/* nag_complex_svd (f02xec) Example Program. * * Copyright 1990 Numerical Algorithms Group. * * Mark 1, 1990. * Mark 8 revised, 2004. */ #include #include #include #include #define COMPLEX(A) A.re, A.im #define COMPLEX_CONJ(A) A.re, -A.im static int ex1(void), ex2(void); int main(void) { Integer exit_status_ex1 = 0; Integer exit_status_ex2 = 0; printf("nag_complex_svd (f02xec) Example Program Results\n"); scanf(" %*[^\n]"); /* Skip heading in data file */ exit_status_ex1 = ex1(); exit_status_ex2 = ex2(); return (exit_status_ex1 == 0 && exit_status_ex2 == 0) ? 0 : 1; } #define A(I, J) a[(I) *tda + J] #define B(I, J) b[(I) *tdb + J] #define PH(I, J) ph[(I) *tdph + J] static int ex1(void) { Nag_Boolean wantp, wantq; Complex *a = 0, *b = 0, *dummy = 0, *ph = 0; Integer exit_status = 0, failinfo, i, iter, j, m, n, ncolb, tda, tdb, tdph; NagError fail; double *e = 0, *sv = 0; INIT_FAIL(fail); printf("Example 1\n\n"); scanf(" %*[^\n]"); /* Skip heading in data file */ if (scanf("%ld%ld", &m, &n) != EOF) { if (m >= 0 && n >= 0) { ncolb = 1; if (!(e = NAG_ALLOC(MIN(m, n)-1, double)) || !(sv = NAG_ALLOC(MIN(m, n), double)) || !(a = NAG_ALLOC(m*n, Complex)) || !(b = NAG_ALLOC(m*ncolb, Complex)) || !(ph = NAG_ALLOC(n*n, Complex)) || !(dummy = NAG_ALLOC(1, Complex))) { printf("Allocation failure\n"); exit_status = -1; goto END; } tda = n; tdb = ncolb; tdph = n; } else { printf("Invalid m or n.\n"); exit_status = 1; return exit_status; } for (i = 0; i < m; ++i) for (j = 0; j < n; ++j) scanf("%lf%lf", COMPLEX(&A(i, j))); for (i = 0; i < m; ++i) for (j = 0; j < ncolb; ++j) scanf("%lf%lf", COMPLEX(&B(i, j))); /* Find the SVD of A. */ wantq = Nag_TRUE; wantp = Nag_TRUE; /* nag_complex_svd (f02xec). * SVD of complex matrix */ nag_complex_svd(m, n, a, tda, ncolb, b, tdb, wantq, dummy, (Integer) 1, sv, wantp, ph, tdph, &iter, e, &failinfo, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_complex_svd (f02xec).\n%s\n", fail.message); exit_status = 1; goto END; } printf("Singular value decomposition of A\n\nSingular values\n"); for (i = 0; i < n; ++i) printf("%9.4f%s", sv[i], (i%5 == 4 || i == n-1)?"\n":" "); printf("\nLeft-hand singular vectors, by column\n"); for (i = 0; i < m; ++i) for (j = 0; j < n; ++j) printf("%7.4f %7.4f%s", COMPLEX(A(i, j)), (j%3 == 2 || j == n-1)?"\n":" "); printf("\nRight-hand singular vectors, by column\n"); for (i = 0; i < n; ++i) for (j = 0; j < n; ++j) printf("%7.4f %7.4f%s", COMPLEX_CONJ(PH(j, i)), (j%3 == 2 || j == n-1)?"\n":" "); printf("\nVector conjg(Q')*B\n"); for (i = 0; i < m; ++i) for (j = 0; j < ncolb; ++j) printf("%7.4f %7.4f%s", COMPLEX(B(i, j)), (i%3 == 2 || i == m-1)?"\n":" "); } END: NAG_FREE(e); NAG_FREE(sv); NAG_FREE(a); NAG_FREE(b); NAG_FREE(ph); NAG_FREE(dummy); return exit_status; } #define A(I, J) a[(I) *tda + J] #define Q(I, J) q[(I) *tdq + J] static int ex2(void) { Nag_Boolean wantp, wantq; Complex *a = 0, *dummy = 0, *q = 0; Integer exit_status = 0, failinfo, i, iter, j, m, n, ncolb, tda, tdq; NagError fail; double *e = 0, *sv = 0; INIT_FAIL(fail); printf("\nExample 2\n\n"); scanf(" %*[^\n]"); /* Skip heading in data file */ if (scanf("%ld%ld", &m, &n) != EOF) { if (m >= 0 && n >= 0) { if (!(e = NAG_ALLOC(MIN(m, n)-1, double)) || !(sv = NAG_ALLOC(MIN(m, n), double)) || !(a = NAG_ALLOC(m*n, Complex)) || !(q = NAG_ALLOC(m*m, Complex)) || !(dummy = NAG_ALLOC(1, Complex))) { printf("Allocation failure\n"); exit_status = -1; goto END; } tda = n; tdq = m; } else { printf("Invalid m or n.\n"); exit_status = 1; return exit_status; } for (i = 0; i < m; ++i) for (j = 0; j < n; ++j) if (scanf("%lf%lf", COMPLEX(&A(i, j))) != 2) { printf("Data input error: program terminated.\n"); exit_status = 1; goto END; } /* Find the SVD of A. */ wantq = Nag_TRUE; wantp = Nag_TRUE; ncolb = 0; /* nag_complex_svd (f02xec), see above. */ nag_complex_svd(m, n, a, tda, ncolb, dummy, (Integer) 1, wantq, q, tdq, sv, wantp, dummy, (Integer) 1, &iter, e, &failinfo, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_complex_svd (f02xec).\n%s\n", fail.message); exit_status = 1; goto END; } printf("Singular value decomposition of A\n\nSingular values\n"); for (i = 0; i < m; ++i) printf("%9.4f%s", sv[i], (i%5 == 4 || i == m-1)?"\n":" "); printf("\nLeft-hand singular vectors, by column\n"); for (i = 0; i < m; ++i) for (j = 0; j < m; ++j) printf("%7.4f %7.4f%s", COMPLEX(Q(i, j)), (j%3 == 2 || j == n-1)?"\n":" "); printf("\nRight-hand singular vectors, by column\n"); for (i = 0; i < n; ++i) for (j = 0; j < m; ++j) printf("%7.4f %7.4f%s", COMPLEX_CONJ(A(j, i)), (j%3 == 2 || j == n-1)?"\n":" "); } END: NAG_FREE(e); NAG_FREE(sv); NAG_FREE(a); NAG_FREE(q); NAG_FREE(dummy); return exit_status; }