: Int, q: Int): SymTriMatrixC

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: BidMatrixC → MatriC

def diag(b: MatriC): MatriC

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: BidMatrixC → MatriC

lazy val dim1: Int

Dimension 1

Definition Classes: BidMatrixC → MatriC

lazy val dim2: Int

Dimension 2

Definition Classes: BidMatrixC → MatriC

def dot(b: MatriC): VectorC

Compute the dot product of 'this' matrix with matrix 'b' to produce a vector.

b: the second matrix of the dot product

Definition Classes: BidMatrixC → MatriC

def dot(u: VectoC): VectorC

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: BidMatrixC → MatriC

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')

Attributes: protected
Definition Classes: MatriC

def flatten: VectoC

Flatten 'this' matrix in row-major fashion, returning a vector containing all the elements from the matrix.

Definition Classes: MatriC

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[Complex]) ⇒ U): Unit

Iterate over 'this' matrix row by row applying method 'f'.

f: the function to apply

Definition Classes: MatriC

final def getClass(): Class[_]

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

def getDiag(k: Int = 0): VectorC

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: BidMatrixC → MatriC

def hashCode(): Int

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

def inverse: MatriC

Invert 'this' bidiagonal matrix.

Definition Classes: BidMatrixC → MatriC

def inverse_ip(): BidMatrixC

Invert in-place 'this' matrix (requires a 'squareMatrix') and use partial pivoting.

Definition Classes: BidMatrixC → MatriC

def isBidiagonal: Boolean

Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal).

Definition Classes: BidMatrixC → MatriC

final def isInstanceOf[T0]: Boolean

Definition Classes: Any

def isNonnegative: Boolean

Check whether 'this' bidiagonal matrix is nonnegative (has no negative elements).

Definition Classes: BidMatrixC → MatriC

def isRectangular: Boolean

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

Definition Classes: BidMatrixC → MatriC

def isSquare: Boolean

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

Definition Classes: MatriC

def isSymmetric: Boolean

Check whether 'this' matrix is symmetric.

Definition Classes: MatriC

def isTridiagonal: Boolean

Check whether 'this' matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal).

Definition Classes: BidMatrixC → MatriC

def leDimensions(b: MatriC): 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: MatriC

def lowerT: MatrixC

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

Definition Classes: BidMatrixC → MatriC

def lud_ip(): (MatriC, MatriC)

Factor in-place 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.

Definition Classes: BidMatrixC → MatriC

def lud_npp: (MatriC, MatriC)

Factor 'this' matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm.

Definition Classes: BidMatrixC → MatriC

def mag: Complex

Find the magnitude of 'this' matrix, the element value farthest from zero.

Definition Classes: MatriC

def map(f: (VectoC) ⇒ VectoC): MatriC

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: MatriC

def max(e: Int = dim1): Complex

Find the maximum element in 'this' bidiagonal matrix.

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

Definition Classes: BidMatrixC → MatriC

def mdot(b: MatriC): MatrixC

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: BidMatrixC → MatriC

def mdot(b: BidMatrixC): MatrixC

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: VectoC

Compute the column means of 'this' matrix.

Definition Classes: MatriC

def meanNZ: VectoC

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: MatriC

def meanR: VectoC

Compute the row means of 'this' matrix.

Definition Classes: MatriC

def meanRNZ: VectoC

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: MatriC

def min(e: Int = dim1): Complex

Find the minimum element in 'this' bidiagonal matrix.

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

Definition Classes: BidMatrixC → MatriC

final def ne(arg0: AnyRef): Boolean

Definition Classes: AnyRef

def norm1: Complex

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: MatriC
See also: en.wikipedia.org/wiki/Matrix_norm

def normF: Complex

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 MatriC should take absolute values, first.

Definition Classes: MatriC
See also: en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm

def normFSq: Complex

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 MatriC should take absolute values, first.

Definition Classes: MatriC
See also: en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm

def normINF: Complex

Compute the (infinity) INF-norm of 'this' matrix, i.e., the maximum 1-norm of the row vectors.

Definition Classes: MatriC
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: VectorC

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: BidMatrixC → MatriC
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(): VectorC

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: BidMatrixC → MatriC
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)

Definition Classes: MatriC

val range2: Range

Range for the storage array on dimension 2 (columns)

Definition Classes: MatriC

def reduce: BidMatrixC

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: BidMatrixC → MatriC

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: BidMatrixC → MatriC

def sameCrossDimensions(b: MatriC): Boolean

Check whether 'this' matrix and the other matrix 'b' have the same cross dimensions.

b: the other matrix

Definition Classes: MatriC

def sameDimensions(b: MatriC): Boolean

Check whether 'this' matrix and the other matrix 'b' have the same dimensions.

b: the other matrix

Definition Classes: MatriC

def sd: VectorC

Get the sup-diagonal of this bidiagonal matrix.

def sd_(v: VectorC): Unit

Set the sup-diagonal of 'this' bidiagonal matrix.

v: the vector to assign to the sup-diagonal

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

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: BidMatrixC → MatriC

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

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

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

Definition Classes: BidMatrixC → MatriC

def selectRows(rowIndex: VectoI): MatriC

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

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

Definition Classes: MatriC

def selectRowsEx(rowIndex: VectoI): MatriC

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

rowIndex: the row indices to exclude

Definition Classes: MatriC

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

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

rowIndex: the row indices to exclude

Definition Classes: MatriC

def set(i: Int, u: VectoC, j: Int = 0): Unit

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: BidMatrixC → MatriC

def set(u: MatriC): Unit

Set the values in 'this' matrix as copies of the values in matrix 'u'.

u: the matrix of values to assign

Definition Classes: BidMatrixC → MatriC

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

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: BidMatrixC → MatriC

def set(x: Complex): Unit

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

x: the scalar value to assign

Definition Classes: BidMatrixC → MatriC

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

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: BidMatrixC → MatriC

def setDiag(x: Complex): 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: BidMatrixC → MatriC

def setDiag(u: VectoC, 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: BidMatrixC → MatriC

def setFormat(newFormat: String): Unit

Set the format to the 'newFormat'.

newFormat: the new format string

Definition Classes: MatriC

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

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: BidMatrixC → MatriC

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

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: BidMatrixC → MatriC

def slice(rg: Range): MatriC

Slice 'this' matrix row-wise over the given range 'rg'.

rg: the range specifying the slice

Definition Classes: MatriC

def sliceCol(from: Int, end: Int): BidMatrixC

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: BidMatrixC → MatriC

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

Slice 'this' bidiagonal matrix excluding the given 'row' and 'col'umn.

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

Definition Classes: BidMatrixC → MatriC

def sliceEx(rg: Range): MatriC

Slice 'this' matrix row-wise excluding the given range 'rg'.

rg: the excluded range of the slice

Definition Classes: MatriC

def solve(l: MatriC, u: MatriC, b: VectoC): VectorC

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: BidMatrixC → MatriC

def solve(b: VectoC): VectorC

Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' bidiagonal matrix.

b: the constant vector

Definition Classes: BidMatrixC → MatriC

def solve(lu: (MatriC, MatriC), b: VectoC): VectoC

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: MatriC

def splitRows(rowIndex: VectoI): (MatriC, MatriC)

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: MatriC

def splitRows(rowIndex: Array[Int]): (MatriC, MatriC)

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: MatriC

def sum: Complex

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

Definition Classes: BidMatrixC → MatriC

def sumAbs: Complex

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: BidMatrixC → MatriC

def sumLower: Complex

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

Definition Classes: BidMatrixC → MatriC

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: MatriC

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: MatriC

final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes: AnyRef

def t: BidMatrixC

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

Definition Classes: BidMatrixC → MatriC

def toDense: MatrixC

Convert 'this' tridiagonal matrix to a dense matrix.

Definition Classes: BidMatrixC → MatriC

def toDouble: BidMatrixD

Convert 'this' BidMatrixC into a double matrix BidMatrixD.

Definition Classes: BidMatrixC → MatriC

def toInt: BidMatrixI

Convert 'this' BidMatrixC into an integer matrix BidMatrixI.

Definition Classes: BidMatrixC → MatriC

def toString(): String

Convert 'this' bidiagonal matrix to a string showing the diagonal vector followed by the sup-diagonal vector.

Definition Classes: BidMatrixC → AnyRef → Any

def trace: Complex

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: BidMatrixC → MatriC
See also: Eigen.scala

def update(ir: Range, jr: Range, b: MatriC): 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: BidMatrixC → MatriC

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

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: BidMatrixC → MatriC

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

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: BidMatrixC → MatriC

def update(i: Int, jr: Range, u: VectoC): 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: MatriC

def update(ir: Range, j: Int, u: VectoC): 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: MatriC

def upperT: MatrixC

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

Definition Classes: BidMatrixC → MatriC

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'.

fileName: the name of file to hold the data

Definition Classes: BidMatrixC → MatriC

def zero(m: Int = dim1, n: Int = dim2): BidMatrixC

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

m: the number of rows
n: the number of columns

Definition Classes: BidMatrixC → MatriC

def ~^(p: Int): BidMatrixC

Raise 'this' bidiagonal matrix to the 'p'th power (for some integer 'p' >= 2).

p: the power to raise 'this' matrix to

Definition Classes: BidMatrixC → MatriC

Packages

BidMatrixC

Companion object BidMatrixC

class BidMatrixC extends MatriC with Error with Serializable

Instance Constructors

Value Members

Deprecated Value Members

Inherited from Serializable

Inherited from Serializable

Inherited from MatriC

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped

Packages

BidMatrixC 

Companion object BidMatrixC

class BidMatrixC extends MatriC with Error with Serializable

Instance Constructors

Value Members

Deprecated Value Members

Inherited from Serializable

Inherited from Serializable

Inherited from MatriC

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped

BidMatrixC