Example #1
0
/*
 * Reduce upper triangular matrix to tridiagonal.
 *
 * Elementary reflectors Q = H(n-1)...H(2)H(1) are stored on upper
 * triangular part of A. Reflector H(n-1) saved at column A(n) and
 * scalar multiplier to tau[n-1]. If parameter `tail` is true then
 * this function is used to reduce tail part of partially reduced
 * matrix and tau-vector partitioning is starting from last position.
 */
func unblkReduceTridiagUpper(A, tauq, W *cmat.FloatMatrix, tail bool) {
	var ATL, ABR cmat.FloatMatrix
	var A00, a01, a11, A22 cmat.FloatMatrix
	var tqT, tqB, tq0, tauq1, tq2 cmat.FloatMatrix
	var y21 cmat.FloatMatrix
	var v0 float64

	toff := 1
	if tail {
		toff = 0
	}
	util.Partition2x2(
		&ATL, nil,
		nil, &ABR, A, 0, 0, util.PBOTTOMRIGHT)
	util.Partition2x1(
		&tqT,
		&tqB, tauq, toff, util.PBOTTOM)

	for n(&ATL) > 0 {
		util.Repartition2x2to3x3(&ATL,
			&A00, &a01, nil,
			nil, &a11, nil,
			nil, nil, &A22, A, 1, util.PTOPLEFT)
		util.Repartition2x1to3x1(&tqT,
			&tq0,
			&tauq1,
			&tq2, tauq, 1, util.PTOP)
		// set temp vectors for this round
		y21.SetBuf(n(&A00), 1, n(&A00), W.Data())
		// ------------------------------------------------------

		// Compute householder to zero super-diagonal entries
		computeHouseholderRev(&a01, &tauq1)
		tauqv := tauq1.Get(0, 0)

		// set superdiagonal to unit
		v0 = a01.Get(-1, 0)
		a01.Set(-1, 0, 1.0)

		// y21 := A22*a12t
		blasd.MVMultSym(&y21, &A00, &a01, tauqv, 0.0, gomas.UPPER)
		// beta := tauq*a12t*y21
		beta := tauqv * blasd.Dot(&a01, &y21)
		// y21  := y21 - 0.5*beta*a125
		blasd.Axpy(&y21, &a01, -0.5*beta)
		// A22 := A22 - a12t*y21.T - y21*a12.T
		blasd.MVUpdate2Sym(&A00, &a01, &y21, -1.0, gomas.UPPER)

		// restore superdiagonal value
		a01.Set(-1, 0, v0)
		// ------------------------------------------------------
		util.Continue3x3to2x2(
			&ATL, nil,
			nil, &ABR, &A00, &a11, &A22, A, util.PTOPLEFT)
		util.Continue3x1to2x1(
			&tqT,
			&tqB, &tq0, &tauq1, tauq, util.PTOP)
	}
}
Example #2
0
func TestDSyr2(t *testing.T) {

	const N = 911

	A := cmat.NewMatrix(N, N)
	X := cmat.NewMatrix(N, 1)
	Y := cmat.NewMatrix(N, 1)
	B := cmat.NewMatrix(N, N)

	ones := cmat.NewFloatConstSource(1.0)
	twos := cmat.NewFloatConstSource(2.0)
	zeromean := cmat.NewFloatUniformSource(0.5, 2.0)

	A.SetFrom(zeromean, cmat.LOWER)
	X.SetFrom(ones)
	Y.SetFrom(twos)
	B.Copy(A)

	// B = A*B
	blasd.MVUpdate(B, X, Y, 1.0)
	blasd.MVUpdate(B, Y, X, 1.0)
	cmat.TriL(B, cmat.NONE)
	blasd.MVUpdate2Sym(A, X, Y, 1.0, gomas.LOWER)
	ok := B.AllClose(A)
	if N < 10 {
		t.Logf("A:\n%v\n", A)
		t.Logf("B:\n%v\n", B)
	}
	t.Logf("MVUpdate2Sym(A, X, Y, L) == TriL(MVUpdate(A, X, Y);MVUpdate(A, Y, X)) : %v\n", ok)

	A.SetFrom(zeromean, cmat.UPPER)
	cmat.TriU(A, cmat.NONE)
	B.Copy(A)
	blasd.MVUpdate(B, X, Y, 1.0)
	blasd.MVUpdate(B, Y, X, 1.0)
	cmat.TriU(B, cmat.NONE)
	blasd.MVUpdate2Sym(A, X, Y, 1.0, gomas.UPPER)
	ok = B.AllClose(A)
	if N < 10 {
		t.Logf("A:\n%v\n", A)
		t.Logf("B:\n%v\n", B)
	}
	t.Logf("MVUpdate2Sym(A, X, Y, U) == TriU(MVUpdate(A, X, Y);MVUpdate(A, Y, X)) : %v\n", ok)
}
Example #3
0
/*
 * Tridiagonal reduction of LOWER triangular symmetric matrix, zero elements below 1st
 * subdiagonal:
 *
 *   A =  (1 - tau*u*u.t)*A*(1 - tau*u*u.T)
 *     =  (I - tau*( 0   0   )) (a11 a12) (I - tau*( 0  0   ))
 *        (        ( 0  u*u.t)) (a21 A22) (        ( 0 u*u.t))
 *
 *  a11, a12, a21 not affected
 *
 *  from LEFT:
 *    A22 = A22 - tau*u*u.T*A22
 *  from RIGHT:
 *    A22 = A22 - tau*A22*u.u.T
 *
 *  LEFT and RIGHT:
 *    A22   = A22 - tau*u*u.T*A22 - tau*(A22 - tau*u*u.T*A22)*u*u.T
 *          = A22 - tau*u*u.T*A22 - tau*A22*u*u.T + tau*tau*u*u.T*A22*u*u.T
 *    [x    = tau*A22*u (vector)]  (SYMV)
 *    A22   = A22 - u*x.T - x*u.T + tau*u*u.T*x*u.T
 *    [beta = tau*u.T*x (scalar)]  (DOT)
 *          = A22 - u*x.T - x*u.T + beta*u*u.T
 *          = A22 - u*(x - 0.5*beta*u).T - (x - 0.5*beta*u)*u.T
 *    [w    = x - 0.5*beta*u]      (AXPY)
 *          = A22 - u*w.T - w*u.T  (SYR2)
 *
 * Result of reduction for N = 5:
 *    ( d  .  .  . . )
 *    ( e  d  .  . . )
 *    ( v1 e  d  . . )
 *    ( v1 v2 e  d . )
 *    ( v1 v2 v3 e d )
 */
func unblkReduceTridiagLower(A, tauq, W *cmat.FloatMatrix) {
	var ATL, ABR cmat.FloatMatrix
	var A00, a11, a21, A22 cmat.FloatMatrix
	var tqT, tqB, tq0, tauq1, tq2 cmat.FloatMatrix
	var y21 cmat.FloatMatrix
	var v0 float64

	util.Partition2x2(
		&ATL, nil,
		nil, &ABR, A, 0, 0, util.PTOPLEFT)
	util.Partition2x1(
		&tqT,
		&tqB, tauq, 0, util.PTOP)

	for m(&ABR) > 0 && n(&ABR) > 0 {
		util.Repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			nil, &a11, nil,
			nil, &a21, &A22, A, 1, util.PBOTTOMRIGHT)
		util.Repartition2x1to3x1(&tqT,
			&tq0,
			&tauq1,
			&tq2, tauq, 1, util.PBOTTOM)
		// set temp vectors for this round
		y21.SetBuf(n(&A22), 1, n(&A22), W.Data())
		// ------------------------------------------------------

		// Compute householder to zero subdiagonal entries
		computeHouseholderVec(&a21, &tauq1)
		tauqv := tauq1.Get(0, 0)

		// set subdiagonal to unit
		v0 = a21.Get(0, 0)
		a21.Set(0, 0, 1.0)

		// y21 := tauq*A22*a21
		blasd.MVMultSym(&y21, &A22, &a21, tauqv, 0.0, gomas.LOWER)
		// beta := tauq*a21.T*y21
		beta := tauqv * blasd.Dot(&a21, &y21)
		// y21  := y21 - 0.5*beta*a21
		blasd.Axpy(&y21, &a21, -0.5*beta)
		// A22 := A22 - a21*y21.T - y21*a21.T
		blasd.MVUpdate2Sym(&A22, &a21, &y21, -1.0, gomas.LOWER)

		// restore subdiagonal
		a21.Set(0, 0, v0)
		// ------------------------------------------------------
		util.Continue3x3to2x2(
			&ATL, nil,
			nil, &ABR, &A00, &a11, &A22, A, util.PBOTTOMRIGHT)
		util.Continue3x1to2x1(
			&tqT,
			&tqB, &tq0, &tauq1, tauq, util.PBOTTOM)
	}
}