// test: min || B - A.T*X || func TestLeastSquaresLQ(t *testing.T) { M := 723 N := 811 K := 273 nb := 32 conf := gomas.NewConf() conf.LB = nb tau := cmat.NewMatrix(M, 1) A := cmat.NewMatrix(M, N) src := cmat.NewFloatNormSource() A.SetFrom(src) B0 := cmat.NewMatrix(M, K) B0.SetFrom(src) B := cmat.NewMatrix(N, K) // B = A.T*B0 blasd.Mult(B, A, B0, 1.0, 0.0, gomas.TRANSA, conf) W := lapackd.Workspace(lapackd.LQFactorWork(A, conf)) lapackd.LQFactor(A, tau, W, conf) // B' = A.-1*B lapackd.LQSolve(B, A, tau, W, gomas.TRANS, conf) // expect B[0:M,0:K] == B0[0:M,0:K], B[M:N,0:K] == 0 var X cmat.FloatMatrix X.SubMatrix(B, 0, 0, M, K) blasd.Plus(&X, B0, 1.0, -1.0, gomas.NONE) nrm := lapackd.NormP(&X, lapackd.NORM_ONE) t.Logf("M=%d, N=%d ||B0 - min( ||A.T*X - B0|| ) ||_1: %e\n", M, N, nrm) }
// test: min ||X|| s.t. A*X = B func TestSolveLQ(t *testing.T) { M := 743 N := 809 K := 281 nb := 32 conf := gomas.NewConf() conf.LB = nb tau := cmat.NewMatrix(N, 1) A := cmat.NewMatrix(M, N) src := cmat.NewFloatNormSource() A.SetFrom(src) A0 := cmat.NewCopy(A) B0 := cmat.NewMatrix(N, K) B0.SetFrom(src) B := cmat.NewCopy(B0) W := lapackd.Workspace(lapackd.LQFactorWork(A, conf)) lapackd.LQFactor(A, tau, W, conf) lapackd.LQSolve(B, A, tau, W, gomas.NONE, conf) var Bmin cmat.FloatMatrix Bmin.SubMatrix(B0, 0, 0, M, K) blasd.Mult(&Bmin, A0, B, 1.0, -1.0, gomas.NONE, conf) nrm := lapackd.NormP(&Bmin, lapackd.NORM_ONE) t.Logf("M=%d, N=%d ||B - A*X||_1: %e\n", M, N, nrm) }