iphone - Is it possible to solve a non-square under/over constrained matrix using Accelerate/LAPACK? -
is possible solve non-square under/over constrained matrix using accelerate/lapack? such following 2 matrices. if variables under constrained should equal 0 instead of being infinite.
so in under constrained case: a, d & e equal 0, while b, c & f equal -1.
in on constrained case variables equal -1.
under constrained:
____ ____ | (a) (b) (c) (d) (e) (f) | | -1 0 0 1 0 0 | 0 | | 1 0 0 0 -1 0 | 0 | | 0 -1 1 0 0 0 | 0 | | 0 1 0 0 0 -1 | 0 | | 0 1 0 0 0 0 | -1 | |____ ____| over constrained:
____ ____ | | | -1 0 0 1 0 0 | 0 | | 1 0 0 0 -1 0 | 0 | | 0 -1 1 0 0 0 | 0 | | 0 1 0 0 0 -1 | 0 | | 0 1 0 0 0 0 | -1 | | 0 0 1 -1 0 0 | 0 | | 1 -1 0 0 0 0 | 0 | |____ ____|
yes!
void solveunderdeterminedsystem() { __clpk_integer m = 5; __clpk_integer n = 6; __clpk_integer nrhs = 1; double a[30] = { -1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0 }; __clpk_integer lda = 5; double x[6] = { 0.0, 0.0, 0.0, 0.0, -1.0, 0.0 }; __clpk_integer ldb = 6; /* need allocate @ least 2*min(m,n) workspace. */ double work[12]; __clpk_integer worksize = 12; __clpk_integer info; dgels_("n", &m, &n, &nrhs, a, &lda, x, &ldb, work, &worksize, &info); if (info) printf("could not solve system; dgels exited error %d\n", info); else printf("solution [%f, %f, %f, %f, %f, %f]\n", x[0], x[1], x[2], x[3], x[4], x[5]); } the same routine solve over-determined systems in least-squares sense (the result minimizer of residual ||ax - b||).
note dgels_ assumes matrix has full rank (i.e., rank(a) = min(m, n)). if not case, need use different routine (dgelsd_) uses svd factorization instead of qr.
you seem asking lot of questions lapack. worth time read the documentation.
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