/* nag_dgelss (f08kac) Example Program. * * Copyright 2011 Numerical Algorithms Group. * * Mark 23, 2011. */ #include #include #include #include #include int main(void) { /* Scalars */ double rcond, rnorm; Integer exit_status = 0, i, j, m, n, nrhs, rank, pda, pdb; /* Arrays */ double *a = 0, *b = 0, *s = 0; /* Nag Types */ NagError fail; Nag_OrderType order; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J - 1) * pda + I - 1] #define B(I, J) b[(J - 1) * pdb + 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] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dgelss (f08kac) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n]"); scanf("%ld%ld%ld%*[^\n]", &m, &n, &nrhs); if (m < 0 || n < 0 || nrhs < 0) { printf("Invalid m, n or nrhs\n"); exit_status = 1; goto END; } #ifdef NAG_COLUMN_MAJOR pda = m; pdb = m; #else pda = n; pdb = nrhs; #endif /* Allocate memory */ if (!(a = NAG_ALLOC(m * n, double)) || !(b = NAG_ALLOC(MAX(m, n) * nrhs, double)) || !(s = NAG_ALLOC(MIN(m, n), double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read A and B from data file */ for (i = 1; i <= m; ++i) for (j = 1; j <= n; ++j) scanf("%lf", &A(i, j)); scanf("%*[^\n]"); for (i = 1; i <= m; ++i) for (j = 1; j <= nrhs; ++j) scanf("%lf", &B(i, j)); scanf("%*[^\n]"); /* Choose rcond to reflect the relative accuracy of the input data */ rcond = 0.01; /* Solve the least squares problem min( norm2(b - Ax) ) for the x * of minimum norm using nag_dgelss (f08kac). */ nag_dgelss(order, m, n, nrhs, a, pda, b, pdb, s, rcond, &rank, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dgelss (f08kac).\n%s\n", fail.message); exit_status = 1; goto END; } printf("Least squares solution\n"); for (i = 1; i <= n; ++i) { for (j = 1; j <= nrhs; ++j) printf(" %10.4f%s", B(i, j), j%7==0?"\n":""); printf("\n"); } /* Print the effective rank of A */ printf("\nTolerance used to estimate the rank of A\n%11.2e\n", rcond); printf("\nEstimated rank of A\n%6ld\n", rank); /* Print singular values of A */ printf("\nSingular values of A\n"); for (i = 0; i < n; ++i) printf(" %10.4f%s", s[i], i%7 == 6?"\n":""); printf("\n"); /* Compute and print estimate of the square root of the * residual sum of squares using nag_dge_norm (f16rac). */ if (rank == n) { nag_dge_norm(order, Nag_FrobeniusNorm, m - n, 1, &B(n+1,1), pdb, &rnorm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message); exit_status = 1; goto END; } printf("\nSquare root of the residual sum of squares\n%11.2e\n", rnorm); } END: if (a) NAG_FREE(a); if (b) NAG_FREE(b); if (s) NAG_FREE(s); return exit_status; } #undef A #undef B