final def !=(arg0: Any): Boolean

Definition Classes: AnyRef → Any

final def ##(): Int

Definition Classes: AnyRef → Any

def *(x: Double): SymTriMatrixD

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

x: the scalar to multiply by

Definition Classes: SymTriMatrixD → MatriD

def *(u: VectoD): VectorD

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

u: the vector to multiply by

Definition Classes: SymTriMatrixD → MatriD

def *(b: SymTriMatrixD): MatrixD

Multiply 'this' tridiagonal matrix by matrix 'b'.

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

b: the matrix to multiply by

def *(b: MatriD): SymTriMatrixD

Multiply 'this' tridiagonal matrix by matrix 'b'.

b: the matrix to multiply by

Definition Classes: SymTriMatrixD → MatriD

def **(u: VectoD): MatrixD

Multiply 'this' tridiagonal matrix by vector 'u' to produce another matrix 'a_ij * u_j'.

Multiply 'this' tridiagonal 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: SymTriMatrixD → MatriD

def **(b: MatriD): MatriD

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

b: the matrix to multiply by

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

def **:(u: VectoD): MatrixD

Multiply vector 'u' by 'this' tridiagonal matrix to produce another matrix 'u_i * a_ij'.

Multiply vector 'u' by 'this' tridiagonal 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: SymTriMatrixD → MatriD

def **=(u: VectoD): MatrixD

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

Multiply in-place 'this' tridiagonal 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: SymTriMatrixD → MatriD

def *:(u: VectoD): VectoD

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: MatriD

def *=(x: Double): SymTriMatrixD

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

x: the scalar to multiply by

Definition Classes: SymTriMatrixD → MatriD

def *=(b: MatriD): SymTriMatrixD

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

b: the matrix to multiply by

Definition Classes: SymTriMatrixD → MatriD

def +(x: Double): SymTriMatrixD

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

x: the scalar to add

Definition Classes: SymTriMatrixD → MatriD

def +(u: VectoD): MatrixD

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

u: the vector to add

Definition Classes: SymTriMatrixD → MatriD

def +(b: MatriD): SymTriMatrixD

Add 'this' tridiagonal matrix and matrix 'b'.

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

Definition Classes: SymTriMatrixD → MatriD

def ++(b: MatriD): SymTriMatrixD

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

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

Definition Classes: SymTriMatrixD → MatriD

def ++^(b: MatriD): SymTriMatrixD

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

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

Definition Classes: SymTriMatrixD → MatriD

def +:(u: VectoD): SymTriMatrixD

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: SymTriMatrixD → MatriD

def +=(x: Double): SymTriMatrixD

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

x: the scalar to add

Definition Classes: SymTriMatrixD → MatriD

def +=(u: VectoD): MatrixD

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

u: the vector to add

Definition Classes: SymTriMatrixD → MatriD

def +=(b: MatriD): SymTriMatrixD

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

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

Definition Classes: SymTriMatrixD → MatriD

def +^:(u: VectoD): SymTriMatrixD

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: SymTriMatrixD → MatriD

def -(x: Double): SymTriMatrixD

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

x: the scalar to subtract

Definition Classes: SymTriMatrixD → MatriD

def -(u: VectoD): MatrixD

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

u: the vector to subtract

Definition Classes: SymTriMatrixD → MatriD

def -(b: MatriD): SymTriMatrixD

From 'this' tridiagonal matrix subtract matrix 'b'.

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

Definition Classes: SymTriMatrixD → MatriD

def -=(x: Double): SymTriMatrixD

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

x: the scalar to subtract

Definition Classes: SymTriMatrixD → MatriD

def -=(u: VectoD): MatrixD

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

u: the vector to subtract

Definition Classes: SymTriMatrixD → MatriD

def -=(b: MatriD): SymTriMatrixD

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

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

Definition Classes: SymTriMatrixD → MatriD

def /(x: Double): SymTriMatrixD

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

x: the scalar to divide by

Definition Classes: SymTriMatrixD → MatriD

def /=(x: Double): SymTriMatrixD

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

x: the scalar to divide by

Definition Classes: SymTriMatrixD → MatriD

def :+(u: VectoD): SymTriMatrixD

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: SymTriMatrixD → MatriD

def :^+(u: VectoD): SymTriMatrixD

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: SymTriMatrixD → MatriD

final def ==(arg0: Any): Boolean

Definition Classes: AnyRef → Any

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

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

Get a slice 'this' tridiagonal 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: SymTriMatrixD → MatriD

def apply(i: Int): VectorD

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

i: the row index

Definition Classes: SymTriMatrixD → MatriD

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

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

i: the row index
j: the column index

Definition Classes: SymTriMatrixD → MatriD

def apply(iv: VectoI): MatriD

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

iv: the vector of row indices

Definition Classes: MatriD

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

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: MatriD

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

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: MatriD

final def asInstanceOf[T0]: T0

Definition Classes: Any

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

Get 'this' tridiagonal matrix's element at the 'i,j'-th index position, returning 0, if off tridiagonal.

i: the row index
j: the column index

def bsolve(y: VectoD): VectorD

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: SymTriMatrixD → MatriD

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

Clean values in 'this' tridiagonal matrix at or below the threshold by setting them to zero.

Clean values in 'this' tridiagonal 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: SymTriMatrixD → MatriD

def clone(): AnyRef

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

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

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

col: the column to extract from the matrix
from: the position to start extracting from

Definition Classes: SymTriMatrixD → MatriD

def copy(): SymTriMatrixD

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

Definition Classes: SymTriMatrixD → MatriD

val d1: Int

def det: Double

Compute the determinant of 'this' tridiagonal matrix.

Definition Classes: SymTriMatrixD → MatriD

def dg: VectorD

Get the diagonal of 'this' tridiagonal matrix.

def dg_(v: VectorD): Unit

Set the diagonal of 'this' tridiagonal matrix.

v: the vector to assign to the diagonal

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

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: SymTriMatrixD → MatriD

def diag(b: MatriD): MatriD

Combine 'this' tridiagonal 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' tridiagonal matrix

Definition Classes: SymTriMatrixD → MatriD

lazy val dim1: Int

Dimension 1

Definition Classes: SymTriMatrixD → MatriD

lazy val dim2: Int

Dimension 2

Definition Classes: SymTriMatrixD → MatriD

def dot(b: MatriD): VectorD

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

b: the second matrix of the dot product

Definition Classes: SymTriMatrixD → MatriD

def dot(b: SymTriMatrixD): VectorD

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

b: the second matrix of the dot product

def dot(u: VectoD): VectorD

Compute the dot product of 'this' tridiagonal matrix and vector 'u', by first transposing 'this' tridiagonal matrix and then multiplying by 'u' (i.e., 'a dot u = a.t * u').

Compute the dot product of 'this' tridiagonal matrix and vector 'u', by first transposing 'this' tridiagonal matrix and then multiplying by 'u' (i.e., 'a dot u = a.t * u'). Since 'this' is symmetric, the result is the same as 'a * u'.

u: the vector to multiply by (requires same first dimensions)

Definition Classes: SymTriMatrixD → MatriD

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: MatriD

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[Double]) ⇒ U): Unit

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

f: the function to apply

Definition Classes: MatriD

final def getClass(): Class[_]

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

def getDiag(k: Int = 0): VectorD

Get the 'k'th diagonal of 'this' tridiagonal matrix.

Get the 'k'th diagonal of 'this' tridiagonal matrix. Assumes 'dim2 >= dim1'.

k: how far above the main diagonal, e.g., (-1, 0, 1) for (sub, main, super)

Definition Classes: SymTriMatrixD → MatriD

def hashCode(): Int

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

def inverse: MatriD

Invert 'this' tridiagonal matrix.

Definition Classes: SymTriMatrixD → MatriD
See also: www.amm.shu.edu.cn/EN/article/downloadArticleFile.do?attachType=PDF&id=4339

def inverse_ip(): SymTriMatrixD

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

Definition Classes: SymTriMatrixD → MatriD

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: MatriD

final def isInstanceOf[T0]: Boolean

Definition Classes: Any

def isNonnegative: Boolean

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

Definition Classes: SymTriMatrixD → MatriD

def isRectangular: Boolean

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

Definition Classes: SymTriMatrixD → MatriD

def isSquare: Boolean

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

Definition Classes: MatriD

def isSymmetric: Boolean

Check whether 'this' tridiagonal matrix is symmetric.

Definition Classes: SymTriMatrixD → MatriD

def isTridiagonal: Boolean

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

Check whether 'this' tridiagonal matrix is bidiagonal (has non-zero elements only in main diagonal and super-diagonal). The method may be overriding for efficiency.

Definition Classes: SymTriMatrixD → MatriD

def leDimensions(b: MatriD): 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: MatriD

def lowerT: SymTriMatrixD

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

Definition Classes: SymTriMatrixD → MatriD

def lud_ip(): (MatriD, MatriD)

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

Definition Classes: SymTriMatrixD → MatriD

def lud_npp: (MatriD, MatriD)

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

Factor 'this' tridiagonal matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Factorization algorithm. 'l' is lower bidiagonal and 'u' is upper bidiagonal. FIX: would be more efficient to use tridiagonal matrices than dense matrices.

Definition Classes: SymTriMatrixD → MatriD
See also: www.webpages.uidaho.edu/~barannyk/Teaching/LU_factorization_tridiagonal.pdf

def mag: Double

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

Definition Classes: MatriD

def map(f: (VectoD) ⇒ VectoD): MatriD

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: MatriD

def max(e: Int = dim1): Double

Find the maximum element in 'this' tridiagonal matrix.

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

Definition Classes: SymTriMatrixD → MatriD

def mdot(b: MatriD): MatrixD

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: SymTriMatrixD → MatriD

def mdot(b: SymTriMatrixD): MatrixD

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: VectoD

Compute the column means of 'this' matrix.

Definition Classes: MatriD

def meanNZ: VectoD

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: MatriD

def meanR: VectoD

Compute the row means of 'this' matrix.

Definition Classes: MatriD

def meanRNZ: VectoD

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: MatriD

def min(e: Int = dim1): Double

Find the minimum element in 'this' tridiagonal matrix.

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

Definition Classes: SymTriMatrixD → MatriD

final def ne(arg0: AnyRef): Boolean

Definition Classes: AnyRef

def norm1: Double

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

def normF: Double

Compute the Frobenius-norm of 'this' matrix, i.e., the sum of the absolute values squared of all the elements.

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

def normINF: Double

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

Definition Classes: MatriD
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: VectorD

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: SymTriMatrixD → MatriD
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(): VectorD

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: SymTriMatrixD → MatriD
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: MatriD

val range2: Range

Range for the storage array on dimension 2 (columns)

Definition Classes: MatriD

def reduce: SymTriMatrixD

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: SymTriMatrixD → MatriD

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: SymTriMatrixD → MatriD

def sameCrossDimensions(b: MatriD): Boolean

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

b: the other matrix

Definition Classes: MatriD

def sameDimensions(b: MatriD): Boolean

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

b: the other matrix

Definition Classes: MatriD

def sd: VectorD

Get the sub-diagonal of 'this' tridiagonal matrix.

def sd_(v: VectorD): Unit

Set the sub-diagonal of 'this' tridiagonal matrix.

v: the vector to assign to the sub-diagonal

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

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

Select columns from 'this' tridiagonal 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: SymTriMatrixD → MatriD

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

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

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

Definition Classes: SymTriMatrixD → MatriD

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

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

rowIndex: the row indices to exclude

Definition Classes: MatriD

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

Set 'this' tridiagonal 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: SymTriMatrixD → MatriD

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

Set all the values in 'this' tridiagonal matrix as copies of the values in 2D array 'u'.

Set all the values in 'this' tridiagonal matrix as copies of the values in 2D array 'u'. Ignore parts of array not corresponding to tridiagonal.

u: the 2D array of values to assign

Definition Classes: SymTriMatrixD → MatriD

def set(x: Double): Unit

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

x: the scalar value to assign

Definition Classes: SymTriMatrixD → MatriD

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

Set column 'col' of 'this' tridiagonal matrix to a vector.

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

Definition Classes: SymTriMatrixD → MatriD

def setDiag(x: Double): Unit

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

Set the main diagonal of 'this' tridiagonal matrix to the scalar 'x'. Assumes 'dim2 >= dim1'.

x: the scalar to set the diagonal to

Definition Classes: SymTriMatrixD → MatriD

def setDiag(u: VectoD, k: Int = 0): Unit

Set the 'k'th diagonal of 'this' tridiagonal matrix to the vector 'u'.

Set the 'k'th diagonal of 'this' tridiagonal 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: SymTriMatrixD → MatriD

def setFormat(newFormat: String): Unit

Set the format to the 'newFormat'.

newFormat: the new format string

Definition Classes: MatriD

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

Slice 'this' tridiagonal 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: SymTriMatrixD → MatriD

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

Slice 'this' tridiagonal matrix row-wise 'from' to 'end'.

from: the start row of the slice (inclusive)
end: the end row of the slice (exclusive)

Definition Classes: SymTriMatrixD → MatriD

def slice(rg: Range): MatriD

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

rg: the range specifying the slice

Definition Classes: MatriD

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

Slice 'this' tridiagonal matrix column-wise 'from' to 'end'.

from: the start column of the slice (inclusive)
end: the end column of the slice (exclusive)

Definition Classes: SymTriMatrixD → MatriD

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

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

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

Definition Classes: SymTriMatrixD → MatriD

def sliceEx(rg: Range): MatriD

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

rg: the excluded range of the slice

Definition Classes: MatriD

def solve(b: VectoD): VectoD

Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' tridiagonal matrix, using the Thomas Algorithm.

Solve for 'x' in the equation 'a*x = b' where 'a' is 'this' tridiagonal matrix, using the Thomas Algorithm. Caveat: Stability vs. diagonal dominance. This method is more efficient, since a 'lud_npp' creates dense matrices.

b: the constant vector

Definition Classes: SymTriMatrixD → MatriD
See also: en.wikibooks.org/wiki/Algorithm_Implementation/Linear_Algebra/Tridiagonal_matrix_algorithm

def solve(l: MatriD, u: MatriD, b: VectoD): VectoD

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

l: the lower triangular matrix
u: the upper triangular matrix
b: the constant vector

Definition Classes: SymTriMatrixD → MatriD

def solve(lu: (MatriD, MatriD), b: VectoD): VectoD

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: MatriD

def sum: Double

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

Definition Classes: SymTriMatrixD → MatriD

def sumAbs: Double

Compute the 'abs' sum of 'this' tridiagonal matrix, i.e., the sum of the absolute value of its elements.

Compute the 'abs' sum of 'this' tridiagonal matrix, i.e., the sum of the absolute value of its elements. This is useful for comparing matrices '(a - b).sumAbs'.

Definition Classes: SymTriMatrixD → MatriD

def sumLower: Double

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

Definition Classes: SymTriMatrixD → MatriD

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: MatriD

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: MatriD

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

Definition Classes: AnyRef

def t: SymTriMatrixD

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

Transpose 'this' tridiagonal matrix (rows => columns). Note, since the matrix is symmetric, it returns itself.

Definition Classes: SymTriMatrixD → MatriD

def toDense: MatrixD

Convert 'this' tridiagonal matrix to a dense matrix.

Definition Classes: SymTriMatrixD → MatriD

def toInt: SymTriMatrixI

Convert 'this' SymTriMatrixD into a SymTriMatrixI.

Definition Classes: SymTriMatrixD → MatriD

def toString(): String

Convert 'this' tridiagonal matrix to a string showing the diagonal vector followed by the sub-diagonal vector.

Definition Classes: SymTriMatrixD → AnyRef → Any

def trace: Double

Compute the trace of 'this' tridiagonal matrix, i.e., the sum of the elements on the main diagonal.

Compute the trace of 'this' tridiagonal matrix, i.e., the sum of the elements on the main diagonal. Should also equal the sum of the eigenvalues.

Definition Classes: SymTriMatrixD → MatriD
See also: Eigen.scala

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

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

Set a slice 'this' tridiagonal 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: SymTriMatrixD → MatriD

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

Set 'this' tridiagonal 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: SymTriMatrixD → MatriD

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

Set 'this' tridiagonal 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: SymTriMatrixD → MatriD

def update(i: Int, jr: Range, u: VectoD): 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: MatriD

def update(ir: Range, j: Int, u: VectoD): 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: MatriD

def upperT: SymTriMatrixD

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

Definition Classes: SymTriMatrixD → MatriD

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

fileName: the name of file to hold the data

Definition Classes: SymTriMatrixD → MatriD

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

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

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

Definition Classes: SymTriMatrixD → MatriD

def ~^(p: Int): SymTriMatrixD

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

p: the power to raise this tridiagonal matrix to

Definition Classes: SymTriMatrixD → MatriD

Packages

SymTriMatrixD

Companion object SymTriMatrixD

class SymTriMatrixD extends MatriD with Error with Serializable

Instance Constructors

Value Members

Inherited from Serializable

Inherited from Serializable

Inherited from MatriD

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped

Packages

SymTriMatrixD 

Companion object SymTriMatrixD

class SymTriMatrixD extends MatriD with Error with Serializable

Instance Constructors

Value Members

Inherited from Serializable

Inherited from Serializable

Inherited from MatriD

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped

SymTriMatrixD