Operator.Linalgval inv : Symbol.Shape.Type.arr -> Symbol.Shape.Type.arrinv a computes the inverse of the matrix a. Returns a new array representing the inverse matrix.
val logdet : Symbol.Shape.Type.arr -> Symbol.Shape.Type.eltlogdet a computes the natural logarithm of the determinant of the matrix a. Returns the logarithm of the determinant as a scalar.
val chol : ?upper:bool -> Symbol.Shape.Type.arr -> Symbol.Shape.Type.arrchol ?upper a performs the Cholesky decomposition of the positive-definite matrix a.
upper specifies whether to return the upper or lower triangular matrix. If upper is true, returns the upper triangular matrix, otherwise the lower triangular matrix. Returns a new array representing the Cholesky factor.val qr : Symbol.Shape.Type.arr -> Symbol.Shape.Type.arr * Symbol.Shape.Type.arrqr a performs the QR decomposition of the matrix a. Returns a tuple of two arrays (Q, R), where Q is an orthogonal matrix and R is an upper triangular matrix.
val lq : Symbol.Shape.Type.arr -> Symbol.Shape.Type.arr * Symbol.Shape.Type.arrlq a performs the LQ decomposition of the matrix a. Returns a tuple of two arrays (L, Q), where L is a lower triangular matrix and Q is an orthogonal matrix.
val svd :
?thin:bool ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arr * Symbol.Shape.Type.arr * Symbol.Shape.Type.arrsvd ?thin a performs the Singular Value Decomposition (SVD) of the matrix a.
thin specifies whether to return the reduced form of the SVD. Returns a tuple of three arrays (U, S, V), where U and V are orthogonal matrices, and S is a diagonal matrix containing the singular values.val sylvester :
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arrsylvester a b c solves the Sylvester equation A*X + X*B = C for the unknown matrix X. Returns a new array representing the solution matrix X.
val lyapunov :
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arrlyapunov a q solves the continuous Lyapunov equation A*X + X*A^T = Q for the unknown matrix X. Returns a new array representing the solution matrix X.
val discrete_lyapunov :
?solver:[ `default | `bilinear | `direct ] ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arrdiscrete_lyapunov ?solver a q solves the discrete Lyapunov equation A*X*A^T - X + Q = 0 for the unknown matrix X.
solver specifies the method to use: `default`, `bilinear`, or `direct`. Returns a new array representing the solution matrix X.val linsolve :
?trans:bool ->
?typ:[ `n | `u | `l ] ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arrlinsolve ?trans ?typ a b solves the linear system A*X = B for the unknown matrix X.
trans specifies whether to transpose the matrix A.typ specifies the type of matrix A: `n` for normal, `u` for upper triangular, and `l` for lower triangular. Returns a new array representing the solution matrix X.val care :
?diag_r:bool ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arrcare ?diag_r a b q r solves the Continuous-time Algebraic Riccati Equation (CARE) A*X + X*A^T - X*B*R^-1*B^T*X + Q = 0 for the unknown matrix X.
diag_r if true, R is assumed to be diagonal. Returns a new array representing the solution matrix X.val dare :
?diag_r:bool ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arr ->
Symbol.Shape.Type.arrdare ?diag_r a b q r solves the Discrete-time Algebraic Riccati Equation (DARE) A*X*A^T - X - (A*X*B^T)*inv(B*X*B^T + R)*(A*X*B^T)^T + Q = 0 for the unknown matrix X.
diag_r if true, R is assumed to be diagonal. Returns a new array representing the solution matrix X.