359 lines
13 KiB
C
359 lines
13 KiB
C
/*------------------------------------------------------------------------------
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* lambda.c : integer ambiguity resolution
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*
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* Copyright (C) 2007-2008 by T.TAKASU, All rights reserved.
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*
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* reference :
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* [1] P.J.G.Teunissen, The least-square ambiguity decorrelation adjustment:
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* a method for fast GPS ambiguity estimation, J.Geodesy, Vol.70, 65-82,
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* 1995
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* [2] X.-W.Chang, X.Yang, T.Zhou, MLAMBDA: A modified LAMBDA method for
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* integer least-squares estimation, J.Geodesy, Vol.79, 552-565, 2005
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*
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* version : $Revision: 1.1 $ $Date: 2008/07/17 21:48:06 $
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* history : 2007/01/13 1.0 new
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* 2015/05/31 1.1 add api lambda_reduction(), lambda_search()
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*-----------------------------------------------------------------------------*/
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#include "rtklib.h"
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/* constants/macros ----------------------------------------------------------*/
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#define LOOPMAX 10000 /* maximum count of search loop */
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#define SGN(x) ((x) <= 0.0 ? -1.0 : 1.0)
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#define ROUND(x) (floor((x) + 0.5))
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#define SWAP(x, y) \
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do \
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{ \
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double tmp_; \
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tmp_ = x; \
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x = y; \
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y = tmp_; \
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} while (0)
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/* LD factorization (Q=L'*diag(D)*L) -----------------------------------------*/
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static int LD(int n, const double *Q, double *L, double *D)
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{
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int i, j, k, info = 0;
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double a, *A = mat(n, n);
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memcpy(A, Q, sizeof(double) * n * n);
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for (i = n - 1; i >= 0; i--)
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{
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if ((D[i] = A[i + i * n]) <= 0.0)
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{
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info = -1;
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break;
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}
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a = sqrt(D[i]);
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for (j = 0; j <= i; j++)
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L[i + j * n] = A[i + j * n] / a;
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for (j = 0; j <= i - 1; j++)
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for (k = 0; k <= j; k++)
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A[j + k * n] -= L[i + k * n] * L[i + j * n];
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for (j = 0; j <= i; j++)
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L[i + j * n] /= L[i + i * n];
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}
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free(A);
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if (info)
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fprintf(stderr, "%s : LD factorization error\n", __FILE__);
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return info;
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}
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/* integer gauss transformation ----------------------------------------------*/
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static void gauss(int n, double *L, double *Z, int i, int j)
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{
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int k, mu;
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if ((mu = (int)ROUND(L[i + j * n])) != 0)
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{
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for (k = i; k < n; k++)
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L[k + n * j] -= (double)mu * L[k + i * n];
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for (k = 0; k < n; k++)
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Z[k + n * j] -= (double)mu * Z[k + i * n];
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}
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}
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/* permutations --------------------------------------------------------------*/
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static void perm(int n, double *L, double *D, int j, double del, double *Z)
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{
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int k;
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double eta, lam, a0, a1;
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eta = D[j] / del;
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lam = D[j + 1] * L[j + 1 + j * n] / del;
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D[j] = eta * D[j + 1];
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D[j + 1] = del;
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for (k = 0; k <= j - 1; k++)
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{
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a0 = L[j + k * n];
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a1 = L[j + 1 + k * n];
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L[j + k * n] = -L[j + 1 + j * n] * a0 + a1;
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L[j + 1 + k * n] = eta * a0 + lam * a1;
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}
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L[j + 1 + j * n] = lam;
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for (k = j + 2; k < n; k++)
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SWAP(L[k + j * n], L[k + (j + 1) * n]);
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for (k = 0; k < n; k++)
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SWAP(Z[k + j * n], Z[k + (j + 1) * n]);
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}
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/* lambda reduction (z=Z'*a, Qz=Z'*Q*Z=L'*diag(D)*L) (ref.[1]) ---------------*/
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static void reduction(int n, double *L, double *D, double *Z)
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{
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int i, j, k;
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double del;
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j = n - 2;
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k = n - 2;
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//<2F><><EFBFBD><EFBFBD><EFBFBD>ĵ<EFBFBD><C4B5><EFBFBD><EFBFBD>任<EFBFBD><E4BBBB><EFBFBD>Ʋ<EFBFBD><C6B2><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>˼·<CBBC><C2B7>
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while (j >= 0)
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{
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//<2F><><EFBFBD>ڵ<EFBFBD>k+1<><31>k+2<><32>...<2E><>n-2<>ж<EFBFBD><D0B6><EFBFBD><EFBFBD>й<EFBFBD><D0B9><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ز<EFBFBD><D8B2><EFBFBD>û<EFBFBD>б<EFBFBD><D0B1><EFBFBD>һ<EFBFBD>ε<EFBFBD><CEB5><EFBFBD><EFBFBD>任Ӱ<E4BBBB>죬
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//<2F><><EFBFBD><EFBFBD>ֻ<EFBFBD><D6BB><EFBFBD>Ե<EFBFBD>0,1<><31>...<2E><>k-1<><31>k<EFBFBD>н<EFBFBD><D0BD>н<EFBFBD><D0BD><EFBFBD><EFBFBD><EFBFBD>
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if (j <= k)
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for (i = j + 1; i < n; i++)
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gauss(n, L, Z, i, j); //<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>п<EFBFBD>ʼ<EFBFBD><CABC><EFBFBD><EFBFBD><EFBFBD>зǶԽ<C7B6><D4BD><EFBFBD>Ԫ<EFBFBD>ش<EFBFBD><D8B4><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ν<EFBFBD><CEBD><EFBFBD><EFBFBD><EFBFBD>
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del = D[j] + L[j + 1 + j * n] * L[j + 1 + j * n] * D[j + 1];
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if (del + 1E-6 < D[j + 1])
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{ /* <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʼ<EFBFBD><CABC><EFBFBD>е<EFBFBD><D0B5><EFBFBD><EFBFBD>任compared considering numerical error */
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perm(n, L, D, j, del, Z); //<2F><><EFBFBD><EFBFBD><EFBFBD>任
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k = j;
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j = n - 2; //<2F><><EFBFBD>ɵ<EFBFBD><C9B5><EFBFBD><EFBFBD>任<EFBFBD><E4BBBB><EFBFBD><EFBFBD><EFBFBD>´<EFBFBD><C2B4><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>п<EFBFBD>ʼ<EFBFBD><CABC><EFBFBD>н<EFBFBD><D0BD><EFBFBD><EFBFBD>ؼ<EFBFBD><D8BC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>k<EFBFBD><6B>¼<EFBFBD><C2BC><EFBFBD><EFBFBD>һ<EFBFBD>ν<EFBFBD><CEBD>й<EFBFBD><D0B9><EFBFBD><EFBFBD><EFBFBD><EFBFBD>任<EFBFBD><E4BBBB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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}
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else
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j--;
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}
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}
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/* modified lambda (mlambda) search (ref. [2]) -------------------------------
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* args : n I number of float parameters
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* m I number of fixed solution
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L,D I transformed covariance matrix
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zs I transformed double-diff phase biases
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zn O fixed solutions
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s O sum of residuals for fixed solutions */
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static int search(int n, int m, const double *L, const double *D,
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const double *zs, double *zn, double *s)
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{
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int i, j, k, c, nn = 0, imax = 0;
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double newdist, maxdist = 1E99, y; // maxdist<73><74><EFBFBD><EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>Բ<EFBFBD>뾶
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double *S = zeros(n, n), *dist = mat(n, 1), *zb = mat(n, 1), *z = mat(n, 1), *step = mat(n, 1);
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k = n - 1;
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dist[k] = 0.0; // k<><6B>ʾ<EFBFBD><CABE>ǰ<EFBFBD>㣬<EFBFBD><E3A3AC><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>㣨n-1<><31><EFBFBD><EFBFBD>ʼ<EFBFBD><CABC><EFBFBD><EFBFBD>
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zb[k] = zs[k]; //<2F><>zn
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z[k] = ROUND(zb[k]); //<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>δȡ<CEB4><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>step<65><70>¼z[k]<5D><><EFBFBD><EFBFBD><EFBFBD>ỹ<EFBFBD><E1BBB9><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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y = zb[k] - z[k];
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step[k] = SGN(y); /* step towards closest integer */
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for (c = 0; c < LOOPMAX; c++)
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{
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newdist = dist[k] + y * y / D[k]; /* newdist=sum(((z(j)-zb(j))^2/d(j))) */
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if (newdist < maxdist)
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{ //<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ǰ<EFBFBD>ۻ<EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֵС<D6B5>ڵ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>Բ<EFBFBD>뾶
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/* Case 1: move down <20><><EFBFBD><EFBFBD>1<EFBFBD><31><EFBFBD><EFBFBD><EFBFBD><EFBFBD>δ<EFBFBD><CEB4><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>㣬<EFBFBD><E3A3AC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ۻ<EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ */
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if (k != 0)
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{
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dist[--k] = newdist; //<2F><>¼<EFBFBD>µ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD><EFBFBD>ۻ<EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5>dist[k]<5D><>ʾ<EFBFBD>˵<EFBFBD>k,k+1,...,n-1<><31><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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for (i = 0; i <= k; i++)
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S[k + i * n] = S[k + 1 + i * n] + (z[k + 1] - zb[k + 1]) * L[k + 1 + i * n];
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zb[k] = zs[k] + S[k + k * n]; //<2F><><EFBFBD><EFBFBD>Zk<5A><6B><EFBFBD><EFBFBD><EFBFBD><EFBFBD>k<EFBFBD><6B><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ģ<EFBFBD><C4A3><EFBFBD>Ȳ<EFBFBD><C8B2><EFBFBD><EFBFBD>ı<EFBFBD>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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z[k] = ROUND(zb[k]); /* next valid integer <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>δȡ<CEB4><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EEA3BB>¼<EFBFBD><C2BC><EFBFBD><EFBFBD><EFBFBD>ỹ<EFBFBD><E1BBB9><EFBFBD><EFBFBD><EFBFBD><EFBFBD>*/
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y = zb[k] - z[k];
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step[k] = SGN(y);
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}
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/* Case 2: store the found candidate and try next valid integer <20><><EFBFBD><EFBFBD>2<EFBFBD><32><EFBFBD><EFBFBD><EFBFBD>Ѿ<EFBFBD><D1BE><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>㣬<EFBFBD><E3A3AC>ζ<EFBFBD><CEB6><EFBFBD><EFBFBD><EFBFBD>в<EFBFBD><D0B2><EFBFBD><EFBFBD>ۻ<EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> */
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else
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{
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// nnΪ<6E><CEAA>ǰ<EFBFBD><C7B0>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>mΪ<6D><CEAA><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ҫ<EFBFBD>Ĺ̶<C4B9><CCB6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ2<CEAA><32><EFBFBD><EFBFBD>ʾ<EFBFBD><CABE>Ҫһ<D2AA><D2BB><EFBFBD><EFBFBD><EFBFBD>Ž⼰һ<E2BCB0><D2BB><EFBFBD><EFBFBD><EFBFBD>Ž<EFBFBD>
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// s<><73>¼<EFBFBD><C2BC>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5>imax<61><78>¼֮ǰ<D6AE><C7B0>ѡ<EFBFBD><D1A1><EFBFBD>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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if (nn < m)
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{ //<2F><><EFBFBD><EFBFBD>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>û<EFBFBD><C3BB>
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/* store the first m initial points */
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if (nn == 0 || newdist > s[imax])
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imax = nn; //<2F><><EFBFBD><EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5>֮ǰ<D6AE><C7B0><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ô<EFBFBD><C3B4><EFBFBD><EFBFBD>imaxʹs[imax]ָ<><D6B8><EFBFBD><EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD>о<EFBFBD><D0BE>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ
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for (i = 0; i < n; i++)
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zn[i + nn * n] = z[i]; // zn<7A><6E><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>к<EFBFBD>ѡ<EFBFBD><D1A1>
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s[nn++] = newdist; // s<><73>¼<EFBFBD><C2BC>ǰĿ<C7B0>꺯<EFBFBD><EABAAF>ֵnewdist<73><74><EFBFBD><EFBFBD><EFBFBD>Ӽӵ<D3BC>ǰ<EFBFBD><C7B0>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD>nn
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}
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else
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{ //<2F><><EFBFBD><EFBFBD>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ǰzn<7A><6E><EFBFBD>Ѿ<EFBFBD><D1BE><EFBFBD><EFBFBD><EFBFBD>2<EFBFBD><32><EFBFBD><EFBFBD>ѡ<EFBFBD>⣩
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if (newdist < s[imax])
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{ //<2F><> <20><>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ <20><> s<>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ С
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for (i = 0; i < n; i++)
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zn[i + imax * n] = z[i]; //<2F>õ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD>滻zn<7A>о<EFBFBD><D0BE>нϴ<D0BD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD>Ľ<EFBFBD>
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s[imax] = newdist; //<2F>õ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD>滻s<E6BBBB>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ
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for (i = imax = 0; i < m; i++)
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if (s[imax] < s[i])
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imax = i; //<2F><><EFBFBD><EFBFBD>imax<61><78>֤imaxʼ<78><CABC>ָ<EFBFBD><D6B8>s<EFBFBD>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ
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}
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maxdist = s[imax]; //<2F>õ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5><EFBFBD>³<EFBFBD><C2B3><EFBFBD>Բ<EFBFBD>뾶
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}
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z[0] += step[0]; /* next valid integer<65>ڵ<EFBFBD>һ<EFBFBD>㣬ȡ<E3A3AC><C8A1>һ<EFBFBD><D2BB><EFBFBD><EFBFBD>Ч<EFBFBD><D0A7><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ģ<EFBFBD><C4A3><EFBFBD>Ȳ<EFBFBD><C8B2><EFBFBD><EFBFBD><EFBFBD><EFBFBD>м<EFBFBD><D0BC>㣨<EFBFBD><E3A3A8>zbΪ5.3<EFBFBD><EFBFBD><EFBFBD><EFBFBD>zȡֵ˳<EFBFBD><EFBFBD>Ϊ5,6,4,7<><37>...<2E><> */
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y = zb[0] - z[0];
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step[0] = -step[0] - SGN(step[0]);
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}
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}
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/* Case 3: exit or move up<75><70><EFBFBD><EFBFBD>3<EFBFBD><33><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ǰ<EFBFBD>ۻ<EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֵ<EFBFBD><D6B5><EFBFBD>ڵ<EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>Բ<EFBFBD>뾶 */
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else
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{
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if (k == n - 1)
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break; //<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ǰ<EFBFBD><C7B0>Ϊ<EFBFBD><CEAA>n-1<>㣬<EFBFBD><E3A3AC>ζ<EFBFBD>ź<EFBFBD><C5BA><EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ļ<EFBFBD><C4BC>㶼<EFBFBD>ᳬ<EFBFBD><E1B3AC><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Բ<EFBFBD>뾶<EFBFBD><EBBEB6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֹ<EFBFBD><D6B9><EFBFBD><EFBFBD>
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else
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{ //<2F><><EFBFBD><EFBFBD>ǰ<EFBFBD>㲻<EFBFBD>ǵ<EFBFBD>n-1<><31>
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k++; /* move up <20>˺<EFBFBD>һ<EFBFBD>㣬<EFBFBD><E3A3AC><EFBFBD>ӵ<EFBFBD>k<EFBFBD><6B><EFBFBD>˵<EFBFBD><CBB5><EFBFBD>k+1<><31>*/
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z[k] += step[k]; /* next valid integer <20><><EFBFBD><EFBFBD><EFBFBD>˺<EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD>Ч<EFBFBD><D0A7>ѡ<EFBFBD><D1A1>*/
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y = zb[k] - z[k];
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step[k] = -step[k] - SGN(step[k]);
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}
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}
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}
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// <20><>s<EFBFBD>е<EFBFBD>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5>zn<7A>еĺ<D0B5>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>s<EFBFBD><73>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵΪ<D6B5><CEAA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><D7BC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
// RTKLIB<49><42><EFBFBD><EFBFBD><EFBFBD>տ<EFBFBD><D5BF>Եõ<D4B5>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD>Ž<EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD>Ž⣬<C5BD><E2A3AC><EFBFBD><EFBFBD>zn<7A>У<EFBFBD><D0A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ӧ<EFBFBD><D3A6>Ŀ<EFBFBD>꺯<EFBFBD><EABAAF>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>s<EFBFBD><73>
|
||
for (i = 0; i < m - 1; i++)
|
||
{ /* sort by s */
|
||
for (j = i + 1; j < m; j++)
|
||
{
|
||
if (s[i] < s[j])
|
||
continue;
|
||
SWAP(s[i], s[j]);
|
||
for (k = 0; k < n; k++)
|
||
SWAP(zn[k + i * n], zn[k + j * n]);
|
||
}
|
||
}
|
||
free(S);
|
||
free(dist);
|
||
free(zb);
|
||
free(z);
|
||
free(step);
|
||
|
||
if (c >= LOOPMAX)
|
||
{
|
||
fprintf(stderr, "%s : search loop count overflow\n", __FILE__);
|
||
return -2;
|
||
}
|
||
return 0;
|
||
}
|
||
/* lambda/mlambda integer least-square estimation ------------------------------
|
||
* integer least-square estimation. reduction is performed by lambda (ref.[1]),
|
||
* and search by mlambda (ref.[2]).
|
||
* args :
|
||
* rtk_t* rtk I
|
||
* int n I number of float parameters
|
||
* int m I number of fixed solutions
|
||
* double *a I float parameters (n x 1) (double-diff phase biases)
|
||
* double *Q I covariance matrix of float parameters (n x n)
|
||
* double *F O fixed solutions (n x m)
|
||
* double *s O sum of squared residulas of fixed solutions (1 x m)
|
||
* return : status (0:ok,other:error)
|
||
* notes : matrix stored by column-major order (fortran convension)
|
||
*-----------------------------------------------------------------------------*/
|
||
extern int lambda(rtk_t* rtk, int n, int m, const double *a, const double *Q, double *F,
|
||
double *s)
|
||
{
|
||
int info;
|
||
double *L, *D, *Z, *z, *E;
|
||
if (n <= 0 || m <= 0)
|
||
return -1;
|
||
L = zeros(n, n);
|
||
D = mat(n, 1);
|
||
Z = eye(n);
|
||
z = mat(n, 1);
|
||
E = mat(n, m);
|
||
|
||
/* LD (lower diaganol) factorization (Q=L'*diag(D)*L) */
|
||
if (!(info = LD(n, Q, L, D)))
|
||
{
|
||
|
||
/* lambda reduction (z=Z'*a, Qz=Z'*Q*Z=L'*diag(D)*L) */
|
||
reduction(n, L, D, Z);
|
||
matmul("TN", n, 1, n, 1.0, Z, a, 0.0, z); /* z=Z'*a */
|
||
/* mlambda search
|
||
z = transformed double-diff phase biases
|
||
L,D = transformed covariance matrix */
|
||
if (!(info = search(n, m, L, D, z, E, s)))
|
||
{ /* returns 0 if no error */
|
||
|
||
/* <20><><EFBFBD><EFBFBD><EFBFBD>¿ռ<C2BF><D5BC>й̶<D0B9><CCB6><EFBFBD>ģ<EFBFBD><C4A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>任<EFBFBD><E4BBBB>˫<EFBFBD><CBAB>ģ<EFBFBD><C4A3><EFBFBD>ȿռ<C8BF><D5BC><EFBFBD> */
|
||
info = solve("T", Z, E, n, m, F); /* F=Z'\E */
|
||
}
|
||
}
|
||
free(L);
|
||
free(D);
|
||
free(Z);
|
||
free(z);
|
||
free(E);
|
||
return info;
|
||
}
|
||
|
||
|
||
|
||
/* lambda reduction ------------------------------------------------------------
|
||
* reduction by lambda (ref [1]) for integer least square
|
||
* args : int n I number of float parameters
|
||
* double *Q I covariance matrix of float parameters (n x n)
|
||
* double *Z O lambda reduction matrix (n x n)
|
||
* return : status (0:ok,other:error)
|
||
*-----------------------------------------------------------------------------*/
|
||
extern int lambda_reduction(int n, const double *Q, double *Z)
|
||
{
|
||
double *L, *D;
|
||
int i, j, info;
|
||
|
||
if (n <= 0)
|
||
return -1;
|
||
|
||
L = zeros(n, n);
|
||
D = mat(n, 1);
|
||
|
||
for (i = 0; i < n; i++)
|
||
for (j = 0; j < n; j++)
|
||
{
|
||
Z[i + j * n] = i == j ? 1.0 : 0.0;
|
||
}
|
||
/* LD factorization */
|
||
if ((info = LD(n, Q, L, D)))
|
||
{
|
||
free(L);
|
||
free(D);
|
||
return info;
|
||
}
|
||
/* lambda reduction */
|
||
reduction(n, L, D, Z);
|
||
|
||
free(L);
|
||
free(D);
|
||
return 0;
|
||
}
|
||
/* mlambda search --------------------------------------------------------------
|
||
* search by mlambda (ref [2]) for integer least square
|
||
* args : int n I number of float parameters
|
||
* int m I number of fixed solutions
|
||
* double *a I float parameters (n x 1)
|
||
* double *Q I covariance matrix of float parameters (n x n)
|
||
* double *F O fixed solutions (n x m)
|
||
* double *s O sum of squared residulas of fixed solutions (1 x m)
|
||
* return : status (0:ok,other:error)
|
||
*-----------------------------------------------------------------------------*/
|
||
extern int lambda_search(int n, int m, const double *a, const double *Q,
|
||
double *F, double *s)
|
||
{
|
||
double *L, *D;
|
||
int info;
|
||
|
||
if (n <= 0 || m <= 0)
|
||
return -1;
|
||
|
||
L = zeros(n, n);
|
||
D = mat(n, 1);
|
||
|
||
/* LD factorization */
|
||
if ((info = LD(n, Q, L, D)))
|
||
{
|
||
free(L);
|
||
free(D);
|
||
return info;
|
||
}
|
||
/* mlambda search */
|
||
info = search(n, m, L, D, a, F, s);
|
||
|
||
free(L);
|
||
free(D);
|
||
return info;
|
||
} |