Beispiel #1
0
// Simple and slow LQ decomposition with Givens rotations
func TestGivensLQ(t *testing.T) {
	var d cmat.FloatMatrix
	M := 149
	N := 167
	A := cmat.NewMatrix(M, N)
	A1 := cmat.NewCopy(A)

	ones := cmat.NewFloatConstSource(1.0)
	src := cmat.NewFloatNormSource()
	A.SetFrom(src)
	A0 := cmat.NewCopy(A)

	Qt := cmat.NewMatrix(N, N)
	d.Diag(Qt)
	d.SetFrom(ones)

	// R = G(n)...G(2)G(1)*A; Q = G(1).T*G(2).T...G(n).T ;  Q.T = G(n)...G(2)G(1)
	for i := 0; i < M; i++ {
		// zero elements right of diagonal
		for j := N - 2; j >= i; j-- {
			c, s, r := lapackd.ComputeGivens(A.Get(i, j), A.Get(i, j+1))
			A.Set(i, j, r)
			A.Set(i, j+1, 0.0)
			// apply rotation to this column starting from row i+1
			lapackd.ApplyGivensRight(A, j, j+1, i+1, M-i-1, c, s)
			// update Qt = G(k)*Qt
			lapackd.ApplyGivensRight(Qt, j, j+1, 0, N, c, s)
		}
	}
	// A = L*Q
	blasd.Mult(A1, A, Qt, 1.0, 0.0, gomas.TRANSB)
	blasd.Plus(A0, A1, 1.0, -1.0, gomas.NONE)
	nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
	t.Logf("M=%d, N=%d ||A - L*G(1)..G(n)||_1: %e\n", M, N, nrm)
}
Beispiel #2
0
// test that unblocked QR and QRT are equal
func TestQRFactor(t *testing.T) {
	M := 411
	N := 375
	nb := 16

	conf := gomas.NewConf()
	conf.LB = nb

	A := cmat.NewMatrix(M, N)
	//W := cmat.NewMatrix(N, nb)
	tau := cmat.NewMatrix(N, 1)
	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)

	A0 := cmat.NewCopy(A)
	tau0 := cmat.NewCopy(tau)

	// blocked: QR = A = Q*R
	W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
	lapackd.QRFactor(A, tau, W, conf)

	conf.LB = 0
	lapackd.QRFactor(A0, tau0, W, conf)

	ok := A.AllClose(A0)
	t.Logf("blk.QRFactor(A) == unblk.QRFactor(A): %v\n", ok)

	ok = tau0.AllClose(tau)
	t.Logf("blk QR.tau == unblk QR.tau: %v\n", ok)
}
Beispiel #3
0
func TestTriRedUpper(t *testing.T) {
	N := 843
	nb := 48
	conf := gomas.NewConf()
	conf.LB = 0

	A := cmat.NewMatrix(N, N)
	tau := cmat.NewMatrix(N, 1)
	src := cmat.NewFloatNormSource()
	A.SetFrom(src, cmat.UPPER)
	A1 := cmat.NewCopy(A)
	tau1 := cmat.NewCopy(tau)
	_ = A1

	W := lapackd.Workspace(N)
	W1 := lapackd.Workspace(N * nb)

	lapackd.TRDReduce(A, tau, W, gomas.UPPER, conf)

	conf.LB = nb
	lapackd.TRDReduce(A1, tau1, W1, gomas.UPPER, conf)

	blasd.Plus(A, A1, -1.0, 1.0, gomas.NONE)
	nrm := lapackd.NormP(A, lapackd.NORM_ONE)
	t.Logf("N=%d, ||unblk.Trired(A) - blk.Trired(A)||_1: %e\n", N, nrm)
	blasd.Axpy(tau, tau1, -1.0)
	nrm = blasd.Nrm2(tau)
	t.Logf("   ||unblk.Trired(tau) - blk.Trired(tau)||_1: %e\n", nrm)
}
Beispiel #4
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// test: min ||X|| s.t A.T*X = B
func TestSolveQR(t *testing.T) {
	M := 799
	N := 711
	K := 241
	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(M, K)
	B0.SetFrom(src)
	B := cmat.NewCopy(B0)

	W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
	lapackd.QRFactor(A, tau, W, conf)

	lapackd.QRSolve(B, A, tau, W, gomas.TRANS, conf)

	var Bmin cmat.FloatMatrix
	Bmin.SubMatrix(B0, 0, 0, N, K)
	blasd.Mult(&Bmin, A0, B, 1.0, -1.0, gomas.TRANSA, conf)

	nrm := lapackd.NormP(&Bmin, lapackd.NORM_ONE)
	t.Logf("M=%d, N=%d ||B - A.T*X||_1: %e\n", M, N, nrm)
}
Beispiel #5
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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)
}
Beispiel #6
0
// m > n: A[m,n], I[m,m] --> A == I*A == Q*Q.T*A
func TestQRTMultLeftIdent(t *testing.T) {
	M := 411
	N := 399
	nb := 16
	A := cmat.NewMatrix(M, N)
	T := cmat.NewMatrix(nb, N)

	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)
	A0 := cmat.NewCopy(A)
	C := cmat.NewCopy(A)
	conf := gomas.NewConf()
	conf.LB = nb
	//t.Logf("A0:\n%v\n", A0)

	// QR = A = Q*R
	W := lapackd.Workspace(lapackd.QRTFactorWork(A, conf))
	lapackd.QRTFactor(A, T, W, conf)
	//t.Logf("T:\n%v\n", T)

	// C = Q.T*A
	W = lapackd.Workspace(lapackd.QRTMultWork(C, T, gomas.LEFT, conf))
	lapackd.QRTMult(C, A, T, W, gomas.LEFT|gomas.TRANS, conf)

	// C = Q*C == Q*Q.T*A
	lapackd.QRTMult(C, A, T, W, gomas.LEFT, conf)
	//t.Logf("A*Q*Q.T:\n%v\n", C)

	// A = A - Q*Q.T*A
	blasd.Plus(A0, C, 1.0, -1.0, gomas.NONE)
	// ||A - Q*Q.T*A||_1
	nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
	t.Logf("M=%d,N=%d  ||A - Q*Q.T*A||_1: %e\n", M, N, nrm)
}
Beispiel #7
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// test: unblk.ReduceHess(A) == blk.ReduceHess(A)
func TestReduceHess(t *testing.T) {
	N := 375
	nb := 16

	conf := gomas.NewConf()
	conf.LB = nb

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

	A0 := cmat.NewCopy(A)
	tau0 := cmat.NewCopy(tau)

	// blocked reduction
	W := lapackd.Workspace(lapackd.HessReduceWork(A, conf))
	lapackd.HessReduce(A, tau, W, conf)

	// unblocked reduction
	conf.LB = 0
	lapackd.HessReduce(A0, tau0, W, conf)

	ok := A.AllClose(A0)
	t.Logf("blk.ReduceHess(A) == unblk.ReduceHess(A): %v\n", ok)

	ok = tau0.AllClose(tau)
	t.Logf("blk HessQ.tau == unblk HessQ.tau: %v\n", ok)

	// ||A - A0||_1
	blasd.Plus(A, A0, 1.0, -1.0, gomas.NONE)
	nrm := lapackd.NormP(A, lapackd.NORM_ONE)
	t.Logf("||H - H0||_1: %e\n", nrm)
}
Beispiel #8
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// QR decompose A, then compute ||A - (R.T*Q.T).T||_1, should be small
func TestUnblkQRMultRight(t *testing.T) {
	M := 711
	N := 593
	A := cmat.NewMatrix(M, N)
	C := cmat.NewMatrix(N, M)
	tau := cmat.NewMatrix(N, 1)

	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)
	A0 := cmat.NewCopy(A)

	conf := gomas.NewConf()
	conf.LB = 0

	// QR = A = Q*R
	W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
	lapackd.QRFactor(A, tau, W, conf)

	// C = transpose(TriU(QR)) = R.T
	C.Transpose(cmat.TriU(cmat.NewCopy(A), cmat.NONE))

	// C = C*Q.T = R.T*Q.T
	W = lapackd.Workspace(lapackd.QRMultWork(C, gomas.RIGHT, conf))
	err := lapackd.QRMult(C, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
	if err != nil {
		t.Logf("err: %v\n", err)
	}

	// A = A - QR
	blasd.Plus(A0, C, 1.0, -1.0, gomas.TRANSB)
	// ||A - Q*R||_1
	nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
	t.Logf("M=%d,N=%d  ||A - (R.T*Q.T).T||_1: %e\n", M, N, nrm)
}
Beispiel #9
0
// QR decompose A, then compute ||A - Q*R||_1, should be small
func TestUnblkQRMultLeft(t *testing.T) {
	M := 711
	N := 593
	A := cmat.NewMatrix(M, N)
	tau := cmat.NewMatrix(N, 1)

	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)
	A0 := cmat.NewCopy(A)

	conf := gomas.NewConf()
	conf.LB = 0

	// QR = A = Q*R
	W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
	lapackd.QRFactor(A, tau, W, conf)

	// C = TriU(QR) = R
	C := cmat.TriU(cmat.NewCopy(A), cmat.NONE)

	// C = Q*C
	W = lapackd.Workspace(lapackd.QRMultWork(C, gomas.LEFT, conf))
	err := lapackd.QRMult(C, A, tau, W, gomas.LEFT, conf)
	if err != nil {
		t.Logf("err: %v\n", err)
	}

	// A = A - QR
	blasd.Plus(A0, C, 1.0, -1.0, gomas.NONE)
	// ||A - Q*R||_1
	nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
	t.Logf("M=%d,N=%d  ||A - Q*R||_1: %e\n", M, N, nrm)
}
Beispiel #10
0
func test_bdsvd(N, flags, kind int, verbose bool, t *testing.T) {
	var At, sD, sE, tmp cmat.FloatMatrix

	uplo := "upper"
	offdiag := 1
	if flags&gomas.LOWER != 0 {
		offdiag = -1
		uplo = "lower"
	}
	A0 := cmat.NewMatrix(N, N)
	desc := setDiagonals(A0, offdiag, kind)
	At.SubMatrix(A0, 0, 0, N, N)
	sD.Diag(A0, 0)
	sE.Diag(A0, offdiag)
	D := cmat.NewCopy(&sD)
	E := cmat.NewCopy(&sE)

	// unit singular vectors
	U := cmat.NewMatrix(N, N)
	sD.Diag(U, 0)
	sD.Add(1.0)

	V := cmat.NewMatrix(N, N)
	sD.Diag(V, 0)
	sD.Add(1.0)

	W := cmat.NewMatrix(4*N, 1)
	C := cmat.NewMatrix(N, N)

	lapackd.BDSvd(D, E, U, V, W, flags|gomas.WANTU|gomas.WANTV)

	blasd.Mult(C, U, U, 1.0, 0.0, gomas.TRANSA)
	sD.Diag(C)
	sD.Add(-1.0)
	nrmu := lapackd.NormP(C, lapackd.NORM_ONE)

	blasd.Mult(C, V, V, 1.0, 0.0, gomas.TRANSB)
	sD.Add(-1.0)
	nrmv := lapackd.NormP(C, lapackd.NORM_ONE)

	blasd.Mult(C, U, A0, 1.0, 0.0, gomas.TRANSA)
	blasd.Mult(&At, C, V, 1.0, 0.0, gomas.TRANSB)
	if verbose && N < 10 {
		t.Logf("D:\n%v\n", asRow(&tmp, D))
		t.Logf("U:\n%v\n", U)
		t.Logf("V:\n%v\n", V)
		t.Logf("U.T*A*V\n%v\n", &At)
	}
	sD.Diag(&At)
	blasd.Axpy(&sD, D, -1.0)
	nrma := lapackd.NormP(&At, lapackd.NORM_ONE)

	t.Logf("N=%d [%s,%s] ||U.T*A*V - bdsvd(A)||_1: %e\n", N, uplo, desc, nrma)
	t.Logf("  ||I - U.T*U||_1: %e\n", nrmu)
	t.Logf("  ||I - V.T*V||_1: %e\n", nrmv)
}
Beispiel #11
0
// test: C = C*Q.T
func TestQLMultRightTrans(t *testing.T) {
	var d, di0, di1 cmat.FloatMatrix
	M := 891
	N := 853
	lb := 36
	conf := gomas.NewConf()

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

	C0 := cmat.NewMatrix(N, M)
	d.Diag(C0, M-N)
	ones := cmat.NewFloatConstSource(1.0)
	d.SetFrom(ones)
	C1 := cmat.NewCopy(C0)

	I0 := cmat.NewMatrix(N, N)
	I1 := cmat.NewCopy(I0)
	di0.Diag(I0)
	di1.Diag(I1)

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

	conf.LB = lb
	lapackd.QLFactor(A, tau, W, conf)

	conf.LB = 0
	lapackd.QLMult(C0, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
	// I = Q*Q.T - I
	blasd.Mult(I0, C0, C0, 1.0, 0.0, gomas.TRANSB, conf)
	blasd.Add(&di0, -1.0)
	n0 := lapackd.NormP(I0, lapackd.NORM_ONE)

	conf.LB = lb
	lapackd.QLMult(C1, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
	// I = Q*Q.T - I
	blasd.Mult(I1, C1, C1, 1.0, 0.0, gomas.TRANSB, conf)
	blasd.Add(&di1, -1.0)
	n1 := lapackd.NormP(I1, lapackd.NORM_ONE)

	if N < 10 {
		t.Logf("unblk C0*Q:\n%v\n", C0)
		t.Logf("blk. C2*Q:\n%v\n", C1)
	}
	blasd.Plus(C0, C1, 1.0, -1.0, gomas.NONE)
	n2 := lapackd.NormP(C0, lapackd.NORM_ONE)

	t.Logf("M=%d, N=%d ||unblk.QLMult(C) - blk.QLMult(C)||_1: %e\n", M, N, n2)
	t.Logf("unblk M=%d, N=%d ||I - Q*Q.T||_1: %e\n", M, N, n0)
	t.Logf("blk   M=%d, N=%d ||I - Q*Q.T||_1: %e\n", M, N, n1)
}
Beispiel #12
0
func TestTrdMultUpper(t *testing.T) {
	var dt, et, da, ea cmat.FloatMatrix
	N := 843
	nb := 48
	conf := gomas.NewConf()
	conf.LB = nb

	A := cmat.NewMatrix(N, N)
	tau := cmat.NewMatrix(N, 1)
	src := cmat.NewFloatNormSource()
	// create symmetric matrix
	A.SetFrom(src, cmat.SYMM)
	A0 := cmat.NewCopy(A)

	W := lapackd.Workspace(lapackd.TRDReduceWork(A, conf))
	lapackd.TRDReduce(A, tau, W, gomas.UPPER, conf)

	// make tridiagonal matrix T
	T0 := cmat.NewMatrix(N, N)
	dt.Diag(T0)
	da.Diag(A)
	blasd.Copy(&dt, &da)

	ea.Diag(A, 1)
	et.Diag(T0, 1)
	blasd.Copy(&et, &ea)
	et.Diag(T0, -1)
	blasd.Copy(&et, &ea)
	T1 := cmat.NewCopy(T0)

	// compute Q*T*Q.T (unblocked)
	conf.LB = 0
	lapackd.TRDMult(T0, A, tau, W, gomas.LEFT|gomas.UPPER, conf)
	lapackd.TRDMult(T0, A, tau, W, gomas.RIGHT|gomas.TRANS|gomas.UPPER, conf)

	blasd.Plus(T0, A0, 1.0, -1.0, gomas.NONE)
	nrm := lapackd.NormP(T0, lapackd.NORM_ONE)
	t.Logf("N=%d, unblk.||A - Q*T*Q.T||_1: %e\n", N, nrm)

	// compute Q*T*Q.T (blocked)
	conf.LB = nb
	W = lapackd.Workspace(lapackd.TRDMultWork(A, gomas.LEFT|gomas.UPPER, conf))
	lapackd.TRDMult(T1, A, tau, W, gomas.LEFT|gomas.UPPER, conf)
	lapackd.TRDMult(T1, A, tau, W, gomas.RIGHT|gomas.TRANS|gomas.UPPER, conf)

	blasd.Plus(T1, A0, 1.0, -1.0, gomas.NONE)
	nrm = lapackd.NormP(T1, lapackd.NORM_ONE)
	t.Logf("N=%d,   blk.||A - Q*T*Q.T||_1: %e\n", N, nrm)
}
Beispiel #13
0
func test_trdevd(N, flags, kind int, verbose bool, t *testing.T) {
	var At, sD, sE, tmp cmat.FloatMatrix

	A0 := cmat.NewMatrix(N, N)
	desc := setTrdDiagonals(A0, kind)
	At.SubMatrix(A0, 0, 0, N, N)
	sD.Diag(A0, 0)
	sE.Diag(A0, 1)
	D := cmat.NewCopy(&sD)
	E := cmat.NewCopy(&sE)

	V := cmat.NewMatrix(N, N)
	sD.Diag(V, 0)
	sD.Add(1.0)

	W := cmat.NewMatrix(4*N, 1)
	C := cmat.NewMatrix(N, N)

	if verbose && N < 10 {
		t.Logf("A0:\n%v\n", A0.ToString("%6.3f"))
		t.Logf("V.pre:\n%v\n", V.ToString("%6.3f"))
	}
	lapackd.TRDEigen(D, E, V, W, flags|gomas.WANTV)
	for k := 0; k < N-1; k++ {
		if E.GetAt(k) != 0.0 {
			t.Logf("E[%d] != 0.0 (%e)\n", k, E.GetAt(k))
		}
	}

	blasd.Mult(C, V, V, 1.0, 0.0, gomas.TRANSB)
	sD.Diag(C)
	sD.Add(-1.0)
	nrmv := lapackd.NormP(C, lapackd.NORM_ONE)

	blasd.Mult(C, V, A0, 1.0, 0.0, gomas.TRANSA)
	blasd.Mult(&At, C, V, 1.0, 0.0, gomas.NONE)
	if verbose && N < 10 {
		t.Logf("D:\n%v\n", asRow(&tmp, D).ToString("%6.3f"))
		t.Logf("V:\n%v\n", V.ToString("%6.3f"))
		t.Logf("V.T*A*V\n%v\n", At.ToString("%6.3f"))
	}
	sD.Diag(&At)
	blasd.Axpy(&sD, D, -1.0)
	nrma := lapackd.NormP(&At, lapackd.NORM_ONE)

	t.Logf("N=%d [%s] ||V.T*A*V - eigen(A)||_1: %e\n", N, desc, nrma)
	t.Logf("  ||I - V.T*V||_1: %e\n", nrmv)
}
Beispiel #14
0
// m > n: A[m,n], I[m,m] --> A.T == A.T*I == A.T*Q*Q.T
func TestBlockedQRMultRightIdent(t *testing.T) {
	M := 511
	N := 489
	A := cmat.NewMatrix(M, N)
	C := cmat.NewMatrix(N, M)
	tau := cmat.NewMatrix(N, 1)

	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)
	A0 := cmat.NewCopy(A)
	C.Transpose(A)
	conf := gomas.NewConf()
	conf.LB = 32

	// QR = A = Q*R
	W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
	lapackd.QRFactor(A, tau, W, conf)

	// C = A.T*Q
	W = lapackd.Workspace(lapackd.QRMultWork(C, gomas.RIGHT, conf))
	lapackd.QRMult(C, A, tau, W, gomas.RIGHT, conf)

	// C = C*Q.T == A.T*Q*Q.T
	lapackd.QRMult(C, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)
	//t.Logf("A*Q*Q.T:\n%v\n", C)

	// A = A - (A.T*Q*Q.T).T
	blasd.Plus(A0, C, 1.0, -1.0, gomas.TRANSB)
	// ||A - (A.T*Q*Q.T).T||_1
	nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
	t.Logf("M=%d,N=%d  ||A - (A.T*Q*Q.T).T||_1: %e\n", M, N, nrm)
}
Beispiel #15
0
func TestSolveBKLowerBig(t *testing.T) {
	N := 427
	normsrc := cmat.NewFloatNormSource(5.0, 10.0)
	A := cmat.NewMatrix(N, N)
	A.SetFrom(normsrc, cmat.LOWER)

	X := cmat.NewMatrix(N, 2)
	X.SetFrom(normsrc)
	B := cmat.NewCopy(X)
	blasd.MultSym(B, A, X, 1.0, 0.0, gomas.LOWER|gomas.LEFT)

	ipiv := lapackd.NewPivots(N)

	conf := gomas.NewConf()
	conf.LB = 16
	W := lapackd.Workspace(lapackd.BKFactorWork(A, conf))
	lapackd.BKFactor(A, W, ipiv, gomas.LOWER, conf)

	lapackd.BKSolve(B, A, ipiv, gomas.LOWER, conf)
	ok := B.AllClose(X)
	t.Logf("N=%d unblk.BK(X) == A.-1*B : %v\n", N, ok)
	blasd.Plus(B, X, 1.0, -1.0, gomas.NONE)
	nrm := lapackd.NormP(B, lapackd.NORM_ONE)
	t.Logf("  ||X - A.-1*B||_1: %.4e\n", nrm)

}
Beispiel #16
0
// test that unblocked and blocked QRT are equal
func TestDecomposeQRT(t *testing.T) {
	M := 615
	N := 591
	nb := 16

	conf := gomas.NewConf()
	conf.LB = nb

	A := cmat.NewMatrix(M, N)
	T := cmat.NewMatrix(nb, N)
	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)

	A0 := cmat.NewCopy(A)
	T0 := cmat.NewMatrix(N, N)

	// blocked: QR = A = Q*R
	W := lapackd.Workspace(lapackd.QRTFactorWork(A, conf))
	lapackd.QRTFactor(A, T, W, conf)

	conf.LB = 0
	lapackd.QRTFactor(A0, T0, W, conf)

	ok := A.AllClose(A0)
	t.Logf("blk.DecomposeQRT(A) == unblk.DecomposeQRT(A): %v\n", ok)

}
Beispiel #17
0
// test: A - Q*Hess(A)*Q.T  == 0
func TestMultHess(t *testing.T) {
	N := 377
	nb := 16

	conf := gomas.NewConf()
	conf.LB = nb

	A := cmat.NewMatrix(N, N)
	tau := cmat.NewMatrix(N, 1)
	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)
	A0 := cmat.NewCopy(A)

	// reduction
	W := lapackd.Workspace(lapackd.HessReduceWork(A, conf))
	lapackd.HessReduce(A, tau, W, conf)

	var Hlow cmat.FloatMatrix
	H := cmat.NewCopy(A)

	// set triangular part below first subdiagonal to zeros
	zeros := cmat.NewFloatConstSource(0.0)
	Hlow.SubMatrix(H, 1, 0, N-1, N-1)
	Hlow.SetFrom(zeros, cmat.LOWER|cmat.UNIT)
	H1 := cmat.NewCopy(H)

	// H := Q*H*Q.T
	conf.LB = nb
	lapackd.HessMult(H, A, tau, W, gomas.LEFT, conf)
	lapackd.HessMult(H, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)

	// H := Q*H*Q.T
	conf.LB = 0
	lapackd.HessMult(H1, A, tau, W, gomas.LEFT, conf)
	lapackd.HessMult(H1, A, tau, W, gomas.RIGHT|gomas.TRANS, conf)

	// compute ||Q*Hess(A)*Q.T - A||_1
	blasd.Plus(H, A0, 1.0, -1.0, gomas.NONE)
	nrm := lapackd.NormP(H, lapackd.NORM_ONE)
	t.Logf("  blk.|| Q*Hess(A)*Q.T - A ||_1 : %e\n", nrm)

	blasd.Plus(H1, A0, 1.0, -1.0, gomas.NONE)
	nrm = lapackd.NormP(H1, lapackd.NORM_ONE)
	t.Logf("unblk.|| Q*Hess(A)*Q.T - A ||_1 : %e\n", nrm)
}
Beispiel #18
0
// test: unblk.QLFactor == blk.QLFactor
func TestQLFactor(t *testing.T) {
	var t0 cmat.FloatMatrix
	M := 911
	N := 835
	nb := 32
	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)

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

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

	conf.LB = nb
	W1 := lapackd.Workspace(lapackd.QLFactorWork(A1, conf))
	lapackd.QLFactor(A1, tau1, W1, conf)

	if N < 10 {
		t.Logf("unblkQL(A):\n%v\n", A)
		t0.SetBuf(1, tau.Len(), 1, tau.Data())
		t.Logf("unblkQL.tau:\n%v\n", &t0)
		t.Logf("blkQL(A):\n%v\n", A1)
		t0.SetBuf(1, tau1.Len(), 1, tau1.Data())
		t.Logf("blkQL.tau:\n%v\n", &t0)
	}

	blasd.Plus(A1, A, 1.0, -1.0, gomas.NONE)
	nrm := lapackd.NormP(A1, lapackd.NORM_ONE)
	t.Logf("M=%d, N=%d ||blkQL(A) - unblkQL(A)||_1: %e\n", M, N, nrm)

	blasd.Axpy(tau1, tau, -1.0)
	nrm = blasd.Nrm2(tau1)
	t.Logf("     ||blkQL.tau - unblkQL.tau||_1: %e\n", nrm)

}
Beispiel #19
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)
}
Beispiel #20
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)
}
Beispiel #21
0
// QR decompose A, then compute ||A - Q*R||_1, should be small
func TestMultQTLeft(t *testing.T) {
	M := 513
	N := 477
	nb := 16
	A := cmat.NewMatrix(M, N)
	T := cmat.NewMatrix(nb, N)

	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)
	A0 := cmat.NewCopy(A)

	conf := gomas.NewConf()
	conf.LB = nb
	//t.Logf("A0:\n%v\n", A0)

	// QR = A = Q*R
	W := lapackd.Workspace(lapackd.QRTFactorWork(A, conf))
	lapackd.QRTFactor(A, T, W, conf)
	//t.Logf("T:\n%v\n", T)

	// C = TriU(QR) = R
	C := cmat.TriU(cmat.NewCopy(A), cmat.NONE)
	//t.Logf("R:\n%v\n", C)

	// C = Q*C
	W = lapackd.Workspace(lapackd.QRTMultWork(C, T, gomas.LEFT, conf))
	err := lapackd.QRTMult(C, A, T, W, gomas.LEFT, conf)
	if err != nil {
		t.Logf("err: %v\n", err)
	}

	// A = A - QR
	blasd.Plus(A0, C, 1.0, -1.0, gomas.NONE)
	// ||A - Q*R||_1
	nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
	t.Logf("M=%d,N=%d  ||A - Q*R||_1: %e\n", M, N, nrm)
}
Beispiel #22
0
// Simple and slow QR decomposition with Givens rotations
func TestGivensQR(t *testing.T) {
	var d cmat.FloatMatrix
	M := 181
	N := 159
	A := cmat.NewMatrix(M, N)
	A1 := cmat.NewCopy(A)

	ones := cmat.NewFloatConstSource(1.0)
	src := cmat.NewFloatNormSource()
	A.SetFrom(src)
	A0 := cmat.NewCopy(A)

	Qt := cmat.NewMatrix(M, M)
	d.Diag(Qt)
	d.SetFrom(ones)

	// R = G(n)...G(2)G(1)*A; Q = G(1).T*G(2).T...G(n).T ;  Q.T = G(n)...G(2)G(1)

	// for all columns ...
	for j := 0; j < N; j++ {
		// ... zero elements below diagonal, starting from bottom
		for i := M - 2; i >= j; i-- {
			c, s, r := lapackd.ComputeGivens(A.Get(i, j), A.Get(i+1, j))
			A.Set(i, j, r)
			A.Set(i+1, j, 0.0)
			// apply rotations on this row starting from column j, N-j column
			lapackd.ApplyGivensLeft(A, i, i+1, j+1, N-j-1, c, s)
			// update Qt = G(k)*Qt
			lapackd.ApplyGivensLeft(Qt, i, i+1, 0, M, c, s)
		}
	}
	// check: A = Q*R
	blasd.Mult(A1, Qt, A, 1.0, 0.0, gomas.TRANSA)
	blasd.Plus(A0, A1, 1.0, -1.0, gomas.NONE)
	nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
	t.Logf("M=%d, N=%d ||A - G(n)..G(1)*R||_1: %e\n", M, N, nrm)
}
Beispiel #23
0
func TestQLBuildwithK(t *testing.T) {
	var dc cmat.FloatMatrix
	M := 711
	N := 707
	K := 691
	lb := 36
	conf := gomas.NewConf()

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

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

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

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

	conf.LB = lb
	W1 := lapackd.Workspace(lapackd.QLBuildWork(A1, conf))
	lapackd.QLBuild(A1, tau, W1, K, conf)
	if N < 10 {
		t.Logf("blk.QLBuild Q:\n%v\n", A1)
	}
	// compute: I - Q.T*Q
	blasd.Mult(C, A1, A1, 1.0, 0.0, gomas.TRANSA, 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.QLBuild(A) - blk.QLBuild(A)||_1 :%e\n", M, N, K, n2)
	t.Logf("unblk M=%d, N=%d, K=%d ||Q.T*Q - I||_1 : %e\n", M, N, K, n0)
	t.Logf("blk   M=%d, N=%d, K=%d ||Q.T*Q - I||_1 : %e\n", M, N, K, n1)
}
Beispiel #24
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)
}
Beispiel #25
0
func main() {
	flag.Parse()

	M := N + N/10

	conf := gomas.CurrentConf()

	A := cmat.NewMatrix(M, N)
	A0 := cmat.NewCopy(A)
	tau := cmat.NewMatrix(N, 1)
	W := lapackd.Workspace(lapackd.QRFactorWork(A, conf))
	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)

	cumtime := 0.0
	mintime := 0.0
	maxtime := 0.0
	for i := 0; i < count; i++ {
		flushCache()

		t1 := time.Now()
		// ----------------------------------------------

		lapackd.QRFactor(A, tau, W, conf)

		// ----------------------------------------------
		t2 := time.Now()
		tm := t2.Sub(t1)

		if mintime == 0.0 || tm.Seconds() < mintime {
			mintime = tm.Seconds()
		}
		if maxtime == 0.0 || tm.Seconds() > maxtime {
			maxtime = tm.Seconds()
		}
		cumtime += tm.Seconds()
		if verbose {
			fmt.Printf("%3d  %12.4f msec, %9.4f gflops\n",
				i, 1e+3*tm.Seconds(), gflops(M, N, tm.Seconds()))
		}
		blasd.Copy(A, A0)
	}
	cumtime /= float64(count)
	minflops := gflops(M, N, maxtime)
	avgflops := gflops(M, N, cumtime)
	maxflops := gflops(M, N, mintime)
	fmt.Printf("%5d %5d %3d %9.4f %9.4f %9.4f Gflops\n", M, N, conf.LB, minflops, avgflops, maxflops)
}
Beispiel #26
0
func TestBiredWide(t *testing.T) {
	N := 811
	M := 693
	nb := 32
	conf := gomas.NewConf()
	conf.LB = 0
	ediag := -1

	zeromean := cmat.NewFloatNormSource()
	A := cmat.NewMatrix(M, N)
	A.SetFrom(zeromean)
	A0 := cmat.NewCopy(A)

	tauq := cmat.NewMatrix(N, 1)
	taup := cmat.NewMatrix(N, 1)

	W := lapackd.Workspace(M + N)
	lapackd.BDReduce(A, tauq, taup, W, conf)

	var D, E, Bd, Be cmat.FloatMatrix
	D.Diag(A)
	E.Diag(A, ediag)

	B := cmat.NewMatrix(M, N)
	Bd.Diag(B)
	Be.Diag(B, ediag)
	blasd.Copy(&Bd, &D)
	blasd.Copy(&Be, &E)

	Bt := cmat.NewMatrix(N, M)
	blasd.Transpose(Bt, B)

	conf.LB = nb
	W0 := lapackd.Workspace(lapackd.BDMultWork(B, conf))
	lapackd.BDMult(B, A, tauq, W0, gomas.MULTQ|gomas.LEFT, conf)
	lapackd.BDMult(Bt, A, tauq, W0, gomas.MULTQ|gomas.RIGHT|gomas.TRANS, conf)

	lapackd.BDMult(B, A, taup, W0, gomas.MULTP|gomas.RIGHT|gomas.TRANS, conf)
	lapackd.BDMult(Bt, A, taup, W0, gomas.MULTP|gomas.LEFT, conf)

	blasd.Plus(B, A0, 1.0, -1.0, gomas.NONE)
	nrm := lapackd.NormP(B, lapackd.NORM_ONE)
	t.Logf("M=%d, N=%d ||A - Q*B*P.T||_1   : %e\n", M, N, nrm)
	blasd.Plus(Bt, A0, 1.0, -1.0, gomas.TRANSB)
	nrm = lapackd.NormP(Bt, lapackd.NORM_ONE)
	t.Logf("M=%d, N=%d ||A.T - P*B.T*Q.T||_1 : %e\n", M, N, nrm)
}
Beispiel #27
0
func TestQRBuild(t *testing.T) {
	var d cmat.FloatMatrix

	M := 911
	N := 899
	K := 873
	lb := 36
	conf := gomas.NewConf()

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

	C := cmat.NewMatrix(N, N)
	d.Diag(C)

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

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

	blasd.Mult(C, A, A, 1.0, 0.0, gomas.TRANSA, conf)
	blasd.Add(&d, -1.0)
	n0 := lapackd.NormP(C, lapackd.NORM_ONE)

	conf.LB = lb
	W2 := lapackd.Workspace(lapackd.QRBuildWork(A, conf))
	lapackd.QRBuild(A1, tau, W2, K, conf)

	blasd.Mult(C, A1, A1, 1.0, 0.0, gomas.TRANSA, conf)
	blasd.Add(&d, -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.QRBuild(A) - blk.QRBuild(A)||_1 :%e\n", M, N, K, n2)
	t.Logf("unblk M=%d, N=%d, K=%d ||I - Q.T*Q||_1: %e\n", M, N, K, n0)
	t.Logf("  blk M=%d, N=%d, K=%d ||I - Q.T*Q||_1: %e\n", M, N, K, n1)
}
Beispiel #28
0
func testEigen(N int, bits int, t *testing.T) {
	var A, A0, W, D, V *cmat.FloatMatrix
	var sD cmat.FloatMatrix
	var s string = "lower"

	if bits&gomas.UPPER != 0 {
		s = "upper"
	}

	wsize := N * N
	if wsize < 100 {
		wsize = 100
	}

	D = cmat.NewMatrix(N, 1)
	A = cmat.NewMatrix(N, N)
	V = cmat.NewMatrix(N, N)

	src := cmat.NewFloatNormSource()
	A.SetFrom(src, cmat.SYMM)
	A0 = cmat.NewCopy(A)
	W = cmat.NewMatrix(wsize, 1)

	if err := lapackd.EigenSym(D, A, W, bits|gomas.WANTV); err != nil {
		t.Errorf("EigenSym error: %v\n", err)
		return
	}

	// ||I - V.T*V||
	sD.Diag(V)
	blasd.Mult(V, A, A, 1.0, 0.0, gomas.TRANSA)
	blasd.Add(&sD, -1.0)
	nrm1 := lapackd.NormP(V, lapackd.NORM_ONE)

	// left vectors are M-by-N
	V.Copy(A)
	lapackd.MultDiag(V, D, gomas.RIGHT)
	blasd.Mult(A0, V, A, -1.0, 1.0, gomas.TRANSB)
	nrm2 := lapackd.NormP(A0, lapackd.NORM_ONE)

	t.Logf("N=%d, [%s] ||A - V*D*V.T||_1 :%e\n", N, s, nrm2)
	t.Logf("  ||I - V.T*V||_1 : %e\n", nrm1)
}
Beispiel #29
0
func TestBKLowerBig(t *testing.T) {
	N := 411
	normsrc := cmat.NewFloatNormSource(5.0, 10.0)
	A := cmat.NewMatrix(N, N)
	A.SetFrom(normsrc, cmat.LOWER)
	A0 := cmat.NewCopy(A)

	ipiv := lapackd.NewPivots(N)
	ipiv0 := lapackd.NewPivots(N)

	conf := gomas.NewConf()
	conf.LB = 0

	// unblocked
	W := lapackd.Workspace(lapackd.BKFactorWork(A, conf))
	err := lapackd.BKFactor(A, W, ipiv, gomas.LOWER, conf)
	if err != nil {
		t.Logf("unblk.err: %v\n", err)
	}

	// blocked
	conf.LB = 8
	W = lapackd.Workspace(lapackd.BKFactorWork(A0, conf))
	err = lapackd.BKFactor(A0, W, ipiv0, gomas.LOWER, conf)
	if err != nil {
		t.Logf("blk.err: %v\n", err)
	}
	ok := A.AllClose(A0)
	t.Logf("N=%d unblk.A == blk.A : %v\n", N, ok)

	if !ok {
		r, c := errorLoc(A, A0)
		t.Logf("unblk.A != blk.A at: %d, %d\n", r, c)
		for k, _ := range ipiv {
			t.Logf("%3d  %3d  %3d\n", k, ipiv[k], ipiv0[k])
		}
	}
}
Beispiel #30
0
// m > n: A[m,n], I[m,m] --> A.T == A.T*I == A.T*Q*Q.T
func TestQRTMultRightIdent(t *testing.T) {
	M := 511
	N := 399
	nb := 16
	A := cmat.NewMatrix(M, N)
	C := cmat.NewMatrix(N, M)
	T := cmat.NewMatrix(nb, N)

	zeromean := cmat.NewFloatNormSource()
	A.SetFrom(zeromean)
	A0 := cmat.NewCopy(A)
	C.Transpose(A)

	conf := gomas.NewConf()
	conf.LB = nb

	// QR = A = Q*R
	W := lapackd.Workspace(lapackd.QRTFactorWork(A, conf))
	lapackd.QRTFactor(A, T, W, conf)

	// C = A*Q
	W = lapackd.Workspace(lapackd.QRTMultWork(C, T, gomas.RIGHT, conf))
	err := lapackd.QRTMult(C, A, T, W, gomas.RIGHT, conf)
	if err != nil {
		t.Logf("err: %v\n", err)
	}
	// C = C*Q.T == A*Q*Q.T
	err = lapackd.QRTMult(C, A, T, W, gomas.RIGHT|gomas.TRANS, conf)
	if err != nil {
		t.Logf("err: %v\n", err)
	}

	// A = A - (A.T*Q*Q.T).T
	blasd.Plus(A0, C, 1.0, -1.0, gomas.TRANSB)
	// ||A - Q*R||_1
	nrm := lapackd.NormP(A0, lapackd.NORM_ONE)
	t.Logf("M=%d,N=%d  ||A - (A.T*Q*Q.T).T||_1: %e\n", M, N, nrm)
}