예제 #1
0
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)

}
예제 #2
0
파일: perf_qr.go 프로젝트: sguzwf/algorithm
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
}
예제 #3
0
파일: perf_qr.go 프로젝트: sguzwf/algorithm
// 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
}
예제 #4
0
func TestQRBlk(t *testing.T) {
	M := 8
	N := 6
	nb := 2

	A := matrix.FloatUniform(M, N)
	Tau := matrix.FloatZeros(M, 1)
	Tz := matrix.FloatZeros(N, N)
	Tx := matrix.FloatZeros(N, N)

	DecomposeBlockSize(0)
	Z, _ := DecomposeQRT(A.Copy(), Tz, nil, 0)
	_ = Z

	DecomposeBlockSize(nb)
	//X, _ := DecomposeQR(A.Copy(), Tau, nil)
	X, _ := DecomposeQRT(A.Copy(), Tx, nil, nb)

	Tau0 := matrix.FloatZeros(M, 1)
	A0 := A.Copy()
	lapack.Geqrf(A0, Tau0)
	ok := X.AllClose(A0)
	var dx matrix.FloatMatrix
	dx.DiagOf(Tx)
	//okt := Tau.AllClose(Tau0)
	okt := true
	_ = Tau
	t.Logf("lapack QR == DecomposeQR: %v\n", ok && okt)
	if !ok || !okt || true {
		t.Logf("A0: %d, %d, %d\n", A0.Rows(), A0.Cols(), A0.LeadingIndex())
		t.Logf("A\n%v\n", A)
		t.Logf("X\n%v\n", X)
		t.Logf("Tz\n%v\n", Tz)
		t.Logf("Tx\n%v\n", Tx)
		t.Logf("Tau\n%v\n", &dx)
		t.Logf("lapack X\n%v\n", A0)
		t.Logf("lapack Tau\n%v\n", Tau0)
	}
}
예제 #5
0
func TestQRT(t *testing.T) {
	M := 6
	N := 5

	var Tau matrix.FloatMatrix
	A := matrix.FloatUniform(M, N)
	T := matrix.FloatZeros(A.Cols(), A.Cols())
	T0 := T.Copy()

	X, _ := DecomposeQRT(A.Copy(), T, nil, 0)
	Tau.DiagOf(T)

	Tau0 := matrix.FloatZeros(M, 1)
	A0 := A.Copy()
	lapack.Geqrf(A0, Tau0)
	ok := X.AllClose(A0)
	okt := Tau.AllClose(Tau0)
	t.Logf("lapack QR == DecomposeQR: %v\n", ok && okt)
	if !ok || !okt {
		t.Logf("A0: %d, %d, %d\n", A0.Rows(), A0.Cols(), A0.LeadingIndex())
		t.Logf("A\n%v\n", A)
		t.Logf("X\n%v\n", X)
		t.Logf("Tau\n%v\n", &Tau)
		t.Logf("lapack X\n%v\n", A0)
		t.Logf("lapack Tau\n%v\n", Tau0)
	}

	// build block reflectors
	//unblkQRBlockReflector(X, Tau, T)
	V := TriLU(A0.Copy())
	lapack.LarftFloat(V, Tau0, T0)

	ok = T0.AllClose(T)
	t.Logf("lapack.dlarft == QRBlockReflector: %v\n", ok)
	if !ok {
		t.Logf("T:\n%v\n", T)
		t.Logf("lapack T0:\n%v\n", T0)
	}
}
예제 #6
0
파일: kkt.go 프로젝트: sguzwf/algorithm
//    Solution of KKT equations by reduction to a 2 x 2 system, a QR
//    factorization to eliminate the equality constraints, and a dense
//    Cholesky factorization of order n-p.
//
//    Computes the QR factorization
//
//        A' = [Q1, Q2] * [R; 0]
//
//    and returns a function that (1) computes the Cholesky factorization
//
//        Q_2^T * (H + GG^T * W^{-1} * W^{-T} * GG) * Q2 = L * L^T,
//
//    given H, Df, W, where GG = [Df; G], and (2) returns a function for
//    solving
//
//        [ H    A'   GG'    ]   [ ux ]   [ bx ]
//        [ A    0    0      ] * [ uy ] = [ by ].
//        [ GG   0    -W'*W  ]   [ uz ]   [ bz ]
//
//    H is n x n,  A is p x n, Df is mnl x n, G is N x n where
//    N = dims['l'] + sum(dims['q']) + sum( k**2 for k in dims['s'] ).
//
func kktChol(G *matrix.FloatMatrix, dims *sets.DimensionSet, A *matrix.FloatMatrix, mnl int) (kktFactor, error) {

	p, n := A.Size()
	cdim := mnl + dims.Sum("l", "q") + dims.SumSquared("s")
	cdim_pckd := mnl + dims.Sum("l", "q") + dims.SumPacked("s")

	QA := A.Transpose()
	tauA := matrix.FloatZeros(p, 1)
	lapack.Geqrf(QA, tauA)

	Gs := matrix.FloatZeros(cdim, n)
	K := matrix.FloatZeros(n, n)
	bzp := matrix.FloatZeros(cdim_pckd, 1)
	yy := matrix.FloatZeros(p, 1)
	checkpnt.AddMatrixVar("tauA", tauA)
	checkpnt.AddMatrixVar("Gs", Gs)
	checkpnt.AddMatrixVar("K", K)

	factor := func(W *sets.FloatMatrixSet, H, Df *matrix.FloatMatrix) (KKTFunc, error) {
		// Compute
		//
		//     K = [Q1, Q2]' * (H + GG' * W^{-1} * W^{-T} * GG) * [Q1, Q2]
		//
		// and take the Cholesky factorization of the 2,2 block
		//
		//     Q_2' * (H + GG^T * W^{-1} * W^{-T} * GG) * Q2.

		var err error = nil
		minor := 0
		if !checkpnt.MinorEmpty() {
			minor = checkpnt.MinorTop()
		}
		// Gs = W^{-T} * GG in packed storage.
		if mnl > 0 {
			Gs.SetSubMatrix(0, 0, Df)
		}
		Gs.SetSubMatrix(mnl, 0, G)
		checkpnt.Check("00factor_chol", minor)
		scale(Gs, W, true, true)
		pack2(Gs, dims, mnl)
		//checkpnt.Check("10factor_chol", minor)

		// K = [Q1, Q2]' * (H + Gs' * Gs) * [Q1, Q2].
		blas.SyrkFloat(Gs, K, 1.0, 0.0, la.OptTrans, &la.IOpt{"k", cdim_pckd})
		if H != nil {
			K.SetSubMatrix(0, 0, matrix.Plus(H, K.GetSubMatrix(0, 0, H.Rows(), H.Cols())))
		}
		//checkpnt.Check("20factor_chol", minor)
		symm(K, n, 0)
		lapack.Ormqr(QA, tauA, K, la.OptLeft, la.OptTrans)
		lapack.Ormqr(QA, tauA, K, la.OptRight)
		//checkpnt.Check("30factor_chol", minor)

		// Cholesky factorization of 2,2 block of K.
		lapack.Potrf(K, &la.IOpt{"n", n - p}, &la.IOpt{"offseta", p * (n + 1)})
		checkpnt.Check("40factor_chol", minor)

		solve := func(x, y, z *matrix.FloatMatrix) (err error) {
			// Solve
			//
			//     [ 0          A'  GG'*W^{-1} ]   [ ux   ]   [ bx        ]
			//     [ A          0   0          ] * [ uy   ] = [ by        ]
			//     [ W^{-T}*GG  0   -I         ]   [ W*uz ]   [ W^{-T}*bz ]
			//
			// and return ux, uy, W*uz.
			//
			// On entry, x, y, z contain bx, by, bz.  On exit, they contain
			// the solution ux, uy, W*uz.
			//
			// If we change variables ux = Q1*v + Q2*w, the system becomes
			//
			//     [ K11 K12 R ]   [ v  ]   [Q1'*(bx+GG'*W^{-1}*W^{-T}*bz)]
			//     [ K21 K22 0 ] * [ w  ] = [Q2'*(bx+GG'*W^{-1}*W^{-T}*bz)]
			//     [ R^T 0   0 ]   [ uy ]   [by                           ]
			//
			//     W*uz = W^{-T} * ( GG*ux - bz ).
			minor := 0
			if !checkpnt.MinorEmpty() {
				minor = checkpnt.MinorTop()
			}

			// bzp := W^{-T} * bz in packed storage
			scale(z, W, true, true)
			pack(z, bzp, dims, &la.IOpt{"mnl", mnl})

			// x := [Q1, Q2]' * (x + Gs' * bzp)
			//    = [Q1, Q2]' * (bx + Gs' * W^{-T} * bz)
			blas.GemvFloat(Gs, bzp, x, 1.0, 1.0, la.OptTrans, &la.IOpt{"m", cdim_pckd})
			lapack.Ormqr(QA, tauA, x, la.OptLeft, la.OptTrans)

			// y := x[:p]
			//    = Q1' * (bx + Gs' * W^{-T} * bz)
			blas.Copy(y, yy)
			blas.Copy(x, y, &la.IOpt{"n", p})

			// x[:p] := v = R^{-T} * by
			blas.Copy(yy, x)
			lapack.Trtrs(QA, x, la.OptUpper, la.OptTrans, &la.IOpt{"n", p})

			// x[p:] := K22^{-1} * (x[p:] - K21*x[:p])
			//        = K22^{-1} * (Q2' * (bx + Gs' * W^{-T} * bz) - K21*v)
			blas.GemvFloat(K, x, x, -1.0, 1.0, &la.IOpt{"m", n - p}, &la.IOpt{"n", p},
				&la.IOpt{"offseta", p}, &la.IOpt{"offsety", p})
			lapack.Potrs(K, x, &la.IOpt{"n", n - p}, &la.IOpt{"offseta", p * (n + 1)},
				&la.IOpt{"offsetb", p})

			// y := y - [K11, K12] * x
			//    = Q1' * (bx + Gs' * W^{-T} * bz) - K11*v - K12*w
			blas.GemvFloat(K, x, y, -1.0, 1.0, &la.IOpt{"m", p}, &la.IOpt{"n", n})

			// y := R^{-1}*y
			//    = R^{-1} * (Q1' * (bx + Gs' * W^{-T} * bz) - K11*v
			//      - K12*w)
			lapack.Trtrs(QA, y, la.OptUpper, &la.IOpt{"n", p})

			// x := [Q1, Q2] * x
			lapack.Ormqr(QA, tauA, x, la.OptLeft)

			// bzp := Gs * x - bzp.
			//      = W^{-T} * ( GG*ux - bz ) in packed storage.
			// Unpack and copy to z.
			blas.GemvFloat(Gs, x, bzp, 1.0, -1.0, &la.IOpt{"m", cdim_pckd})
			unpack(bzp, z, dims, &la.IOpt{"mnl", mnl})

			checkpnt.Check("90solve_chol", minor)
			return nil
		}
		return solve, err
	}
	return factor, nil
}
예제 #7
0
파일: kkt.go 프로젝트: sguzwf/algorithm
// Solution of KKT equations with zero 1,1 block, by eliminating the
// equality constraints via a QR factorization, and solving the
// reduced KKT system by another QR factorization.
//
// Computes the QR factorization
//
//        A' = [Q1, Q2] * [R1; 0]
//
// and returns a function that (1) computes the QR factorization
//
//        W^{-T} * G * Q2 = Q3 * R3
//
// (with columns of W^{-T}*G in packed storage), and (2) returns a function for solving
//
//        [ 0    A'   G'    ]   [ ux ]   [ bx ]
//        [ A    0    0     ] * [ uy ] = [ by ].
//        [ G    0   -W'*W  ]   [ uz ]   [ bz ]
//
// A is p x n and G is N x n where N = dims['l'] + sum(dims['q']) +
// sum( k**2 for k in dims['s'] ).
//
func kktQr(G *matrix.FloatMatrix, dims *sets.DimensionSet, A *matrix.FloatMatrix, mnl int) (kktFactor, error) {

	p, n := A.Size()
	cdim := dims.Sum("l", "q") + dims.SumSquared("s")
	cdim_pckd := dims.Sum("l", "q") + dims.SumPacked("s")

	QA := A.Transpose()
	tauA := matrix.FloatZeros(p, 1)
	lapack.Geqrf(QA, tauA)

	Gs := matrix.FloatZeros(cdim, n)
	tauG := matrix.FloatZeros(n-p, 1)
	u := matrix.FloatZeros(cdim_pckd, 1)
	vv := matrix.FloatZeros(n, 1)
	w := matrix.FloatZeros(cdim_pckd, 1)
	checkpnt.AddMatrixVar("tauA", tauA)
	checkpnt.AddMatrixVar("tauG", tauG)
	checkpnt.AddMatrixVar("Gs", Gs)
	checkpnt.AddMatrixVar("qr_u", u)
	checkpnt.AddMatrixVar("qr_vv", vv)

	factor := func(W *sets.FloatMatrixSet, H, Df *matrix.FloatMatrix) (KKTFunc, error) {
		var err error = nil
		minor := 0
		if !checkpnt.MinorEmpty() {
			minor = checkpnt.MinorTop()
		}

		// Gs = W^{-T}*G, in packed storage.
		blas.Copy(G, Gs)
		//checkpnt.Check("00factor_qr", minor)
		scale(Gs, W, true, true)
		//checkpnt.Check("01factor_qr", minor)
		pack2(Gs, dims, 0)
		//checkpnt.Check("02factor_qr", minor)

		// Gs := [ Gs1, Gs2 ]
		//     = Gs * [ Q1, Q2 ]
		lapack.Ormqr(QA, tauA, Gs, la.OptRight, &la.IOpt{"m", cdim_pckd})
		//checkpnt.Check("03factor_qr", minor)

		// QR factorization Gs2 := [ Q3, Q4 ] * [ R3; 0 ]
		lapack.Geqrf(Gs, tauG, &la.IOpt{"n", n - p}, &la.IOpt{"m", cdim_pckd},
			&la.IOpt{"offseta", Gs.Rows() * p})
		checkpnt.Check("10factor_qr", minor)

		solve := func(x, y, z *matrix.FloatMatrix) (err error) {
			// On entry, x, y, z contain bx, by, bz.  On exit, they
			// contain the solution x, y, W*z of
			//
			//     [ 0         A'  G'*W^{-1} ]   [ x   ]   [bx       ]
			//     [ A         0   0         ] * [ y   ] = [by       ].
			//     [ W^{-T}*G  0   -I        ]   [ W*z ]   [W^{-T}*bz]
			//
			// The system is solved in five steps:
			//
			//       w := W^{-T}*bz - Gs1*R1^{-T}*by
			//       u := R3^{-T}*Q2'*bx + Q3'*w
			//     W*z := Q3*u - w
			//       y := R1^{-1} * (Q1'*bx - Gs1'*(W*z))
			//       x := [ Q1, Q2 ] * [ R1^{-T}*by;  R3^{-1}*u ]

			minor := 0
			if !checkpnt.MinorEmpty() {
				minor = checkpnt.MinorTop()
			}

			// w := W^{-T} * bz in packed storage
			scale(z, W, true, true)
			pack(z, w, dims)
			//checkpnt.Check("00solve_qr", minor)

			// vv := [ Q1'*bx;  R3^{-T}*Q2'*bx ]
			blas.Copy(x, vv)
			lapack.Ormqr(QA, tauA, vv, la.OptTrans)
			lapack.Trtrs(Gs, vv, la.OptUpper, la.OptTrans, &la.IOpt{"n", n - p},
				&la.IOpt{"offseta", Gs.Rows() * p}, &la.IOpt{"offsetb", p})
			//checkpnt.Check("10solve_qr", minor)

			// x[:p] := R1^{-T} * by
			blas.Copy(y, x)
			lapack.Trtrs(QA, x, la.OptUpper, la.OptTrans, &la.IOpt{"n", p})
			//checkpnt.Check("20solve_qr", minor)

			// w := w - Gs1 * x[:p]
			//    = W^{-T}*bz - Gs1*by
			blas.GemvFloat(Gs, x, w, -1.0, 1.0, &la.IOpt{"n", p}, &la.IOpt{"m", cdim_pckd})
			//checkpnt.Check("30solve_qr", minor)

			// u := [ Q3'*w + v[p:];  0 ]
			//    = [ Q3'*w + R3^{-T}*Q2'*bx; 0 ]
			blas.Copy(w, u)
			lapack.Ormqr(Gs, tauG, u, la.OptTrans, &la.IOpt{"k", n - p},
				&la.IOpt{"offseta", Gs.Rows() * p}, &la.IOpt{"m", cdim_pckd})
			blas.AxpyFloat(vv, u, 1.0, &la.IOpt{"offsetx", p}, &la.IOpt{"n", n - p})
			blas.ScalFloat(u, 0.0, &la.IOpt{"offset", n - p})
			//checkpnt.Check("40solve_qr", minor)

			// x[p:] := R3^{-1} * u[:n-p]
			blas.Copy(u, x, &la.IOpt{"offsety", p}, &la.IOpt{"n", n - p})
			lapack.Trtrs(Gs, x, la.OptUpper, &la.IOpt{"n", n - p},
				&la.IOpt{"offset", Gs.Rows() * p}, &la.IOpt{"offsetb", p})
			//checkpnt.Check("50solve_qr", minor)

			// x is now [ R1^{-T}*by;  R3^{-1}*u[:n-p] ]
			// x := [Q1 Q2]*x
			lapack.Ormqr(QA, tauA, x)
			//checkpnt.Check("60solve_qr", minor)

			// u := [Q3, Q4] * u - w
			//    = Q3 * u[:n-p] - w
			lapack.Ormqr(Gs, tauG, u, &la.IOpt{"k", n - p}, &la.IOpt{"m", cdim_pckd},
				&la.IOpt{"offseta", Gs.Rows() * p})
			blas.AxpyFloat(w, u, -1.0)
			//checkpnt.Check("70solve_qr", minor)

			// y := R1^{-1} * ( v[:p] - Gs1'*u )
			//    = R1^{-1} * ( Q1'*bx - Gs1'*u )
			blas.Copy(vv, y, &la.IOpt{"n", p})
			blas.GemvFloat(Gs, u, y, -1.0, 1.0, &la.IOpt{"m", cdim_pckd},
				&la.IOpt{"n", p}, la.OptTrans)
			lapack.Trtrs(QA, y, la.OptUpper, &la.IOpt{"n", p})
			//checkpnt.Check("80solve_qr", minor)

			unpack(u, z, dims)
			checkpnt.Check("90solve_qr", minor)
			return nil
		}
		return solve, err
	}
	return factor, nil
}