/* nag_ztrsyl (f08qvc) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include #include #include #include int main(void) { /* Scalars */ Complex alpha, beta; Integer i, j, m, n, pda, pdb, pdc, pdd, pde, pdf; Integer exit_status = 0; double norm, scale; NagError fail; Nag_OrderType order; Nag_SignType sign = Nag_Minus; /* Arrays */ Complex *a = 0, *b = 0, *c = 0, *d = 0, *e = 0, *f = 0; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J-1)*pda + I - 1] #define B(I, J) b[(J-1)*pdb + I - 1] #define C(I, J) c[(J-1)*pdc + I - 1] #define D(I, J) c[(J-1)*pdd + I - 1] #define E(I, J) c[(J-1)*pde + I - 1] #define F(I, J) c[(J-1)*pdf + I - 1] order = Nag_ColMajor; #else #define A(I, J) a[(I-1)*pda + J - 1] #define B(I, J) b[(I-1)*pdb + J - 1] #define C(I, J) c[(I-1)*pdc + J - 1] #define D(I, J) d[(I-1)*pdd + J - 1] #define E(I, J) e[(I-1)*pde + J - 1] #define F(I, J) f[(I-1)*pdf + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_ztrsyl (f08qvc) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n] "); scanf("%ld%ld%*[^\n] ", &m, &n); #ifdef NAG_COLUMN_MAJOR pda = m; pdb = n; pdc = m; pdd = m; pde = m; pdf = m; #else pda = m; pdb = n; pdc = n; pdd = n; pde = n; pdf = n; #endif /* Allocate memory */ if (!(a = NAG_ALLOC(m * m, Complex)) || !(b = NAG_ALLOC(n * m, Complex)) || !(c = NAG_ALLOC(m * n, Complex)) || !(d = NAG_ALLOC(m * n, Complex)) || !(e = NAG_ALLOC(m * n, Complex)) || !(f = NAG_ALLOC(m * n, Complex)) ) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read A, B and C from data file */ for (i = 1; i <= m; ++i) { for (j = 1; j <= m; ++j) scanf(" ( %lf , %lf ) ", &A(i, j).re, &A(i, j).im); } scanf("%*[^\n] "); for (i = 1; i <= n; ++i) { for (j = 1; j <= n; ++j) scanf(" ( %lf , %lf ) ", &B(i, j).re, &B(i, j).im); } scanf("%*[^\n] "); for (i = 1; i <= m; ++i) { for (j = 1; j <= n; ++j) scanf(" ( %lf , %lf ) ", &C(i, j).re, &C(i, j).im); } scanf("%*[^\n] "); /* Copy C into F */ for(i = 1; i <= m; i++) { for(j = 1; j <= m; j++) { F(i, j).re = C(i, j).re; F(i, j).im = C(i, j).im; } } /* nag_gen_complx_mat_print_comp (x04dbc): Print matrix C */ fflush(stdout); nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, c, pdc, Nag_BracketForm, "%7.4f", "Matrix C", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); printf("\n"); if (fail.code != NE_NOERROR) { printf( "Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Reorder the Schur factorization T */ /* nag_ztrsyl (f08qvc). * Solve complex Sylvester matrix equation AX + XB = C, A * and B are upper triangular or conjugate-transposes */ nag_ztrsyl(order, Nag_NoTrans, Nag_NoTrans, sign, m, n, a, pda, b, pdb, c, pdc, &scale, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_ztrsyl (f08qvc).\n%s\n", fail.message); exit_status = 1; goto END; } /* nag_zgemm (f16zac): Compute aC - (A*X + X*B*sign) from the solution */ /* and store in matrix E*/ alpha.re = 1.0; alpha.im = 0.0; beta.re = 0.0; beta.im = 0.0; nag_zgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, m, alpha, a, pda, c, pdc, beta, d, pdd, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zgemm (f16zac).\n%s\n", fail.message); exit_status = 1; goto END; } if(sign == Nag_Minus) alpha.re = -1.0; else alpha.re = 1.0; beta.re = 1.0; nag_zgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, n, alpha, c, pdc, b, pdb, beta, d, pdd, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_zgemm (f16zac).\n%s\n", fail.message); exit_status = 1; goto END; } for(i = 1; i <= m; i++) { for(j = 1; j <= n; j++) { E(i, j).re = scale * F(i, j).re - D(i, j).re; E(i, j).im = scale * F(i, j).im - D(i, j).im; } } /* nag_zge_norm (f16uac): Find norm of matrix E and print warning if */ /* it is too large */ nag_zge_norm(order, Nag_OneNorm, m, n, e, pde, &norm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message); exit_status = 1; goto END; } if (norm > pow(x02ajc(),0.8)) { printf("%s\n%s\n","Norm of aC - (A*X + X*B*sign) is much greater than 0.", "Schur factorization has failed."); } else { printf(" SCALE = %11.2e\n", scale); } END: if (a) NAG_FREE(a); if (b) NAG_FREE(b); if (c) NAG_FREE(c); if (d) NAG_FREE(d); if (e) NAG_FREE(e); if (f) NAG_FREE(f); return exit_status; }