/**************************************************************************\ MODULE: mat_RR SUMMARY: Defines the class mat_RR. \**************************************************************************/ #include #include NTL_matrix_decl(RR,vec_RR,vec_vec_RR,mat_RR) NTL_io_matrix_decl(RR,vec_RR,vec_vec_RR,mat_RR) NTL_eq_matrix_decl(RR,vec_RR,vec_vec_RR,mat_RR) void add(mat_RR& X, const mat_RR& A, const mat_RR& B); // X = A + B void sub(mat_RR& X, const mat_RR& A, const mat_RR& B); // X = A - B void negate(mat_RR& X, const mat_RR& A); // X = - A void mul(mat_RR& X, const mat_RR& A, const mat_RR& B); // X = A * B void mul(vec_RR& x, const mat_RR& A, const vec_RR& b); // x = A * b void mul(vec_RR& x, const vec_RR& a, const mat_RR& B); // x = a * B void mul(mat_RR& X, const mat_RR& A, const RR& b); void mul(mat_RR& X, const mat_RR& A, double b); // X = A * b void mul(mat_RR& X, const RR& a, const mat_RR& B); void mul(mat_RR& X, double a, const mat_RR& B); // X = a * B void determinant(RR& d, const mat_RR& A); RR determinant(const mat_RR& A); // d = determinant(A) void transpose(mat_RR& X, const mat_RR& A); mat_RR transpose(const mat_RR& A); // X = transpose of A void solve(RR& d, vec_RR& X, const mat_RR& A, const vec_RR& b); // A is an n x n matrix, b is a length n vector. Computes d = // determinant(A). If d != 0, solves x*A = b. void inv(RR& d, mat_RR& X, const mat_RR& A); // A is an n x n matrix. Computes d = determinant(A). If d != 0, // computes X = A^{-1}. void sqr(mat_RR& X, const mat_RR& A); mat_RR sqr(const mat_RR& A); // X = A*A void inv(mat_RR& X, const mat_RR& A); mat_RR inv(const mat_RR& A); // X = A^{-1}; error is raised if A is singular void power(mat_RR& X, const mat_RR& A, const ZZ& e); mat_RR power(const mat_RR& A, const ZZ& e); void power(mat_RR& X, const mat_RR& A, long e); mat_RR power(const mat_RR& A, long e); // X = A^e; e may be negative (in which case A must be nonsingular). void ident(mat_RR& X, long n); mat_RR ident_mat_RR(long n); // X = n x n identity matrix long IsIdent(const mat_RR& A, long n); // test if A is the n x n identity matrix void diag(mat_RR& X, long n, const RR& d); mat_RR diag(long n, const RR& d); // X = n x n diagonal matrix with d on diagonal long IsDiag(const mat_RR& A, long n, const RR& d); // test if X is an n x n diagonal matrix with d on diagonal // miscellaneous: void clear(mat_RR& a); // x = 0 (dimension unchanged) long IsZero(const mat_RR& a); // test if a is the zero matrix (any dimension) // operator notation: mat_RR operator+(const mat_RR& a, const mat_RR& b); mat_RR operator-(const mat_RR& a, const mat_RR& b); mat_RR operator*(const mat_RR& a, const mat_RR& b); mat_RR operator-(const mat_RR& a); // matrix/scalar multiplication: mat_RR operator*(const mat_RR& a, const RR& b); mat_RR operator*(const mat_RR& a, double b); mat_RR operator*(const RR& a, const mat_RR& b); mat_RR operator*(double a, const mat_RR& b); // matrix/vector multiplication: vec_RR operator*(const mat_RR& a, const vec_RR& b); vec_RR operator*(const vec_RR& a, const mat_RR& b); // assignment operator notation: mat_RR& operator+=(mat_RR& x, const mat_RR& a); mat_RR& operator-=(mat_RR& x, const mat_RR& a); mat_RR& operator*=(mat_RR& x, const mat_RR& a); mat_RR& operator*=(mat_RR& x, const RR& a); mat_RR& operator*=(mat_RR& x, double a); vec_RR& operator*=(vec_RR& x, const mat_RR& a);