final def !=(arg0: Any): Boolean

Definition Classes: AnyRef → Any

final def ##(): Int

Definition Classes: AnyRef → Any

def *(x: Int): SymTriMatrixI

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

x: the scalar to multiply by

Definition Classes: SymTriMatrixI → MatriI

def *(u: VectoI): VectorI

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

u: the vector to multiply by

Definition Classes: SymTriMatrixI → MatriI

def *(b: SymTriMatrixI): MatrixI

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

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

b: the matrix to multiply by

def *(b: MatriI): SymTriMatrixI

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

b: the matrix to multiply by

Definition Classes: SymTriMatrixI → MatriI

def **(u: VectoI): MatrixI

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: SymTriMatrixI → MatriI

def **:(u: VectoI): MatrixI

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: SymTriMatrixI → MatriI

def **=(u: VectoI): MatrixI

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: SymTriMatrixI → MatriI

def *:(u: VectoI): VectoI

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: MatriI

def *=(x: Int): SymTriMatrixI

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

x: the scalar to multiply by

Definition Classes: SymTriMatrixI → MatriI

def *=(b: MatriI): SymTriMatrixI

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

b: the matrix to multiply by

Definition Classes: SymTriMatrixI → MatriI

def +(x: Int): SymTriMatrixI

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

x: the scalar to add

Definition Classes: SymTriMatrixI → MatriI

def +(u: VectoI): MatrixI

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

u: the vector to add

Definition Classes: SymTriMatrixI → MatriI

def +(b: MatriI): SymTriMatrixI

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

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

Definition Classes: SymTriMatrixI → MatriI

def ++(b: MatriI): SymTriMatrixI

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

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

Definition Classes: SymTriMatrixI → MatriI

def ++^(b: MatriI): SymTriMatrixI

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

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

Definition Classes: SymTriMatrixI → MatriI

def +:(u: VectoI): SymTriMatrixI

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: SymTriMatrixI → MatriI

def +=(x: Int): SymTriMatrixI

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

x: the scalar to add

Definition Classes: SymTriMatrixI → MatriI

def +=(u: VectoI): MatrixI

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

u: the vector to add

Definition Classes: SymTriMatrixI → MatriI

def +=(b: MatriI): SymTriMatrixI

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

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

Definition Classes: SymTriMatrixI → MatriI

def +^:(u: VectoI): SymTriMatrixI

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: SymTriMatrixI → MatriI

def -(x: Int): SymTriMatrixI

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

x: the scalar to subtract

Definition Classes: SymTriMatrixI → MatriI

def -(u: VectoI): MatrixI

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

u: the vector to subtract

Definition Classes: SymTriMatrixI → MatriI

def -(b: MatriI): SymTriMatrixI

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

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

Definition Classes: SymTriMatrixI → MatriI

def -=(x: Int): SymTriMatrixI

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

x: the scalar to subtract

Definition Classes: SymTriMatrixI → MatriI

def -=(u: VectoI): MatrixI

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

u: the vector to subtract

Definition Classes: SymTriMatrixI → MatriI

def -=(b: MatriI): SymTriMatrixI

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

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

Definition Classes: SymTriMatrixI → MatriI

def /(x: Int): SymTriMatrixI

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

x: the scalar to divide by

Definition Classes: SymTriMatrixI → MatriI

def /=(x: Int): SymTriMatrixI

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

x: the scalar to divide by

Definition Classes: SymTriMatrixI → MatriI

def :+(u: VectoI): SymTriMatrixI

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: SymTriMatrixI → MatriI

def :^+(u: VectoI): SymTriMatrixI

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: SymTriMatrixI → MatriI

final def ==(arg0: Any): Boolean

Definition Classes: AnyRef → Any

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

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: SymTriMatrixI → MatriI

def apply(i: Int): VectorI

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

i: the row index

Definition Classes: SymTriMatrixI → MatriI

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

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

i: the row index
j: the column index

Definition Classes: SymTriMatrixI → MatriI

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

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: MatriI

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

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: MatriI

final def asInstanceOf[T0]: T0

Definition Classes: Any

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

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: VectoI): VectorI

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: SymTriMatrixI → MatriI

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

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: SymTriMatrixI → MatriI

def clone(): AnyRef

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

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

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: SymTriMatrixI → MatriI

def copy(): SymTriMatrixI

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

Definition Classes: SymTriMatrixI → MatriI

val d1: Int

def det: Int

Compute the determinant of 'this' tridiagonal matrix.

Definition Classes: SymTriMatrixI → MatriI

def dg: VectorI

Get the diagonal of 'this' tridiagonal matrix.

def dg_(v: VectorI): Unit

Set the diagonal of 'this' tridiagonal matrix.

v: the vector to assign to the diagonal

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

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: SymTriMatrixI → MatriI

def diag(b: MatriI): MatriI

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: SymTriMatrixI → MatriI

lazy val dim1: Int

Dimension 1

Definition Classes: SymTriMatrixI → MatriI

lazy val dim2: Int

Dimension 2

Definition Classes: SymTriMatrixI → MatriI

def dot(b: MatriI): VectorI

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

b: the second matrix of the dot product

Definition Classes: SymTriMatrixI → MatriI

def dot(b: SymTriMatrixI): VectorI

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: VectoI): VectorI

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: SymTriMatrixI → MatriI

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: MatriI

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[Int]) ⇒ U): Unit

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

f: the function to apply

Definition Classes: MatriI

final def getClass(): Class[_]

Definition Classes: AnyRef → Any

def getDiag(k: Int = 0): VectorI

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: SymTriMatrixI → MatriI

def hashCode(): Int

Definition Classes: AnyRef → Any

def inverse: MatriI

Invert 'this' tridiagonal matrix.

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

def inverse_ip(): SymTriMatrixI

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

Definition Classes: SymTriMatrixI → MatriI

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: MatriI

final def isInstanceOf[T0]: Boolean

Definition Classes: Any

def isNonnegative: Boolean

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

Definition Classes: SymTriMatrixI → MatriI

def isRectangular: Boolean

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

Definition Classes: SymTriMatrixI → MatriI

def isSquare: Boolean

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

Definition Classes: MatriI

def isSymmetric: Boolean

Check whether 'this' tridiagonal matrix is symmetric.

Definition Classes: SymTriMatrixI → MatriI

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: SymTriMatrixI → MatriI

def leDimensions(b: MatriI): 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: MatriI

def lowerT: SymTriMatrixI

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

Definition Classes: SymTriMatrixI → MatriI

def lud_ip(): (MatriI, MatriI)

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

Definition Classes: SymTriMatrixI → MatriI

def lud_npp: (MatriI, MatriI)

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: SymTriMatrixI → MatriI
See also: www.webpages.uidaho.edu/~barannyk/Teaching/LU_factorization_tridiagonal.pdf

def mag: Int

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

Definition Classes: MatriI

def max(e: Int = dim1): Int

Find the maximum element in 'this' tridiagonal matrix.

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

Definition Classes: SymTriMatrixI → MatriI

def mdot(b: MatriI): MatrixI

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: SymTriMatrixI → MatriI

def mdot(b: SymTriMatrixI): MatrixI

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: VectoI

Compute the column means of this matrix.

Definition Classes: MatriI

def min(e: Int = dim1): Int

Find the minimum element in 'this' tridiagonal matrix.

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

Definition Classes: SymTriMatrixI → MatriI

final def ne(arg0: AnyRef): Boolean

Definition Classes: AnyRef

def norm1: Int

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: MatriI

final def notify(): Unit

Definition Classes: AnyRef

final def notifyAll(): Unit

Definition Classes: AnyRef

def nullspace: VectorI

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: SymTriMatrixI → MatriI
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(): VectorI

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: SymTriMatrixI → MatriI
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: MatriI

val range2: Range

Range for the storage array on dimension 2 (columns)

Definition Classes: MatriI

def reduce: SymTriMatrixI

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: SymTriMatrixI → MatriI

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: SymTriMatrixI → MatriI

def sameCrossDimensions(b: MatriI): Boolean

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

b: the other matrix

Definition Classes: MatriI

def sameDimensions(b: MatriI): Boolean

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

b: the other matrix

Definition Classes: MatriI

def sd: VectorI

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

def sd_(v: VectorI): Unit

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

v: the vector to assign to the sub-diagonal

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

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: SymTriMatrixI → MatriI

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

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

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

Definition Classes: SymTriMatrixI → MatriI

def set(i: Int, u: VectoI, 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: SymTriMatrixI → MatriI

def set(u: Array[Array[Int]]): 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: SymTriMatrixI → MatriI

def set(x: Int): Unit

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

x: the scalar value to assign

Definition Classes: SymTriMatrixI → MatriI

def setCol(col: Int, u: VectoI): 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: SymTriMatrixI → MatriI

def setDiag(x: Int): 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: SymTriMatrixI → MatriI

def setDiag(u: VectoI, 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: SymTriMatrixI → MatriI

def setFormat(newFormat: String): Unit

Set the format to the 'newFormat'.

newFormat: the new format string

Definition Classes: MatriI

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

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: SymTriMatrixI → MatriI

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

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: SymTriMatrixI → MatriI

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

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: SymTriMatrixI → MatriI

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

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

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

Definition Classes: SymTriMatrixI → MatriI

def solve(b: VectoI): VectoI

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: SymTriMatrixI → MatriI
See also: en.wikibooks.org/wiki/Algorithm_Implementation/Linear_Algebra/Tridiagonal_matrix_algorithm

def solve(l: MatriI, u: MatriI, b: VectoI): VectoI

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: SymTriMatrixI → MatriI

def solve(lu: (MatriI, MatriI), b: VectoI): VectoI

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: MatriI

def sum: Int

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

Definition Classes: SymTriMatrixI → MatriI

def sumAbs: Int

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: SymTriMatrixI → MatriI

def sumLower: Int

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

Definition Classes: SymTriMatrixI → MatriI

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: MatriI

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: MatriI

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

Definition Classes: AnyRef

def t: SymTriMatrixI

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

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

Definition Classes: SymTriMatrixI → MatriI

def toDense: MatrixI

Convert 'this' tridiagonal matrix to a dense matrix.

Definition Classes: SymTriMatrixI → MatriI

def toInt: SymTriMatrixI

Convert 'this' SymTriMatrixI into a SymTriMatrixI.

Definition Classes: SymTriMatrixI → MatriI

def toString(): String

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

Definition Classes: SymTriMatrixI → AnyRef → Any

def trace: Int

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: SymTriMatrixI → MatriI
See also: Eigen.scala

def update(ir: Range, jr: Range, b: MatriI): 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: SymTriMatrixI → MatriI

def update(i: Int, u: VectoI): 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: SymTriMatrixI → MatriI

def update(i: Int, j: Int, x: Int): 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: SymTriMatrixI → MatriI

def update(i: Int, jr: Range, u: VectoI): 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: MatriI

def update(ir: Range, j: Int, u: VectoI): 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: MatriI

def upperT: SymTriMatrixI

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

Definition Classes: SymTriMatrixI → MatriI

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

fileName: the name of file to hold the data

Definition Classes: SymTriMatrixI → MatriI

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

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: SymTriMatrixI → MatriI

def ~^(p: Int): SymTriMatrixI

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: SymTriMatrixI → MatriI

Packages

SymTriMatrixI

Companion object SymTriMatrixI

class SymTriMatrixI extends MatriI with Error with Serializable

Instance Constructors

Value Members

Inherited from Serializable

Inherited from Serializable

Inherited from MatriI

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped

Packages

SymTriMatrixI 

Companion object SymTriMatrixI

class SymTriMatrixI extends MatriI with Error with Serializable

Instance Constructors

Value Members

Inherited from Serializable

Inherited from Serializable

Inherited from MatriI

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped

SymTriMatrixI