$title Simple Gaussian Elimination Steps (PIVOT,SEQ=70) $onText Simple Gaussian Elimination steps are performed on a matrix with identically labeled rows and columns. The implied pivot sequence is 1.1, 2.2, etc. GAMS Development Corporation, Formulation and Language Example. Keywords: Gaussian elimination, mathematics $offText Set i 'matrix labels' / 1*6 / r(i) 'pivot sequence' k(i) 'non pivot rows' l(i) 'non pivot columns'; Alias (i,j); Parameter a(i,j) 'original matrix' b(i,j) 'inverse of a' piv det; a(i,j) = uniform(-.3,0); a(i,i) = 1; r(i) = yes; k(i) = yes; l(j) = yes; b(i,j) = a(i,j); det = 1; loop(r, k(r) = no; l(r) = no; piv = 1/b(r,r); det = det/piv; b(r,l) = b(r,l)*piv; b(k,l) = b(k,l) - b(r,l)*b(k,r); b(k,r) = -b(k,r)*piv; b(r,r) = piv; k(r) = yes; l(r) = yes; ); display det, a, b; Parameter check(i,j); check(i,j) = sum(k, a(i,k)*b(k,j)); display check;