/**************************************************************************\
MODULE: mat_RR
SUMMARY:
Defines the class mat_RR.
\**************************************************************************/
#include <NTL/matrix.h>
#include <NTL/vec_vec_RR.h>
typedef Mat<RR> mat_RR; // backward compatibility
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);