Example #1
0
func TestLQFactor(t *testing.T) {
	M := 611
	N := 715
	nb := 32
	conf := gomas.NewConf()

	A := cmat.NewMatrix(M, N)
	src := cmat.NewFloatNormSource()
	A.SetFrom(src)
	tau := cmat.NewMatrix(M, 1)

	A1 := cmat.NewCopy(A)
	tau1 := cmat.NewCopy(tau)

	conf.LB = 0
	W := cmat.NewMatrix(M+N, 1)
	lapackd.LQFactor(A, tau, W, conf)

	conf.LB = nb
	W1 := lapackd.Workspace(lapackd.LQFactorWork(A1, conf))
	lapackd.LQFactor(A1, tau1, W1, conf)

	blasd.Plus(A1, A, 1.0, -1.0, gomas.NONE)
	nrm := lapackd.NormP(A1, lapackd.NORM_ONE)
	t.Logf("M=%d, N=%d ||blk.LQ(A) - unblk.LQ(A)||_1: %e\n", M, N, nrm)
}
Example #2
0
// 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)
}
Example #3
0
// 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)
}
Example #4
0
func TestLQBuild(t *testing.T) {
	var dc cmat.FloatMatrix

	M := 877
	N := 913
	K := 831
	lb := 48
	conf := gomas.NewConf()
	_ = lb

	A := cmat.NewMatrix(M, N)
	src := cmat.NewFloatNormSource()
	A.SetFrom(src)
	tau := cmat.NewMatrix(M, 1)
	W := cmat.NewMatrix(M, 1)
	C := cmat.NewMatrix(M, M)
	dc.Diag(C)

	conf.LB = lb
	lapackd.LQFactor(A, tau, W, conf)
	A1 := cmat.NewCopy(A)

	conf.LB = 0
	lapackd.LQBuild(A, tau, W, K, conf)
	if N < 10 {
		t.Logf("unblk.LQBuild Q:\n%v\n", A)
	}
	blasd.Mult(C, A, A, 1.0, 0.0, gomas.TRANSB, conf)
	blasd.Add(&dc, -1.0)
	n0 := lapackd.NormP(C, lapackd.NORM_ONE)

	conf.LB = lb
	W2 := lapackd.Workspace(lapackd.LQBuildWork(A, conf))
	lapackd.LQBuild(A1, tau, W2, K, conf)
	if N < 10 {
		t.Logf("blk.LQBuild Q:\n%v\n", A1)
	}
	blasd.Mult(C, A1, A1, 1.0, 0.0, gomas.TRANSB, conf)
	blasd.Add(&dc, -1.0)
	n1 := lapackd.NormP(C, lapackd.NORM_ONE)

	blasd.Plus(A, A1, 1.0, -1.0, gomas.NONE)
	n2 := lapackd.NormP(A, lapackd.NORM_ONE)

	t.Logf("M=%d, N=%d, K=%d ||unblk.LQBuild(A) - blk.LQBuild(A)||_1 :%e\n", M, N, K, n2)
	t.Logf("unblk M=%d, N=%d, K=%d ||I - Q*Q.T||_1 : %e\n", M, N, K, n0)
	t.Logf("  blk M=%d, N=%d, K=%d ||I - Q*Q.T||_1 : %e\n", M, N, K, n1)
}
Example #5
0
// test: ||C - Q*Q.T*C||_1 ~= 0;
//   multipling from left requires: m(C) == n(A) [n(Q)]
func TestLQMultLeft(t *testing.T) {
	M := 771
	N := 813
	nb := 16
	conf := gomas.NewConf()

	A := cmat.NewMatrix(M, N)
	src := cmat.NewFloatNormSource()
	A.SetFrom(src)
	// C0 := A
	C0 := cmat.NewCopy(A)
	C1t := cmat.NewMatrix(N, M)
	blasd.Transpose(C1t, C0)
	C2t := cmat.NewCopy(C1t)

	tau := cmat.NewMatrix(M, 1)
	W := cmat.NewMatrix(M+N, 1)

	conf.LB = 0
	lapackd.LQFactor(A, tau, W, conf)

	// A0 := Q.T*A0
	conf.LB = 0
	lapackd.LQMult(C2t, A, tau, W, gomas.LEFT, conf)
	lapackd.LQMult(C2t, A, tau, W, gomas.LEFT|gomas.TRANS, conf)

	// A0 := Q.T*A0
	conf.LB = nb
	W1 := lapackd.Workspace(lapackd.LQMultWork(C1t, gomas.LEFT, conf))
	lapackd.LQMult(C1t, A, tau, W1, gomas.LEFT, conf)
	lapackd.LQMult(C1t, A, tau, W1, gomas.LEFT|gomas.TRANS, conf)

	blasd.Plus(C0, C1t, 1.0, -1.0, gomas.TRANSB)
	nrm := lapackd.NormP(C0, lapackd.NORM_ONE)
	t.Logf("M=%d, N=%d, ||C - Q*Q*T*C||_1: %e\n", M, N, nrm)

	blasd.Plus(C1t, C2t, 1.0, -1.0, gomas.NONE)
	nrm = lapackd.NormP(C1t, lapackd.NORM_ONE)
	t.Logf("M=%d, N=%d, ||unblk(Q*Q.T*C) - blk(Q*Q*T*C)||_1: %e\n", M, N, nrm)
}
Example #6
0
// test: ||A - A*Q*Q.T||_1 ~= 0
func TestLQMultRight(t *testing.T) {
	M := 511
	N := 627
	nb := 24
	conf := gomas.NewConf()

	A := cmat.NewMatrix(M, N)
	src := cmat.NewFloatNormSource()
	A.SetFrom(src)
	tau := cmat.NewMatrix(M, 1)
	W := cmat.NewMatrix(M+N, 1)

	A0 := cmat.NewCopy(A)
	A1 := cmat.NewCopy(A)
	A2 := cmat.NewCopy(A)

	conf.LB = 0
	lapackd.LQFactor(A, tau, W, conf)

	// unblocked A1 := A1*Q*Q.T
	conf.LB = 0
	lapackd.LQMult(A1, A, tau, W, gomas.RIGHT, conf)
	lapackd.LQMult(A1, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)

	// blocked A2 := A2*Q*Q.T
	conf.LB = nb
	W = lapackd.Workspace(lapackd.LQMultWork(A2, gomas.RIGHT, conf))
	lapackd.LQMult(A2, A, tau, W, gomas.RIGHT, conf)
	lapackd.LQMult(A2, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)

	// A1 - A0 == 0
	blasd.Plus(A1, A0, 1.0, -1.0, gomas.NONE)
	nrm := lapackd.NormP(A1, lapackd.NORM_ONE)
	t.Logf("M=%d, N=%d, unblk.||A - A*Q*Q.T||_1: %e\n", M, N, nrm)

	// A2 - A0 == 0
	blasd.Plus(A2, A0, 1.0, -1.0, gomas.NONE)
	nrm = lapackd.NormP(A2, lapackd.NORM_ONE)
	t.Logf("M=%d, N=%d, nb=%d blk.||A - A*Q*Q.T||_1: %e\n", M, N, nb, nrm)
}