acos acosh adaptsimp asin asinh atan atan2 atanh betafn BFGS cbind cbrt ceil chol_solve chol_solve cholesky copy copy_recycle copysign cos cosh crossprod dbeta dbinom dchisq det dexp df dgamma diag dlnorm dlogis dnbinom dnorm dpois dt dt1 dunif dweibull eigen epsilon erf erfc exp expm1 eye fabs factorial floor fmod for_each_ij_set gammafn gaxpy gradfdif gradfdifls hesscdif hypot intsimp inv inv invpd invpd j0 j1 jacfdif jn kronecker kurtosis kurtosisc ldexp lgamma linesearch1 linesearch2 lnbetafn lndbeta1 lndmvn lndnorm lndt1 lnfactorial lngammafn log log10 log1p logb lu_decomp lu_solve lu_solve matrix_order matrix_style max maxc maxind maxindc mean meanc median medianc min minc minind minindc mode modec nls_broyden ones operator! operator!= operator% operator& operator* operator* operator+ operator- operator- operator/ operator< operator<< operator<= operator== operator> operator>= operator>> operator^ operator| order pbeta pbinom pchisq pexp pf pgamma plnorm plogis pnbinom pnorm pow ppois prod prodc pt punif pweibull qnorm1 qr_decomp qr_solve qr_solve rbind rint row_interchange sd sd sdc selif seqa sgn sin sinh skew skewc sort sortc sqrt sum sumc svd t tan tanh unique var var varc vech xpnd y0 y1 yn zoom

template<matrix_order RO, matrix_style RS, typename T , matrix_order PO1, matrix_style PS1, matrix_order PO2, matrix_style PS2, matrix_order PO3, matrix_style PS3, matrix_order PO4, matrix_style PS4, matrix_order PO5, matrix_style PS5> Matrix<T, RO, RS> scythe::lu_solve ( const Matrix< T, PO1, PS1 > &  A, const Matrix< T, PO2, PS2 > &  b, const Matrix< T, PO3, PS3 > &  L, const Matrix< T, PO4, PS4 > &  U, const Matrix< unsigned int, PO5, PS5 > &  perm_vec  ) Solve for x via forward and backward substitution, given the results of a LU decomposition. This function solves the system of equations via forward and backward substitution and LU decomposition. A must be a non-singular square matrix for this method to work. This function requires the actual LU decomposition to be performed ahead of time; by lu_decomp() for example. This function is intended for repeatedly solving systems of equations based on A. That is A stays constant while b varies. Parameters: A Non-singular square Matrix to decompose, passed by reference. b Column vector with as many rows as A. L Lower triangular portion of LU decomposition of A. U Upper triangular portion of LU decomposition of A. perm_vec Permutation vector recording the row-wise permutation of A actually decomposed by the algorithm. See also: lu_solve (Matrix<T,PO1,PS1>, const Matrix<T,PO2,PS2>&) lu_decomp(Matrix<T,PO1,PS1>, Matrix<T,PO2,Concrete>&, Matrix<T,PO3,Concrete>&, Matrix<unsigned int, PO4, Concrete>&) chol_solve(const Matrix<T,PO1,PS1> &, const Matrix<T,PO2,PS2> &) chol_solve(const Matrix<T,PO1,PS1> &, const Matrix<T,PO2,PS2> &, const Matrix<T,PO3,PS3> &) Exceptions: scythe_null_error (Level 1) scythe_dimension_error (Level 1) scythe_conformation_error (Level 1) References scythe::Matrix_base< ORDER, STYLE >::cols(), scythe::Matrix_base< ORDER, STYLE >::isColVector(), scythe::Matrix_base< ORDER, STYLE >::isNull(), scythe::Matrix_base< ORDER, STYLE >::isSquare(), row_interchange(), scythe::Matrix_base< ORDER, STYLE >::rows(), and SCYTHE_CHECK_10. Referenced by nls_broyden().