JLCF64LinearAlgebra

jla64.spad line 399 [edit on github]

Linear Algebra functions computed using Julia and its algorithms. 64 bits version.

conditionNumber: (JLComplexF64Matrix, JLFloat64) -> JLFloat64

conditionNumber(m) computes the p-condition number of m.

conditionNumber: JLComplexF64Matrix -> JLFloat64

conditionNumber(m) computes the condition number of m.

condSkeel: JLComplexF64Matrix -> JLFloat64

condSkeel(m) computes the Skeel condition number of m.

eigen!: JLComplexF64Matrix -> Record(values: JLComplexF64Vector, vectors: JLComplexF64Matrix)

eigen!(m) computes the spectral decomposition of m but overwrites m to save memory space.

eigen: JLComplexF64Matrix -> Record(values: JLComplexF64Vector, vectors: JLComplexF64Matrix)

eigen(m) computes the spectral decomposition of m.

eigenSystem!: JLComplexF64Matrix -> Record(values: JLComplexF64Vector, leftVectors: JLComplexF64Matrix, rightVectors: JLComplexF64Matrix)

eigenSystem!(m) computes the spectral decomposition of m but overwrites m to save memory space.

eigenSystem: JLComplexF64Matrix -> Record(values: JLComplexF64Vector, leftVectors: JLComplexF64Matrix, rightVectors: JLComplexF64Matrix)

eigenSystem(m) computes the spectral decomposition of m.

eigvals!: JLComplexF64Matrix -> JLComplexF64Vector

eigvals!(m) returns the eigen values of m but overwrites m to save memory space.

eigvals: JLComplexF64Matrix -> JLComplexF64Vector

eigvals(m) returns the eigen values of m.

eigvecs: JLComplexF64Matrix -> JLComplexF64Matrix

eigvecs(m) returns the eigen vectors of m.

exp: JLComplexF64Matrix -> JLComplexF64Matrix

exp(m) returns the matrix exponential of m.

log: JLComplexF64Matrix -> JLComplexF64Matrix

log(m) tries to compute the principal matrix logarithm of m. Otherwise, returns a non pricipal matrix logarithm of m if possible.

mpInverse: JLComplexF64Matrix -> JLComplexF64Matrix

mpInverse(m) returns the Moore-Penrose pseudo inverse of m.

norm: (JLComplexF64Matrix, JLFloat64) -> JLFloat64

norm(m,p) computes the p-norm of m.

norm: (JLComplexF64Vector, JLFloat64) -> JLFloat64

norm(v,p) computes th p-norm of v.

norm: JLComplexF64Matrix -> JLFloat64

norm(m) computes the 2-norm of m, also known as the Frobenius norm.

norm: JLComplexF64Vector -> JLFloat64

norm(v) computes the 2-norm of v.

normalize!: JLComplexF64Matrix -> JLComplexF64Matrix

normalize!(m) destructively normalize m such that its norm equals to 1.

normalize!: JLComplexF64Vector -> JLComplexF64Vector

normalize!(v) destructively normalize v such that norm(v) equals to 1.

normalize: JLComplexF64Matrix -> JLComplexF64Matrix

normalize(m) returns normalized m such that its norm equals to 1.

normalize: JLComplexF64Vector -> JLComplexF64Vector

normalize(v) returns normalized v such that its norm equals to 1.

operatorNorm: (JLComplexF64Matrix, JLFloat64) -> JLFloat64

operatorNorm(m,p) computes the operator norm of m induced by the vector p-norm.

operatorNorm: JLComplexF64Matrix -> JLFloat64

operatorNorm(m) computes the operator norm of m induced by the vector 2-norm.

rank!: (JLComplexF64Matrix, JLFloat64) -> NonNegativeInteger

rank!(m, tol) computes rank of m. Counts singular value with magnitude greater than tol but overwrites m to save memory space.

rank: (JLComplexF64Matrix, JLFloat64) -> NonNegativeInteger

rank(m, tol) computes rank of m. Counts singular value with magnitude greater than tol.

solve!: (JLComplexF64Matrix, JLComplexF64Matrix) -> JLComplexF64Matrix

solve!(A,B) solves the matrix equation A*X=B. Overwrites B with matrix X and returns X.

solve: (JLComplexF64Matrix, JLComplexF64Matrix) -> JLComplexF64Matrix

solve(A,B) solves the matrix equation A*X=B, and returns X.

sqrt: JLComplexF64Matrix -> JLComplexF64Matrix

sqrt(m) returns the principal square root of m.

svd!: JLComplexF64Matrix -> Record(U: JLComplexF64Matrix, sv: JLFloat64Vector, Vt: JLComplexF64Matrix)

svd!(m) is the same as svd(m) but overwites a to save memory space.

svd: JLComplexF64Matrix -> Record(U: JLComplexF64Matrix, sv: JLFloat64Vector, Vt: JLComplexF64Matrix)

svd(m) computes the singular value decomposition SVD of m such that SVD.U * diagonalMatrix(SVD.sv) * SVD.Vt = m.

svdvals!: JLComplexF64Matrix -> JLFloat64Vector

svdvals!(m) returns the singular values of m but overwrites m to save memory space.

svdvals: JLComplexF64Matrix -> JLFloat64Vector

svdvals(m) returns the singular values of m.