#include "blaswrap.h" /* -- translated by f2c (version 19990503). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Table of constant values */ static doublereal c_b7 = 1.; static integer c__1 = 1; /* Subroutine */ int dort03_(char *rc, integer *mu, integer *mv, integer *n, integer *k, doublereal *u, integer *ldu, doublereal *v, integer *ldv, doublereal *work, integer *lwork, doublereal *result, integer *info) { /* System generated locals */ integer u_dim1, u_offset, v_dim1, v_offset, i__1, i__2; doublereal d__1, d__2, d__3; /* Builtin functions */ double d_sign(doublereal *, doublereal *); /* Local variables */ static integer i__, j; static doublereal s; extern logical lsame_(char *, char *); extern /* Subroutine */ int dort01_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *); extern doublereal dlamch_(char *); extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *); static integer irc, lmx; static doublereal ulp, res1, res2; #define u_ref(a_1,a_2) u[(a_2)*u_dim1 + a_1] #define v_ref(a_1,a_2) v[(a_2)*v_dim1 + a_1] /* -- LAPACK test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University February 29, 1992 Purpose ======= DORT03 compares two orthogonal matrices U and V to see if their corresponding rows or columns span the same spaces. The rows are checked if RC = 'R', and the columns are checked if RC = 'C'. RESULT is the maximum of | V*V' - I | / ( MV ulp ), if RC = 'R', or | V'*V - I | / ( MV ulp ), if RC = 'C', and the maximum over rows (or columns) 1 to K of | U(i) - S*V(i) |/ ( N ulp ) where S is +-1 (chosen to minimize the expression), U(i) is the i-th row (column) of U, and V(i) is the i-th row (column) of V. Arguments ========== RC (input) CHARACTER*1 If RC = 'R' the rows of U and V are to be compared. If RC = 'C' the columns of U and V are to be compared. MU (input) INTEGER The number of rows of U if RC = 'R', and the number of columns if RC = 'C'. If MU = 0 DORT03 does nothing. MU must be at least zero. MV (input) INTEGER The number of rows of V if RC = 'R', and the number of columns if RC = 'C'. If MV = 0 DORT03 does nothing. MV must be at least zero. N (input) INTEGER If RC = 'R', the number of columns in the matrices U and V, and if RC = 'C', the number of rows in U and V. If N = 0 DORT03 does nothing. N must be at least zero. K (input) INTEGER The number of rows or columns of U and V to compare. 0 <= K <= max(MU,MV). U (input) DOUBLE PRECISION array, dimension (LDU,N) The first matrix to compare. If RC = 'R', U is MU by N, and if RC = 'C', U is N by MU. LDU (input) INTEGER The leading dimension of U. If RC = 'R', LDU >= max(1,MU), and if RC = 'C', LDU >= max(1,N). V (input) DOUBLE PRECISION array, dimension (LDV,N) The second matrix to compare. If RC = 'R', V is MV by N, and if RC = 'C', V is N by MV. LDV (input) INTEGER The leading dimension of V. If RC = 'R', LDV >= max(1,MV), and if RC = 'C', LDV >= max(1,N). WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) LWORK (input) INTEGER The length of the array WORK. For best performance, LWORK should be at least N*N if RC = 'C' or M*M if RC = 'R', but the tests will be done even if LWORK is 0. RESULT (output) DOUBLE PRECISION The value computed by the test described above. RESULT is limited to 1/ulp to avoid overflow. INFO (output) INTEGER 0 indicates a successful exit -k indicates the k-th parameter had an illegal value ===================================================================== Check inputs Parameter adjustments */ u_dim1 = *ldu; u_offset = 1 + u_dim1 * 1; u -= u_offset; v_dim1 = *ldv; v_offset = 1 + v_dim1 * 1; v -= v_offset; --work; /* Function Body */ *info = 0; if (lsame_(rc, "R")) { irc = 0; } else if (lsame_(rc, "C")) { irc = 1; } else { irc = -1; } if (irc == -1) { *info = -1; } else if (*mu < 0) { *info = -2; } else if (*mv < 0) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*k < 0 || *k > max(*mu,*mv)) { *info = -5; } else if (irc == 0 && *ldu < max(1,*mu) || irc == 1 && *ldu < max(1,*n)) { *info = -7; } else if (irc == 0 && *ldv < max(1,*mv) || irc == 1 && *ldv < max(1,*n)) { *info = -9; } if (*info != 0) { i__1 = -(*info); xerbla_("DORT03", &i__1); return 0; } /* Initialize result */ *result = 0.; if (*mu == 0 || *mv == 0 || *n == 0) { return 0; } /* Machine constants */ ulp = dlamch_("Precision"); if (irc == 0) { /* Compare rows */ res1 = 0.; i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { lmx = idamax_(n, &u_ref(i__, 1), ldu); s = d_sign(&c_b7, &u_ref(i__, lmx)) * d_sign(&c_b7, &v_ref(i__, lmx)); i__2 = *n; for (j = 1; j <= i__2; ++j) { /* Computing MAX */ d__2 = res1, d__3 = (d__1 = u_ref(i__, j) - s * v_ref(i__, j), abs(d__1)); res1 = max(d__2,d__3); /* L10: */ } /* L20: */ } res1 /= (doublereal) (*n) * ulp; /* Compute orthogonality of rows of V. */ dort01_("Rows", mv, n, &v[v_offset], ldv, &work[1], lwork, &res2); } else { /* Compare columns */ res1 = 0.; i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { lmx = idamax_(n, &u_ref(1, i__), &c__1); s = d_sign(&c_b7, &u_ref(lmx, i__)) * d_sign(&c_b7, &v_ref(lmx, i__)); i__2 = *n; for (j = 1; j <= i__2; ++j) { /* Computing MAX */ d__2 = res1, d__3 = (d__1 = u_ref(j, i__) - s * v_ref(j, i__), abs(d__1)); res1 = max(d__2,d__3); /* L30: */ } /* L40: */ } res1 /= (doublereal) (*n) * ulp; /* Compute orthogonality of columns of V. */ dort01_("Columns", n, mv, &v[v_offset], ldv, &work[1], lwork, &res2); } /* Computing MIN */ d__1 = max(res1,res2), d__2 = 1. / ulp; *result = min(d__1,d__2); return 0; /* End of DORT03 */ } /* dort03_ */ #undef v_ref #undef u_ref .