final def !=(arg0: Any): Boolean

Definition Classes: AnyRef → Any

final def ##(): Int

Definition Classes: AnyRef → Any

def *(x: Rational): BidMatrixQ

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

x: the scalar to multiply by

Definition Classes: BidMatrixQ → MatriQ

def *(u: VectoQ): VectorQ

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

u: the vector to multiply by

Definition Classes: BidMatrixQ → MatriQ

def *(b: BidMatrixQ): MatrixQ

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

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

b: the matrix to multiply by

def *(b: MatriQ): BidMatrixQ

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

b: the matrix to multiply by

Definition Classes: BidMatrixQ → MatriQ

def **(u: VectoQ): MatrixQ

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: BidMatrixQ → MatriQ

def **:(u: VectoQ): MatrixQ

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: BidMatrixQ → MatriQ

def **=(u: VectoQ): MatrixQ

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: BidMatrixQ → MatriQ

def *:(u: VectoQ): VectoQ

Multiply (row) vector 'u' by 'this' matrix.

Multiply (row) vector 'u' by 'this' matrix. Note '*:' is right associative. vector = vector *: matrix

u: the vector to multiply by

Definition Classes: MatriQ

def *=(x: Rational): BidMatrixQ

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

x: the scalar to multiply by

Definition Classes: BidMatrixQ → MatriQ

def *=(b: MatriQ): BidMatrixQ

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

b: the matrix to multiply by

Definition Classes: BidMatrixQ → MatriQ

def +(x: Rational): BidMatrixQ

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

x: the scalar to add

Definition Classes: BidMatrixQ → MatriQ

def +(u: VectoQ): BidMatrixQ

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

u: the vector to add

Definition Classes: BidMatrixQ → MatriQ

def +(b: MatriQ): BidMatrixQ

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

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

Definition Classes: BidMatrixQ → MatriQ

def ++(b: MatriQ): BidMatrixQ

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

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

Definition Classes: BidMatrixQ → MatriQ

def ++^(b: MatriQ): BidMatrixQ

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

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

Definition Classes: BidMatrixQ → MatriQ

def +:(u: VectoQ): BidMatrixQ

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: BidMatrixQ → MatriQ

def +=(x: Rational): BidMatrixQ

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

x: the scalar to add

Definition Classes: BidMatrixQ → MatriQ

def +=(u: VectoQ): MatrixQ

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

u: the vector to add

Definition Classes: BidMatrixQ → MatriQ

def +=(b: MatriQ): BidMatrixQ

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

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

Definition Classes: BidMatrixQ → MatriQ

def +^:(u: VectoQ): BidMatrixQ

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: BidMatrixQ → MatriQ

def -(x: Rational): BidMatrixQ

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

x: the scalar to subtract

Definition Classes: BidMatrixQ → MatriQ

def -(u: VectoQ): BidMatrixQ

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

u: the vector to subtract

Definition Classes: BidMatrixQ → MatriQ

def -(b: MatriQ): BidMatrixQ

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

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

Definition Classes: BidMatrixQ → MatriQ

def -=(x: Rational): BidMatrixQ

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

x: the scalar to subtract

Definition Classes: BidMatrixQ → MatriQ

def -=(u: VectoQ): BidMatrixQ

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

u: the vector to subtract

Definition Classes: BidMatrixQ → MatriQ

def -=(b: MatriQ): BidMatrixQ

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

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

Definition Classes: BidMatrixQ → MatriQ

def /(x: Rational): BidMatrixQ

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

x: the scalar to divide by

Definition Classes: BidMatrixQ → MatriQ

def /=(x: Rational): BidMatrixQ

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

x: the scalar to divide by

Definition Classes: BidMatrixQ → MatriQ

def :+(u: VectoQ): BidMatrixQ

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: BidMatrixQ → MatriQ

def :^+(u: VectoQ): BidMatrixQ

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: BidMatrixQ → MatriQ

final def ==(arg0: Any): Boolean

Definition Classes: AnyRef → Any

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

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: BidMatrixQ → MatriQ

def apply(i: Int): VectorQ

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

i: the row index

Definition Classes: BidMatrixQ → MatriQ

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

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

i: the row index
j: the column index

Definition Classes: BidMatrixQ → 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 at(i: Int, j: Int): Rational

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: VectoQ): VectorQ

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: BidMatrixQ → MatriQ

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

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: BidMatrixQ → MatriQ

def clone(): AnyRef

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

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

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: BidMatrixQ → MatriQ

def copy(): BidMatrixQ

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

Definition Classes: BidMatrixQ → MatriQ

val d1: Int

def det: Rational

Compute the determinant of 'this' bidiagonal matrix.

Definition Classes: BidMatrixQ → MatriQ

def dg: VectorQ

Get the diagonal of 'this' bidiagonal matrix.

def dg_(v: VectorQ): Unit

Set the diagonal of 'this' bidiagonal matrix.

v: the vector to assign to the diagonal

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

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: BidMatrixQ → MatriQ

def diag(b: MatriQ): MatriQ

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: BidMatrixQ → MatriQ

lazy val dim1: Int

Dimension 1

Definition Classes: BidMatrixQ → MatriQ

lazy val dim2: Int

Dimension 2

Definition Classes: BidMatrixQ → MatriQ

def dot(b: MatriQ): VectorQ

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

b: the second matrix of the dot product

Definition Classes: BidMatrixQ → MatriQ

def dot(u: VectoQ): VectorQ

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: BidMatrixQ → MatriQ

final def eq(arg0: AnyRef): Boolean

Definition Classes: AnyRef

def equals(arg0: Any): Boolean

Definition Classes: AnyRef → Any

val fString: String

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

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

def getDiag(k: Int = 0): VectorQ

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: BidMatrixQ → MatriQ

def hashCode(): Int

Definition Classes: AnyRef → Any

def inverse: MatriQ

Invert 'this' bidiagonal matrix.

Definition Classes: BidMatrixQ → MatriQ

def inverse_ip(): BidMatrixQ

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

Definition Classes: BidMatrixQ → MatriQ

def isBidiagonal: Boolean

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

Definition Classes: BidMatrixQ → MatriQ

final def isInstanceOf[T0]: Boolean

Definition Classes: Any

def isNonnegative: Boolean

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

Definition Classes: BidMatrixQ → MatriQ

def isRectangular: Boolean

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

Definition Classes: BidMatrixQ → 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).

Definition Classes: BidMatrixQ → 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: MatrixQ

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

Definition Classes: BidMatrixQ → MatriQ

def lud_ip(): (MatriQ, MatriQ)

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

Definition Classes: BidMatrixQ → MatriQ

def lud_npp: (MatriQ, MatriQ)

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

Definition Classes: BidMatrixQ → MatriQ

def mag: Rational

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

Definition Classes: MatriQ

def max(e: Int = dim1): Rational

Find the maximum element in 'this' bidiagonal matrix.

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

Definition Classes: BidMatrixQ → MatriQ

def mdot(b: MatriQ): MatrixQ

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: BidMatrixQ → MatriQ

def mdot(b: BidMatrixQ): MatrixQ

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: VectoQ

Compute the column means of this matrix.

Definition Classes: MatriQ

def min(e: Int = dim1): Rational

Find the minimum element in 'this' bidiagonal matrix.

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

Definition Classes: BidMatrixQ → MatriQ

final def ne(arg0: AnyRef): Boolean

Definition Classes: AnyRef

def norm1: Rational

Compute the 1-norm of 'this' matrix, i.e., the maximum 1-norm of the column vectors.

Compute the 1-norm of 'this' matrix, i.e., the maximum 1-norm of the column vectors. This is useful for comparing matrices '(a - b).norm1'.

Definition Classes: MatriQ

final def notify(): Unit

Definition Classes: AnyRef

final def notifyAll(): Unit

Definition Classes: AnyRef

def nullspace: VectorQ

Compute the (right) nullspace of 'this' 'm-by-n' matrix (requires 'n = m+1') by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.

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: BidMatrixQ → 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(): VectorQ

Compute in-place the (right) nullspace of 'this' 'm-by-n' matrix (requires 'n = m+1') by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.

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: BidMatrixQ → 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: BidMatrixQ

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: BidMatrixQ → 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.

Definition Classes: BidMatrixQ → 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 sd: VectorQ

Get the sup-diagonal of this bidiagonal matrix.

def sd_(v: VectorQ): Unit

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

v: the vector to assign to the sup-diagonal

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

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: BidMatrixQ → MatriQ

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

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

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

Definition Classes: BidMatrixQ → MatriQ

def set(i: Int, u: VectoQ, 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: BidMatrixQ → MatriQ

def set(u: Array[Array[Rational]]): 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: BidMatrixQ → MatriQ

def set(x: Rational): Unit

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

x: the scalar value to assign

Definition Classes: BidMatrixQ → MatriQ

def setCol(col: Int, u: VectoQ): 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: BidMatrixQ → MatriQ

def setDiag(x: Rational): 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: BidMatrixQ → MatriQ

def setDiag(u: VectoQ, 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: BidMatrixQ → 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): BidMatrixQ

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: BidMatrixQ → MatriQ

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

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: BidMatrixQ → MatriQ

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

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: BidMatrixQ → MatriQ

def sliceExclude(row: Int, col: Int): BidMatrixQ

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

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

Definition Classes: BidMatrixQ → MatriQ

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

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: BidMatrixQ → MatriQ

def solve(b: VectoQ): VectorQ

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

b: the constant vector

Definition Classes: BidMatrixQ → 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' bidiagonal matrix, i.e., the sum of its elements.

Definition Classes: BidMatrixQ → MatriQ

def sumAbs: Rational

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: BidMatrixQ → MatriQ

def sumLower: Rational

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

Definition Classes: BidMatrixQ → 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: BidMatrixQ

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

Definition Classes: BidMatrixQ → MatriQ

def toDense: MatrixQ

Convert 'this' tridiagonal matrix to a dense matrix.

Definition Classes: BidMatrixQ → MatriQ

def toInt: BidMatrixI

Convert 'this' BidMatrixQ into a BidMatrixI.

Definition Classes: BidMatrixQ → MatriQ

def toString(): String

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

Definition Classes: BidMatrixQ → AnyRef → Any

def trace: Rational

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: BidMatrixQ → MatriQ
See also: Eigen.scala

def update(ir: Range, jr: Range, b: MatriQ): 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: BidMatrixQ → MatriQ

def update(i: Int, u: VectoQ): 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: BidMatrixQ → MatriQ

def update(i: Int, j: Int, x: Rational): 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: BidMatrixQ → 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: MatrixQ

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

Definition Classes: BidMatrixQ → 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: @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: BidMatrixQ → MatriQ

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

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

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

Definition Classes: BidMatrixQ → MatriQ

def ~^(p: Int): BidMatrixQ

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

p: the power to raise 'this' matrix to

Definition Classes: BidMatrixQ → MatriQ

Packages

BidMatrixQ

Companion object BidMatrixQ

class BidMatrixQ 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

BidMatrixQ 

Companion object BidMatrixQ

class BidMatrixQ 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

BidMatrixQ