func _TestMultMVTransA(t *testing.T) {
	bM := 1000 * M
	bN := 1000 * N
	A := matrix.FloatNormal(bN, bM)
	X := matrix.FloatWithValue(bN, 1, 1.0)
	Y1 := matrix.FloatZeros(bM, 1)
	Y0 := matrix.FloatZeros(bM, 1)

	Ar := A.FloatArray()
	Xr := X.FloatArray()
	Y1r := Y1.FloatArray()

	blas.GemvFloat(A, X, Y0, 1.0, 1.0, linalg.OptTrans)

	DMultMV(Y1r, Ar, Xr, 1.0, 1.0, TRANSA, 1, A.LeadingIndex(), 1, 0, bN, 0, bM, 4, 4)
	ok := Y0.AllClose(Y1)
	t.Logf("Y0 == Y1: %v\n", ok)
	if !ok {
		var y1, y0 matrix.FloatMatrix
		Y1.SubMatrix(&y1, 0, 0, 5, 1)
		t.Logf("Y1[0:5]:\n%v\n", y1)
		Y0.SubMatrix(&y0, 0, 0, 5, 1)
		t.Logf("Y0[0:5]:\n%v\n", y0)
	}
}

func (gp *gpConvexProg) F1(x *matrix.FloatMatrix) (f, Df *matrix.FloatMatrix, err error) {
    f = nil
    Df = nil
    err = nil
    f = matrix.FloatZeros(gp.mnl+1, 1)
    Df = matrix.FloatZeros(gp.mnl+1, gp.n)
    y := gp.g.Copy()
    blas.GemvFloat(gp.F, x, y, 1.0, 1.0)

    for i, s := range gp.ind {
        start := s[0]
        stop := s[1]
        // yi := exp(yi) = exp(Fi*x+gi)
        ymax := maxvec(y.FloatArray()[start:stop])
        // ynew = exp(y[start:stop] - ymax)
        ynew := matrix.Exp(matrix.FloatVector(y.FloatArray()[start:stop]).Add(-ymax))
        y.SetIndexesFromArray(ynew.FloatArray(), matrix.Indexes(start, stop)...)

        // fi = log sum yi = log sum exp(Fi*x+gi)
        ysum := blas.AsumFloat(y, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
        f.SetIndex(i, ymax+math.Log(ysum))

        blas.ScalFloat(y, 1.0/ysum, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
        blas.GemvFloat(gp.F, y, Df, 1.0, 0.0, la.OptTrans, &la.IOpt{"m", stop - start},
            &la.IOpt{"incy", gp.mnl + 1}, &la.IOpt{"offseta", start},
            &la.IOpt{"offsetx", start}, &la.IOpt{"offsety", i})
    }
    return
}

func _TestMultSymmLowerSmall(t *testing.T) {
	//bM := 5
	bN := 7
	bP := 7
	Adata := [][]float64{
		[]float64{1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
		[]float64{1.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0},
		[]float64{1.0, 2.0, 3.0, 0.0, 0.0, 0.0, 0.0},
		[]float64{1.0, 2.0, 3.0, 4.0, 0.0, 0.0, 0.0},
		[]float64{1.0, 2.0, 3.0, 4.0, 5.0, 0.0, 0.0},
		[]float64{1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 0.0},
		[]float64{1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0}}

	A := matrix.FloatMatrixFromTable(Adata, matrix.RowOrder)
	B := matrix.FloatNormal(bN, bP)
	C0 := matrix.FloatZeros(bN, bP)
	C1 := matrix.FloatZeros(bN, bP)

	Ar := A.FloatArray()
	Br := B.FloatArray()
	C1r := C1.FloatArray()

	blas.SymmFloat(A, B, C0, 1.0, 1.0, linalg.OptLower, linalg.OptRight)

	DMultSymm(C1r, Ar, Br, 1.0, 1.0, LOWER|RIGHT, bN, A.LeadingIndex(), bN,
		bN, 0, bP, 0, bN, 2, 2, 2)
	ok := C0.AllClose(C1)
	t.Logf("C0 == C1: %v\n", ok)
	if !ok {
		t.Logf("A=\n%v\n", A)
		t.Logf("blas: C=A*B\n%v\n", C0)
		t.Logf("C1: C1 = A*X\n%v\n", C1)
	}
}

func TestQRSmal(t *testing.T) {
	data := [][]float64{
		[]float64{12.0, -51.0, 4.0},
		[]float64{6.0, 167.0, -68.0},
		[]float64{-4.0, 24.0, -41.0}}

	A := matrix.FloatMatrixFromTable(data, matrix.RowOrder)
	T := matrix.FloatZeros(A.Cols(), A.Cols())
	T0 := T.Copy()

	M := A.Rows()
	//N := A.Cols()
	Tau := matrix.FloatZeros(M, 1)
	X, _ := DecomposeQR(A.Copy(), Tau, nil, 0)
	t.Logf("A\n%v\n", A)
	t.Logf("X\n%v\n", X)
	t.Logf("Tau\n%v\n", Tau)

	Tau0 := matrix.FloatZeros(M, 1)
	lapack.Geqrf(A, Tau0)
	t.Logf("lapack X\n%v\n", A)
	t.Logf("lapack Tau\n%v\n", Tau0)

	unblkQRBlockReflector(X, Tau, T)
	t.Logf("T:\n%v\n", T)

	V := TriLU(X.Copy())
	lapack.LarftFloat(V, Tau, T0)
	t.Logf("T0:\n%v\n", T0)

}

func _TestMultMV(t *testing.T) {
	bM := 100 * M
	bN := 100 * N
	A := matrix.FloatNormal(bM, bN)
	X := matrix.FloatNormal(bN, 1)
	Y1 := matrix.FloatZeros(bM, 1)
	Y0 := matrix.FloatZeros(bM, 1)

	Ar := A.FloatArray()
	Xr := X.FloatArray()
	Y1r := Y1.FloatArray()

	blas.GemvFloat(A, X, Y0, 1.0, 1.0)

	DMultMV(Y1r, Ar, Xr, 1.0, 1.0, NOTRANS, 1, A.LeadingIndex(), 1, 0, bN, 0, bM, 32, 32)
	t.Logf("Y0 == Y1: %v\n", Y0.AllClose(Y1))
	/*
	   if ! Y0.AllClose(Y1) {
	       y0 := Y0.SubMatrix(0, 0, 2, 1)
	       y1 := Y1.SubMatrix(0, 0, 2, 1)
	       t.Logf("y0=\n%v\n", y0)
	       t.Logf("y1=\n%v\n", y1)
	   }
	*/
}

func TestMultQT(t *testing.T) {
	M := 60
	N := 40
	K := 30
	nb := 12
	A := matrix.FloatUniform(M, N)
	B := matrix.FloatUniform(M, K)
	W := matrix.FloatZeros(N, nb)
	T := matrix.FloatZeros(N, N)

	// QR = Q*R
	QR, err := DecomposeQRT(A.Copy(), T, W, nb)
	if err != nil {
		t.Logf("decompose-err: %v\n", err)
	}

	// compute: B - Q*Q.T*B = 0

	// X = Q*Q.T*B
	X := B.Copy()
	MultQT(X, QR, T, W, LEFT|TRANS, nb)
	MultQT(X, QR, T, W, LEFT, nb)
	B.Minus(X)

	// ||B - Q*Q.T*B||_1
	nrm := NormP(B, NORM_ONE)
	t.Logf("||B - Q*Q.T*B||_1: %e\n", nrm)
}

func TestUpdateTrmMV(t *testing.T) {
	//bM := 5
	bN := 8
	//bP := 4
	nb := 4
	X := matrix.FloatNormal(bN, 1)
	//B := matrix.FloatNormal(bP, bN)
	Y := X.Copy()
	C0 := matrix.FloatZeros(bN, bN)
	C2 := matrix.FloatZeros(bN, bN)
	C1 := matrix.FloatZeros(bN, bN)

	Xr := X.FloatArray()
	Yr := Y.FloatArray()
	C1r := C1.FloatArray()
	C0r := C0.FloatArray()
	C2r := C2.FloatArray()

	// no transpose
	DRankMV(C1r, Xr, Yr, 1.0, C1.LeadingIndex(), 1, 1,
		0, bN, 0, bN, nb, nb)
	DTrmUpdMV(C0r, Xr, Yr, 1.0, LOWER, C0.LeadingIndex(), 1, 1,
		0, bN, nb)
	DTrmUpdMV(C2r, Xr, Yr, 1.0, UPPER, C2.LeadingIndex(), 1, 1,
		0, bN, nb)

	t.Logf("C1:\n%v\nC0:\n%v\nC2:\n%v\n", C1, C0, C2)
	// C0 == C2.T
	t.Logf("C0 == C2.T: %v\n", C0.AllClose(C2.Transpose()))
	// C1 == C1 - C2 + C0.T
	Cn := matrix.Minus(C1, C2)
	Cn.Plus(C0.Transpose())
	t.Logf("C1 == C1 - C2 + C0.T: %v\n", Cn.AllClose(C1))

}

func TestSolveLeastSquaresQRT(t *testing.T) {
	M := 60
	N := 40
	K := 30
	nb := 12

	A := matrix.FloatUniform(M, N)
	B := matrix.FloatZeros(M, K)
	X0 := matrix.FloatUniform(N, K)

	// B = A*X0
	Mult(B, A, X0, 1.0, 0.0, NOTRANS)
	W := matrix.FloatZeros(N, nb)
	T := matrix.FloatZeros(N, N)

	QR, err := DecomposeQRT(A, T, W, nb)
	if err != nil {
		t.Logf("decompose error: %v\n", err)
	}
	// B' = A.-1*B
	err = SolveQRT(B, QR, T, W, NOTRANS, nb)

	// expect B[0:N, 0:K] == X0, B[N:M, 0:K] == 0.0
	var Xref matrix.FloatMatrix
	Bref := matrix.FloatZeros(M, K)
	Bref.SubMatrix(&Xref, 0, 0, N, K)
	Xref.Plus(X0)
	Bref.Minus(B)
	t.Logf("\nmin ||B - A*X0||\n\twhere B = A*X0\n")
	t.Logf("||B - A*X0||_1 ~~ 0.0: %e\n", NormP(Bref, NORM_ONE))
}

func runTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {
	var W *matrix.FloatMatrix = nil
	var mintime time.Duration

	N := A.Cols()
	tau := matrix.FloatZeros(N, 1)
	if LB > 0 {
		W = matrix.FloatZeros(A.Rows(), LB)
	}
	fnc := func() {
		_, ERRmatops = matops.DecomposeQR(A, tau, W, LB)
	}

	A0 := A.Copy()
	for n := 0; n < ntest; n++ {
		if n > 0 {
			// restore original A
			A0.CopyTo(A)
			tau.Scale(0.0)
		}
		mperf.FlushCache()
		time0 := mperf.Timeit(fnc)
		if n == 0 || time0 < mintime {
			mintime = time0
		}
		if verbose {
			fmt.Printf("%.4f ms\n", time0.Seconds()*1000.0)
		}
	}
	return mintime
}

//
// Solves a geometric program
//
//   minimize    log sum exp (F0*x+g0)
//   subject to  log sum exp (Fi*x+gi) <= 0,  i=1,...,m
//               G*x <= h      
//               A*x = b
//
func Gp(K []int, F, g, G, h, A, b *matrix.FloatMatrix, solopts *SolverOptions) (sol *Solution, err error) {

    if err = checkArgK(K); err != nil {
        return
    }
    l := sumdim(K)

    if F == nil || F.Rows() != l {
        err = errors.New(fmt.Sprintf("'F' must matrix with %d rows", l))
        return
    }

    if g == nil || !g.SizeMatch(l, 1) {
        err = errors.New(fmt.Sprintf("'g' must matrix with size (%d,1)", l))
        return
    }
    n := F.Cols()

    if G == nil {
        G = matrix.FloatZeros(0, n)
    }
    if h == nil {
        h = matrix.FloatZeros(0, 1)
    }
    if G.Cols() != n {
        err = errors.New(fmt.Sprintf("'G' must matrix with size %d columns", n))
        return
    }
    ml := G.Rows()
    if h == nil || !h.SizeMatch(ml, 1) {
        err = errors.New(fmt.Sprintf("'h' must matrix with size (%d,1)", ml))
        return
    }

    if A == nil {
        A = matrix.FloatZeros(0, n)
    }
    if b == nil {
        b = matrix.FloatZeros(0, 1)
    }
    if A.Cols() != n {
        err = errors.New(fmt.Sprintf("'A' must matrix with size %d columns", n))
        return
    }
    p := A.Rows()
    if b == nil || !b.SizeMatch(p, 1) {
        err = errors.New(fmt.Sprintf("'b' must matrix with size (%d,1)", p))
        return
    }

    dims := sets.NewDimensionSet("l", "q", "s")
    dims.Set("l", []int{ml})
    gpProg := createGpProg(K, F, g)

    return Cp(gpProg, G, h, A, b, dims, solopts)
}

// Returns min {t | x + t*e >= 0}, where e is defined as follows
//
//  - For the nonlinear and 'l' blocks: e is the vector of ones.
//  - For the 'q' blocks: e is the first unit vector.
//  - For the 's' blocks: e is the identity matrix.
//
// When called with the argument sigma, also returns the eigenvalues
// (in sigma) and the eigenvectors (in x) of the 's' components of x.
func maxStep(x *matrix.FloatMatrix, dims *sets.DimensionSet, mnl int, sigma *matrix.FloatMatrix) (rval float64, err error) {
	/*DEBUGGED*/

	rval = 0.0
	err = nil
	t := make([]float64, 0, 10)
	ind := mnl + dims.Sum("l")
	if ind > 0 {
		t = append(t, -minvec(x.FloatArray()[:ind]))
	}
	for _, m := range dims.At("q") {
		if m > 0 {
			v := blas.Nrm2Float(x, &la_.IOpt{"offset", ind + 1}, &la_.IOpt{"n", m - 1})
			v -= x.GetIndex(ind)
			t = append(t, v)
		}
		ind += m
	}

	//var Q *matrix.FloatMatrix
	//var w *matrix.FloatMatrix
	ind2 := 0
	//if sigma == nil && len(dims.At("s")) > 0 {
	//	mx := dims.Max("s")
	//	Q = matrix.FloatZeros(mx, mx)
	//	w = matrix.FloatZeros(mx, 1)
	//}
	for _, m := range dims.At("s") {
		if sigma == nil {
			Q := matrix.FloatZeros(m, m)
			w := matrix.FloatZeros(m, 1)
			blas.Copy(x, Q, &la_.IOpt{"offsetx", ind}, &la_.IOpt{"n", m * m})
			err = lapack.SyevrFloat(Q, w, nil, 0.0, nil, []int{1, 1}, la_.OptRangeInt,
				&la_.IOpt{"n", m}, &la_.IOpt{"lda", m})
			if m > 0 && err == nil {
				t = append(t, -w.GetIndex(0))
			}
		} else {
			err = lapack.SyevdFloat(x, sigma, la_.OptJobZValue, &la_.IOpt{"n", m},
				&la_.IOpt{"lda", m}, &la_.IOpt{"offseta", ind}, &la_.IOpt{"offsetw", ind2})
			if m > 0 {
				t = append(t, -sigma.GetIndex(ind2))
			}
		}
		ind += m * m
		ind2 += m
	}

	if len(t) > 0 {
		rval = maxvec(t)
	}
	return
}

// single invocation for matops and lapack functions
func runCheck(A *matrix.FloatMatrix, LB int) (bool, time.Duration, time.Duration) {

	var W *matrix.FloatMatrix = nil
	N := A.Cols()
	tau := matrix.FloatZeros(N, 1)
	if LB > 0 {
		W = matrix.FloatZeros(A.Rows(), LB)
	}
	fnc := func() {
		_, ERRmatops = matops.DecomposeQR(A, tau, W, LB)
	}

	if verbose && N < 10 {
		fmt.Fprintf(os.Stderr, "A start:\n%v\n", A)
	}
	A0 := A.Copy()
	tau0 := tau.Copy()

	mperf.FlushCache()
	time0 := mperf.Timeit(fnc)
	if verbose && N < 10 {
		fmt.Fprintf(os.Stderr, "A end:\n%v\n", A)
		tau.SetSize(1, N, 1)
		fmt.Fprintf(os.Stderr, "tau: %v\n", tau)
	}

	fn2 := func() {
		ERRlapack = lapack.Geqrf(A0, tau0)
	}

	mperf.FlushCache()
	time2 := mperf.Timeit(fn2)
	if verbose && N < 10 {
		fmt.Fprintf(os.Stderr, "A0 end:\n%v\n", A0)
		tau0.SetSize(1, N, 1) // row vector
		fmt.Fprintf(os.Stderr, "tau0: %v\n", tau0)
	}
	// now A == A0 && tau == tau0

	ok := A.AllClose(A0)
	oktau := tau.AllClose(tau0)
	if !ok || !oktau {
		// save result to globals
		Rlapack = A0
		Rmatops = A
		TAUlapack = tau0
		TAUmatops = tau
	}
	return ok && oktau, time0, time2
}

func _TestBK2(t *testing.T) {
	Bdata := [][]float64{
		[]float64{10.0, 20.0},
		[]float64{10.0, 20.0},
		[]float64{10.0, 20.0},
		[]float64{10.0, 20.0},
		[]float64{10.0, 20.0},
		[]float64{10.0, 20.0},
		[]float64{10.0, 20.0}}

	N := 7

	A0 := matrix.FloatNormal(N, N)
	A := matrix.FloatZeros(N, N)
	// A is symmetric, posivite definite
	Mult(A, A0, A0, 1.0, 1.0, TRANSB)

	X := matrix.FloatMatrixFromTable(Bdata, matrix.RowOrder)
	B := matrix.FloatZeros(N, 2)
	MultSym(B, A, X, 1.0, 0.0, LOWER|LEFT)
	t.Logf("initial B:\n%v\n", B)

	nb := 0
	W := matrix.FloatWithValue(A.Rows(), 5, 1.0)
	A.SetAt(4, 1, A.GetAt(4, 1)+1.0)
	A.SetAt(1, 4, A.GetAt(4, 1))

	ipiv := make([]int, N, N)
	L, _ := DecomposeBK(A.Copy(), W, ipiv, LOWER, nb)
	t.Logf("ipiv: %v\n", ipiv)
	t.Logf("L:\n%v\n", L)

	ipiv0 := make([]int, N, N)
	nb = 4
	L0, _ := DecomposeBK(A.Copy(), W, ipiv0, LOWER, nb)
	t.Logf("ipiv: %v\n", ipiv0)
	t.Logf("L:\n%v\n", L0)
	B0 := B.Copy()
	SolveBK(B0, L0, ipiv0, LOWER)
	t.Logf("B0:\n%v\n", B0)

	ipiv2 := make([]int32, N, N)
	lapack.Sytrf(A, ipiv2, linalg.OptLower)
	t.Logf("ipiv2: %v\n", ipiv2)
	t.Logf("lapack A:\n%v\n", A)
	lapack.Sytrs(A, B, ipiv2, linalg.OptLower)
	t.Logf("lapack B:\n%v\n", B)
	t.Logf("B == B0: %v\n", B.AllClose(B0))
}

func runRefTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {

	var mintime time.Duration

	N := A.Cols()
	tau := matrix.FloatZeros(N, 1)

	fnc := func() {
		ERRlapack = lapack.Geqrf(A, tau)
	}

	A0 := A.Copy()
	for n := 0; n < ntest; n++ {
		if n > 0 {
			// restore original A
			A0.CopyTo(A)
			tau.Scale(0.0)
		}
		mperf.FlushCache()
		time0 := mperf.Timeit(fnc)
		if n == 0 || time0 < mintime {
			mintime = time0
		}
	}
	return mintime
}

func _TestLDLnoPiv(t *testing.T) {
	N := 42
	nb := 8

	A0 := matrix.FloatUniform(N, N)
	A := matrix.FloatZeros(N, N)
	Mult(A, A0, A0, 1.0, 1.0, TRANSB)

	B := matrix.FloatNormal(A.Rows(), 2)
	w := matrix.FloatWithValue(A.Rows(), 2, 1.0)

	// B0 = A*B
	B0 := B.Copy()

	nb = 2
	L, _ := DecomposeLDLnoPiv(A.Copy(), w, LOWER, nb)
	Mult(B0, A, B, 1.0, 0.0, NOTRANS)
	SolveLDLnoPiv(B0, L, LOWER)
	t.Logf("L*D*L.T: ||B - A*X||_1: %e\n", NormP(B0.Minus(B), NORM_ONE))

	U, _ := DecomposeLDLnoPiv(A.Copy(), w, UPPER, nb)
	Mult(B0, A, B, 1.0, 0.0, NOTRANS)
	SolveLDLnoPiv(B0, U, UPPER)
	t.Logf("U*D*U.T: ||B - A*X||_1: %e\n", NormP(B0.Minus(B), NORM_ONE))

}

func runTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {

	var flags matops.Flags
	var mintime time.Duration

	N := A.Rows()
	ipiv := make([]int, N, N)
	flags = matops.LOWER
	if testUpper {
		flags = matops.UPPER
	}

	W := matrix.FloatZeros(A.Rows(), LB+2)
	fnc := func() {
		_, ERRmatops = matops.DecomposeBK(A, W, ipiv, flags, LB)
	}

	A0 := A.Copy()
	for n := 0; n < ntest; n++ {
		if n > 0 {
			// restore original A
			A0.CopyTo(A)
		}
		mperf.FlushCache()
		time0 := mperf.Timeit(fnc)
		if n == 0 || time0 < mintime {
			mintime = time0
		}
		if verbose {
			fmt.Printf("%.4f ms\n", time0.Seconds()*1000.0)
		}
	}
	return mintime
}

// In-place version of pack(), which also accepts matrix arguments x.
// The columns of x are elements of S, with the 's' components stored
// in unpacked storage.  On return, the 's' components are stored in
// packed storage and the off-diagonal entries are scaled by sqrt(2).
//
func pack2(x *matrix.FloatMatrix, dims *sets.DimensionSet, mnl int) (err error) {
	if len(dims.At("s")) == 0 {
		return nil
	}

	const sqrt2 = 1.41421356237309504880

	iu := mnl + dims.Sum("l", "q")
	ip := iu
	row := matrix.FloatZeros(1, x.Cols())
	//fmt.Printf("x.size = %d %d\n", x.Rows(), x.Cols())
	for _, n := range dims.At("s") {
		for k := 0; k < n; k++ {
			cnt := n - k
			row = x.GetRow(iu+(n+1)*k, row)
			//fmt.Printf("%02d: %v\n", iu+(n+1)*k, x.FloatArray())
			x.SetRow(ip, row)
			for i := 1; i < n-k; i++ {
				row = x.GetRow(iu+(n+1)*k+i, row)
				//fmt.Printf("%02d: %v\n", iu+(n+1)*k+i, x.FloatArray())
				x.SetRow(ip+i, row.Scale(sqrt2))
			}
			ip += cnt
		}
		iu += n * n
	}
	return nil
}

func _TestViewUpdate(t *testing.T) {
	Adata2 := [][]float64{
		[]float64{4.0, 2.0, 2.0},
		[]float64{6.0, 4.0, 2.0},
		[]float64{4.0, 6.0, 1.0},
	}

	A := matrix.FloatMatrixFromTable(Adata2, matrix.RowOrder)
	N := A.Rows()

	// simple LU decomposition without pivoting
	var A11, a10, a01, a00 matrix.FloatMatrix
	for k := 1; k < N; k++ {
		a00.SubMatrixOf(A, k-1, k-1, 1, 1)
		a01.SubMatrixOf(A, k-1, k, 1, A.Cols()-k)
		a10.SubMatrixOf(A, k, k-1, A.Rows()-k, 1)
		A11.SubMatrixOf(A, k, k)
		//t.Logf("A11: %v  a01: %v\n", A11, a01)
		a10.Scale(1.0 / a00.Float())
		MVRankUpdate(&A11, &a10, &a01, -1.0)
	}

	Ld := TriLU(A.Copy())
	Ud := TriU(A)
	t.Logf("Ld:\n%v\nUd:\n%v\n", Ld, Ud)
	An := matrix.FloatZeros(N, N)
	Mult(An, Ld, Ud, 1.0, 1.0, NOTRANS)
	t.Logf("A == Ld*Ud: %v\n", An.AllClose(An))
}

func runRefTest(A *matrix.FloatMatrix, ntest, LB int) time.Duration {

	var flags matops.Flags
	var mintime time.Duration

	N := A.Rows()
	ipiv := make([]int, N, N)
	flags = matops.LOWER
	if testUpper {
		flags = matops.UPPER
	}

	W := matrix.FloatZeros(A.Rows(), LB+2)
	fnc := func() {
		_, ERRref = matops.DecomposeLDL(A, W, ipiv, flags, 0)
	}

	A0 := A.Copy()
	for n := 0; n < ntest; n++ {
		if n > 0 {
			// restore original A
			A0.CopyTo(A)
		}
		mperf.FlushCache()
		time0 := mperf.Timeit(fnc)
		if n == 0 || time0 < mintime {
			mintime = time0
		}
	}
	return mintime
}

func blockedBuildQ(A, tau, W *matrix.FloatMatrix, nb int) error {
	var err error = nil
	var ATL, ATR, ABL, ABR, AL matrix.FloatMatrix
	var A00, A01, A02, A10, A11, A12, A20, A21, A22 matrix.FloatMatrix
	var tT, tB matrix.FloatMatrix
	var t0, tau1, t2, Tw, Wrk matrix.FloatMatrix
	var mb int

	mb = A.Rows() - A.Cols()
	Twork := matrix.FloatZeros(nb, nb)

	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, mb, 0, pBOTTOMRIGHT)
	partition2x1(
		&tT,
		&tB, tau, 0, pBOTTOM)

	// clearing of the columns of the right and setting ABR to unit diagonal
	// (only if not applying all reflectors, kb > 0)

	for ATL.Rows() > 0 && ATL.Cols() > 0 {
		repartition2x2to3x3(&ATL,
			&A00, &A01, &A02,
			&A10, &A11, &A12,
			&A20, &A21, &A22, A, nb, pTOPLEFT)
		repartition2x1to3x1(&tT,
			&t0,
			&tau1,
			&t2, tau, nb, pTOP)

		// --------------------------------------------------------

		// build block reflector from current block
		merge2x1(&AL, &A11, &A21)
		Twork.SubMatrix(&Tw, 0, 0, A11.Cols(), A11.Cols())
		unblkQRBlockReflector(&Tw, &AL, &tau1)

		// update with current block reflector (I - Y*T*Y.T)*Atrailing
		W.SubMatrix(&Wrk, 0, 0, A12.Cols(), A11.Cols())
		updateWithQT(&A12, &A22, &A11, &A21, &Tw, &Wrk, nb, false)

		// use unblocked version to compute current block
		W.SubMatrix(&Wrk, 0, 0, 1, A11.Cols())
		unblockedBuildQ(&AL, &tau1, &Wrk, 0)

		// zero upper part
		A01.SetIndexes(0.0)

		// --------------------------------------------------------
		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &A11, &A22, A, pTOPLEFT)
		continue3x1to2x1(
			&tT,
			&tB, &t0, &tau1, tau, pTOP)
	}
	return err
}