LinearAlgebra

Value Members

final def !=(arg0: AnyRef): Boolean

Definition Classes
AnyRef
final def !=(arg0: Any): Boolean

Definition Classes
Any
final def ##(): Int

Definition Classes
AnyRef → Any
final def ==(arg0: AnyRef): Boolean

Definition Classes
AnyRef
final def ==(arg0: Any): Boolean

Definition Classes
Any
def LU[T](X: Matrix[T])(implicit td: (T) ⇒ Double): (DenseMatrix[Double], Array[Int])

Computes the LU factorization of the given real M-by-N matrix X such that X = P * L * U where P is a permutation matrix (row exchanges).
Computes the LU factorization of the given real M-by-N matrix X such that X = P * L * U where P is a permutation matrix (row exchanges).
Upon completion, a tuple consisting of a matrix A and an integer array P.
The upper triangular portion of A resembles U whereas the lower triangular portion of A resembles L up to but not including the diagonal elements of L which are all equal to 1.
For 0 <= i < M, each element P(i) denotes whether row i of the matrix X was exchanged with row P(i-1) during computation (the offset is caused by the internal call to LAPACK).

Definition Classes
LinearAlgebra
final def asInstanceOf[T0]: T0

Definition Classes
Any
def cholesky(X: Matrix[Double]): DenseMatrix[Double]

Computes the cholesky decomposition A of the given real symmetric positive definite matrix X such that X = A A.
Computes the cholesky decomposition A of the given real symmetric positive definite matrix X such that X = A A.t.
XXX: For higher dimensionalities, the return value really should be a sparse matrix due to its inherent lower triangular nature.

Definition Classes
LinearAlgebra
def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
def cross[V1](a: DenseVector[V1], b: DenseVector[V1])(implicit ring: Ring[V1], man: ClassTag[V1]): DenseVector[V1]

Vector cross product of 3D vectors a and b.
Vector cross product of 3D vectors a and b.

Definition Classes
LinearAlgebra
def det[T](X: Matrix[T])(implicit td: (T) ⇒ Double): Double

Computes the determinant of the given real matrix.
Computes the determinant of the given real matrix.

Definition Classes
LinearAlgebra
def eig(m: Matrix[Double]): (DenseVector[Double], DenseVector[Double], DenseMatrix[Double])

Eigenvalue decomposition (right eigenvectors)
Eigenvalue decomposition (right eigenvectors)
This function returns the real and imaginary parts of the eigenvalues, and the corresponding eigenvectors. For most (?) interesting matrices, the imaginary part of all eigenvalues will be zero (and the corresponding eigenvectors will be real). Any complex eigenvalues will appear in complex-conjugate pairs, and the real and imaginary components of the eigenvector for each pair will be in the corresponding columns of the eigenvector matrix. Take the complex conjugate to find the second eigenvector.
Based on EVD.java from MTJ 0.9.12

Definition Classes
LinearAlgebra
def eigSym(X: Matrix[Double], rightEigenvectors: Boolean): (DenseVector[Double], Option[DenseMatrix[Double]])

Computes all eigenvalues (and optionally right eigenvectors) of the given real symmetric matrix X.
Computes all eigenvalues (and optionally right eigenvectors) of the given real symmetric matrix X.

Definition Classes
LinearAlgebra
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 getClass(): Class[_]

Definition Classes
AnyRef → Any
def hashCode(): Int

Definition Classes
AnyRef → Any
def inv[T](X: Matrix[T])(implicit td: (T) ⇒ Double): DenseMatrix[Double]

Computes the inverse of a given real matrix.
Computes the inverse of a given real matrix.

Definition Classes
LinearAlgebra
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def kron[V1, V2, M, RV](a: DenseMatrix[V1], b: M)(implicit mul: BinaryOp[V1, M, OpMulScalar, DenseMatrix[RV]], asMat: <:<[M, Matrix[V2]], man: ClassTag[RV], dfv: DefaultArrayValue[RV]): DenseMatrix[RV]

Returns the Kronecker product of the two matrices a and b, usually denoted a ⊗ b.
Returns the Kronecker product of the two matrices a and b, usually denoted a ⊗ b.

Definition Classes
LinearAlgebra
def lowerTriangular[T](X: Matrix[T])(implicit arg0: Semiring[T], arg1: ClassTag[T], arg2: DefaultArrayValue[T]): DenseMatrix[T]

The lower triangular portion of the given real quadratic matrix X.
The lower triangular portion of the given real quadratic matrix X. Note that no check will be performed regarding the symmetry of X.

Definition Classes
LinearAlgebra
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
final def notify(): Unit

Definition Classes
AnyRef
final def notifyAll(): Unit

Definition Classes
AnyRef
def pinv[V](X: DenseMatrix[V])(implicit cast: (V) ⇒ Double): DenseMatrix[Double]

Computes the Moore-Penrose pseudo inverse of the given real matrix X.
Computes the Moore-Penrose pseudo inverse of the given real matrix X.

Definition Classes
LinearAlgebra
def pinv(X: DenseMatrix[Double]): DenseMatrix[Double]

Computes the Moore-Penrose pseudo inverse of the given real matrix X.
Computes the Moore-Penrose pseudo inverse of the given real matrix X.

Definition Classes
LinearAlgebra
def pow(m: DenseMatrix[Double], exp: Double): DenseMatrix[Double]

Raises m to the exp'th power via eigenvalue decomposition.
Raises m to the exp'th power via eigenvalue decomposition. Currently requires that m's eigenvalues are real.
m
exp

Definition Classes
LinearAlgebra
def qr(A: DenseMatrix[Double], skipQ: Boolean = false): (DenseMatrix[Double], DenseMatrix[Double])

QR Factorization
QR Factorization
A
m x n matrix
skipQ
(optional) if true, don't reconstruct orthogonal matrix Q (instead returns (null,R))
returns
(Q,R) Q: m x m R: m x n

Definition Classes
LinearAlgebra
def qrp(A: DenseMatrix[Double]): (DenseMatrix[Double], DenseMatrix[Double], DenseMatrix[Int], Array[Int])

QR Factorization with pivoting
QR Factorization with pivoting
input: A m x n matrix output: (Q,R,P,pvt) where AP = QR Q: m x m R: m x n P: n x n : permutation matrix (P(pvt(i),i) = 1) pvt : pivot indices

Definition Classes
LinearAlgebra
def rank(m: DenseMatrix[Double], tol: Option[Double] = None): Int

Computes the rank of a DenseMatrix[Double].
Computes the rank of a DenseMatrix[Double].
The rank of the matrix is computed using the SVD method. The singular values of the SVD which are greater than a specified tolerance are counted.
m
matrix for which to compute the rank
tol
optional tolerance for singular values. If not supplied, the default tolerance is: max(m.cols, m.rows) * eps * sigma_max, where eps is the machine epsilon and sigma_max is the largest singular value of m.
returns
the rank of the matrix (number of singular values)

Definition Classes
LinearAlgebra
def ranks[V](x: Vector[V])(implicit arg0: Ordering[V]): Array[Double]

Returns the rank of each element in the given vector, adjusting for ties.
Returns the rank of each element in the given vector, adjusting for ties.

Definition Classes
LinearAlgebra
def svd(mat: DenseMatrix[Double]): (DenseMatrix[Double], DenseVector[Double], DenseMatrix[Double])

Computes the SVD of a m by n matrix Returns an m*m matrix U, a vector of singular values, and a n*n matrix V'
Computes the SVD of a m by n matrix Returns an m*m matrix U, a vector of singular values, and a n*n matrix V'

Definition Classes
LinearAlgebra
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
def toString(): String

Definition Classes
AnyRef → Any
def upperTriangular[T](X: Matrix[T])(implicit arg0: Semiring[T], arg1: ClassTag[T], arg2: DefaultArrayValue[T]): DenseMatrix[T]

The upper triangular portion of the given real quadratic matrix X.
The upper triangular portion of the given real quadratic matrix X. Note that no check will be performed regarding the symmetry of X.

Definition Classes
LinearAlgebra
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( ... )

object LinearAlgebra extends LinearAlgebra

Value Members

final def !=(arg0: AnyRef): Boolean

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: AnyRef): Boolean

final def ==(arg0: Any): Boolean

def LU[T](X: Matrix[T])(implicit td: (T) ⇒ Double): (DenseMatrix[Double], Array[Int])

final def asInstanceOf[T0]: T0

def cholesky(X: Matrix[Double]): DenseMatrix[Double]

def clone(): AnyRef

def cross[V1](a: DenseVector[V1], b: DenseVector[V1])(implicit ring: Ring[V1], man: ClassTag[V1]): DenseVector[V1]

def det[T](X: Matrix[T])(implicit td: (T) ⇒ Double): Double

def eig(m: Matrix[Double]): (DenseVector[Double], DenseVector[Double], DenseMatrix[Double])

def eigSym(X: Matrix[Double], rightEigenvectors: Boolean): (DenseVector[Double], Option[DenseMatrix[Double]])

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

def finalize(): Unit

final def getClass(): Class[_]

def hashCode(): Int

def inv[T](X: Matrix[T])(implicit td: (T) ⇒ Double): DenseMatrix[Double]

final def isInstanceOf[T0]: Boolean

def kron[V1, V2, M, RV](a: DenseMatrix[V1], b: M)(implicit mul: BinaryOp[V1, M, OpMulScalar, DenseMatrix[RV]], asMat: <:<[M, Matrix[V2]], man: ClassTag[RV], dfv: DefaultArrayValue[RV]): DenseMatrix[RV]

def lowerTriangular[T](X: Matrix[T])(implicit arg0: Semiring[T], arg1: ClassTag[T], arg2: DefaultArrayValue[T]): DenseMatrix[T]

final def ne(arg0: AnyRef): Boolean

final def notify(): Unit

final def notifyAll(): Unit

def pinv[V](X: DenseMatrix[V])(implicit cast: (V) ⇒ Double): DenseMatrix[Double]

def pinv(X: DenseMatrix[Double]): DenseMatrix[Double]

def pow(m: DenseMatrix[Double], exp: Double): DenseMatrix[Double]

def qr(A: DenseMatrix[Double], skipQ: Boolean = false): (DenseMatrix[Double], DenseMatrix[Double])

def qrp(A: DenseMatrix[Double]): (DenseMatrix[Double], DenseMatrix[Double], DenseMatrix[Int], Array[Int])

def rank(m: DenseMatrix[Double], tol: Option[Double] = None): Int

def ranks[V](x: Vector[V])(implicit arg0: Ordering[V]): Array[Double]

def svd(mat: DenseMatrix[Double]): (DenseMatrix[Double], DenseVector[Double], DenseMatrix[Double])

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

def toString(): String

def upperTriangular[T](X: Matrix[T])(implicit arg0: Semiring[T], arg1: ClassTag[T], arg2: DefaultArrayValue[T]): DenseMatrix[T]

final def wait(): Unit

final def wait(arg0: Long, arg1: Int): Unit

final def wait(arg0: Long): Unit

Inherited from LinearAlgebra

Inherited from AnyRef

Inherited from Any

Ungrouped