final def !=(arg0: Any): Boolean

Definition Classes: AnyRef → Any

final def ##(): Int

Definition Classes: AnyRef → Any

def *(x: T): SymTriMatrixN[T]

Multiply this matrix by scalar 'x'.

x: the scalar to multiply by

Definition Classes: SymTriMatrixN → Matrix

def *(u: VectorN[T]): VectorN[T]

Multiply this matrix by vector 'u'.

u: the vector to multiply by

Definition Classes: SymTriMatrixN → Matrix

def *(b: SymTriMatrixN[T]): MatrixN[T]

Multiply this matrix by matrix 'b'.

Multiply this matrix by matrix 'b'. Requires b to have type SymTriMatrixN [T], but returns a more general type of matrix.

b: the matrix to multiply by

def *(b: Matrix[T]): SymTriMatrixN[T]

Multiply this matrix by matrix 'b'.

b: the matrix to multiply by

def **(u: VectorN[T]): SymTriMatrixN[T]

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

u: the vector to multiply by

Definition Classes: SymTriMatrixN → Matrix

def **=(u: VectorN[T]): SymTriMatrixN[T]

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

u: the vector to multiply by

Definition Classes: SymTriMatrixN → Matrix

def *=(x: T): SymTriMatrixN[T]

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

x: the scalar to multiply by

Definition Classes: SymTriMatrixN → Matrix

def *=(b: Matrix[T]): SymTriMatrixN[T]

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

b: the matrix to multiply by

def +(x: T): SymTriMatrixN[T]

Add this matrix and scalar 'x'.

x: the scalar to add

Definition Classes: SymTriMatrixN → Matrix

def +(b: Matrix[T]): SymTriMatrixN[T]

Add this matrix and matrix 'b'.

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

def ++(u: VectorN[T]): SymTriMatrixN[T]

Concatenate this matrix and vector 'u'.

u: the vector to be concatenated as the new last row in matrix

Definition Classes: SymTriMatrixN → Matrix

def +=(x: T): SymTriMatrixN[T]

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

x: the scalar to add

Definition Classes: SymTriMatrixN → Matrix

def +=(b: Matrix[T]): SymTriMatrixN[T]

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

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

def -(x: T): SymTriMatrixN[T]

From this matrix subtract scalar 'x'.

x: the scalar to subtract

Definition Classes: SymTriMatrixN → Matrix

def -(b: Matrix[T]): SymTriMatrixN[T]

From this matrix subtract matrix 'b'.

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

def -=(x: T): SymTriMatrixN[T]

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

x: the scalar to subtract

Definition Classes: SymTriMatrixN → Matrix

def -=(b: Matrix[T]): SymTriMatrixN[T]

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

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

def /(x: T)(implicit fr: Fractional[T]): SymTriMatrixN[T]

Divide this matrix by scalar 'x'.

x: the scalar to divide by

Definition Classes: SymTriMatrixN → Matrix

def /=(x: T)(implicit fr: Fractional[T]): SymTriMatrixN[T]

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

x: the scalar to divide by

Definition Classes: SymTriMatrixN → Matrix

final def ==(arg0: Any): Boolean

Definition Classes: AnyRef → Any

val _0: T

Numeric zero (0)

val _1: T

Numeric one (1)

val _1n: T

Numeric minus one (-1)

def apply(i: Int, jr: Range): VectorN[T]

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: SymTriMatrixN → Matrix

def apply(ir: Range, j: Int): VectorN[T]

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: SymTriMatrixN → Matrix

def apply(ir: Range, jr: Range): SymTriMatrixN[T]

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

Get a slice this matrix row-wise on range 'ir' and column-wise on range 'jr'. Ex: b = a(2..4, 3..5)

ir: the row range
jr: the column range

Definition Classes: SymTriMatrixN → Matrix

def apply(i: Int): VectorN[T]

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

i: the row index

Definition Classes: SymTriMatrixN → Matrix

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

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

i: the row index
j: the column index

Definition Classes: SymTriMatrixN → Matrix

final def asInstanceOf[T0]: T0

Definition Classes: Any

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

Get this matrix's element at the 'i,j'-th index position, returning 0.0 if off tridiagonal.

i: the row index
j: the column index

def clean(thres: T, relative: Boolean = true)(implicit fr: Fractional[T]): SymTriMatrixN[T]

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

Clean values in 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: SymTriMatrixN → Matrix

def clone(): AnyRef

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

def col(col: Int, from: Int = 0): VectorN[T]

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

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

Definition Classes: SymTriMatrixN → Matrix

val d1: Int

def det: T

Compute the determinant of this matrix.

Definition Classes: SymTriMatrixN → Matrix

def dg: VectorN[T]

Get the diagonal of the matrix.

def dg_(v: VectorN[T]): Unit

Set the diagonal of the matrix.

v: the vector to assign to the diagonal

def diag(p: Int, q: Int): SymTriMatrixN[T]

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.

p: the size of identity matrix Ip
q: the size of identity matrix Iq

Definition Classes: SymTriMatrixN → Matrix

def diag(b: Matrix[T]): SymTriMatrixN[T]

lazy val dim1: Int

Dimension 1

Definition Classes: SymTriMatrixN → Matrix

lazy val dim2: Int

Dimension 2

Definition Classes: SymTriMatrixN → Matrix

final def eq(arg0: AnyRef): Boolean

Definition Classes: AnyRef

def equals(arg0: Any): Boolean

Definition Classes: AnyRef → Any

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[T]) ⇒ U): Unit

Iterate over the matrix row by row.

f: the function to apply

Definition Classes: Matrix

final def getClass(): Class[_]

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

def getDiag(k: Int = 0): VectorN[T]

Get the 'k'th diagonal of this matrix.

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

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

Definition Classes: SymTriMatrixN → Matrix

def hashCode(): Int

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

def inverse(implicit fr: Fractional[T]): SymTriMatrixN[T]

Invert this matrix (requires a 'squareMatrix') using partial pivoting.

Definition Classes: SymTriMatrixN → Matrix

def inverse_ip(implicit fr: Fractional[T]): SymTriMatrixN[T]

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

Definition Classes: SymTriMatrixN → Matrix

def inverse_npp(implicit fr: Fractional[T]): SymTriMatrixN[T]

Invert this matrix (requires a 'squareMatrix') not using partial pivoting.

Definition Classes: SymTriMatrixN → Matrix

final def isInstanceOf[T0]: Boolean

Definition Classes: Any

def isNonnegative: Boolean

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

Definition Classes: SymTriMatrixN → Matrix

def isRectangular: Boolean

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

Definition Classes: SymTriMatrixN → Matrix

def isSquare: Boolean

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

Definition Classes: Matrix

def isSymmetric: Boolean

Check whether this matrix is symmetric.

Definition Classes: Matrix

def leDimensions(b: Matrix[T]): Boolean

Check whether this matrix dimensions are less than or equal to 'le' those of the other Matrix.

b: the other matrix

Definition Classes: Matrix

def lud(implicit fr: Fractional[T]): (Matrix[T], Matrix[T])

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

Decompose this matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm. This version uses partial pivoting.

Definition Classes: SymTriMatrixN → Matrix

def lud_ip(implicit fr: Fractional[T]): (Matrix[T], Matrix[T])

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

Decompose in-place this matrix into the product of lower and upper triangular matrices '(l, u)' using the 'LU' Decomposition algorithm. This version uses partial pivoting.

Definition Classes: SymTriMatrixN → Matrix

def mag: T

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

Definition Classes: SymTriMatrixN → Matrix

def max(e: Int = dim1): T

Find the maximum element in this matrix.

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

Definition Classes: SymTriMatrixN → Matrix

def min(e: Int = dim1): T

Find the minimum element in this matrix.

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

Definition Classes: SymTriMatrixN → Matrix

final def ne(arg0: AnyRef): Boolean

Definition Classes: AnyRef

def norm1: T

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: SymTriMatrixN → Matrix

final def notify(): Unit

Definition Classes: AnyRef
Annotations: @native()

final def notifyAll(): Unit

Definition Classes: AnyRef
Annotations: @native()

val nu: Numeric[T]

Import Numeric evidence (gets nu val from superclass)

def nullspace(implicit fr: Fractional[T]): VectorN[T]

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.

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. The nullspace of matrix a is "this vector v times any scalar s", i.e., a*(v*s) = 0. The left nullspace of matrix a is the same as the right nullspace of a.t (a transpose).

Definition Classes: SymTriMatrixN → Matrix

def nullspace_ip(implicit fr: Fractional[T]): VectorN[T]

Compute the (right) nullspace in-place 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.

Compute the (right) nullspace in-place 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. The nullspace of matrix a is "this vector 'v' times any scalar s", i.e., 'a*(v*s) = 0.0'. The left nullspace of matrix 'a' is the same as the right nullspace of a.t (a transpose).

Definition Classes: SymTriMatrixN → Matrix

val range1: Range

Range for the storage array on dimension 1 (rows)

Attributes: protected
Definition Classes: Matrix

val range2: Range

Range for the storage array on dimension 2 (columns)

Attributes: protected
Definition Classes: Matrix

def rank(implicit fr: Fractional[T]): Int

Determine the rank of this 'm-by-n' matrix by taking the upper triangular matrix from the 'LU' Decomposition and counting the number of non-zero diagonal elements.

Determine the rank of this 'm-by-n' matrix by taking the upper triangular matrix from the 'LU' Decomposition and counting the number of non-zero diagonal elements. FIX: should implement in implementing classes.

Definition Classes: Matrix

def reduce(implicit fr: Fractional[T]): SymTriMatrixN[T]

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: SymTriMatrixN → Matrix

def reduce_ip(implicit fr: Fractional[T]): 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: SymTriMatrixN → Matrix

def sameCrossDimensions(b: Matrix[T]): Boolean

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

b: the other matrix

Definition Classes: Matrix

def sameDimensions(b: Matrix[T]): Boolean

Check whether this matrix and the other Matrix have the same dimensions.

b: the other matrix

Definition Classes: Matrix

def sd: VectorN[T]

Get the sub-diagonal of the matrix.

def sd_(v: VectorN[T]): Unit

Set the sub-diagonal of the matrix.

v: the vector to assign to the sub-diagonal

def selectCols(colIndex: Array[Int]): SymTriMatrixN[T]

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

Select columns from this matrix according to the given index/basis. Ex: Can be used to divide a matrix into a basis and a non-basis.

colIndex: the column index positions (e.g., (0, 2, 5))

Definition Classes: SymTriMatrixN → Matrix

def selectRows(rowIndex: Array[Int]): SymTriMatrixN[T]

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

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

Definition Classes: SymTriMatrixN → Matrix

def set(i: Int, u: VectorN[T], j: Int = 0): Unit

Set this matrix's 'i'th row starting at column 'j' to the vector 'u'.

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

Definition Classes: SymTriMatrixN → Matrix

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

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

u: the 2D array of values to assign

Definition Classes: SymTriMatrixN → Matrix

def set(x: T): Unit

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

x: the scalar value to assign

Definition Classes: SymTriMatrixN → Matrix

def setCol(col: Int, u: VectorN[T]): Unit

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

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

Definition Classes: SymTriMatrixN → Matrix

def setDiag(x: T): Unit

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

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

x: the scalar to set the diagonal to

Definition Classes: SymTriMatrixN → Matrix

def setDiag(u: VectorN[T], k: Int = 0): Unit

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

Set the 'k'th diagonal of this matrix to the vector 'u'. Assumes 'dim2 >= dim1'.

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

Definition Classes: SymTriMatrixN → Matrix

def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): SymTriMatrixN[T]

Slice this matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.

r_from: the start of the row slice
r_end: the end of the row slice
c_from: the start of the column slice
c_end: the end of the column slice

Definition Classes: SymTriMatrixN → Matrix

def slice(from: Int, end: Int): SymTriMatrixN[T]

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

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

Definition Classes: SymTriMatrixN → Matrix

def sliceExclude(row: Int, col: Int): SymTriMatrixN[T]

Slice this matrix excluding the given row and column.

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

Definition Classes: SymTriMatrixN → Matrix

def solve(lu: (Matrix[T], Matrix[T]), b: VectorN[T])(implicit fr: Fractional[T]): VectorN[T]

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: SymTriMatrixN → Matrix

def solve(l: Matrix[T], u: Matrix[T], b: VectorN[T])(implicit fr: Fractional[T]): VectorN[T]

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: SymTriMatrixN → Matrix

def solve(d: VectorN[T])(implicit fr: Fractional[T]): VectorN[T]

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

d: the constant vector.

Definition Classes: SymTriMatrixN → Matrix

def sum: T

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

Definition Classes: SymTriMatrixN → Matrix

def sumAbs: T

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

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

Definition Classes: SymTriMatrixN → Matrix

def sumLower: T

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

Definition Classes: SymTriMatrixN → Matrix

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

Definition Classes: AnyRef

def t: SymTriMatrixN[T]

Transpose this matrix (rows => columns).

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

Definition Classes: SymTriMatrixN → Matrix

def toString(): String

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

Definition Classes: SymTriMatrixN → AnyRef → Any

def trace: T

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

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

Definition Classes: SymTriMatrixN → Matrix
See also: Eigen.scala

def update(i: Int, jr: Range, u: VectorN[T]): Unit

Set a slice this matrix row-wise at index 'i' and column-wise on range 'jr'.

Set a slice this matrix row-wise at index 'i' and column-wise on range 'jr'. Ex: a(2, 3..5) = u

i: the row index
jr: the column range
u: the vector to assign

Definition Classes: SymTriMatrixN → Matrix

def update(ir: Range, j: Int, u: VectorN[T]): Unit

Set a slice this matrix row-wise on range 'ir' and column-wise at index 'j'.

Set a slice this matrix row-wise on range 'ir' and column-wise at index 'j'. Ex: a(2..4, 3) = u

ir: the row range
j: the column index
u: the vector to assign

Definition Classes: SymTriMatrixN → Matrix

def update(ir: Range, jr: Range, b: SymTriMatrixN[T]): Unit

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

Set a slice this matrix row-wise on range 'ir' and column-wise on range 'jr'. Ex: a(2..4, 3..5) = b

ir: the row range
jr: the column range
b: the matrix to assign

def update(i: Int, u: VectorN[T]): Unit

Set this matrix's row at the 'i'th index position to the vector 'u'.

i: the row index
u: the vector value to assign

Definition Classes: SymTriMatrixN → Matrix

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

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

Set this matrix's element at the 'i,j'-th index position to the scalar 'x'. Only store x if it is non-zero.

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

Definition Classes: SymTriMatrixN → Matrix

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 ~^(p: Int): SymTriMatrixN[T]

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

p: the power to raise this matrix to

Definition Classes: SymTriMatrixN → Matrix

Packages

SymTriMatrixN

class SymTriMatrixN[T] extends Matrix[T] with Error with Serializable

Instance Constructors

Value Members

Inherited from Serializable

Inherited from Serializable

Inherited from Matrix[T]

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped

Packages

SymTriMatrixN 

class SymTriMatrixN[T] extends Matrix[T] with Error with Serializable

Instance Constructors

Value Members

Inherited from Serializable

Inherited from Serializable

Inherited from Matrix[T]

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped

SymTriMatrixN