/**************************************************************************\MODULE: mat_RRSUMMARY:Defines the class mat_RR.\**************************************************************************/#include <NTL/matrix.h>#include <NTL/vec_vec_RR.h>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 + Bvoid sub(mat_RR& X, const mat_RR& A, const mat_RR& B); // X = A - Bvoid negate(mat_RR& X, const mat_RR& A); // X = - Avoid mul(mat_RR& X, const mat_RR& A, const mat_RR& B); // X = A * Bvoid mul(vec_RR& x, const mat_RR& A, const vec_RR& b); // x = A * bvoid mul(vec_RR& x, const vec_RR& a, const mat_RR& B); // x = a * Bvoid mul(mat_RR& X, const mat_RR& A, const RR& b);void mul(mat_RR& X, const mat_RR& A, double b);// X = A * bvoid mul(mat_RR& X, const RR& a, const mat_RR& B);void mul(mat_RR& X, double a, const mat_RR& B);// X = a * Bvoid 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 Avoid 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*Avoid inv(mat_RR& X, const mat_RR& A);mat_RR inv(const mat_RR& A);// X = A^{-1}; error is raised if A is  singularvoid 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 matrixlong IsIdent(const mat_RR& A, long n);// test if A is the n x n identity matrixvoid 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 diagonallong 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);