Golang FloatMatrix.Get方法代碼示例

/*
 * Applies a real elementary reflector H to a real m by n matrix A,
 * from either the left or the right. H is represented in the form
 *
 *       H = I - tau * ( 1 ) * ( 1 v.T )
 *                     ( v )
 *
 * where tau is a real scalar and v is a real vector.
 *
 * If tau = 0, then H is taken to be the unit cmat.
 *
 * A is /a1\   a1 := a1 - w1
 *      \A2/   A2 := A2 - v*w1
 *             w1 := tau*(a1 + A2.T*v) if side == LEFT
 *                := tau*(a1 + A2*v)   if side == RIGHT
 *
 * Intermediate work space w1 required as parameter, no allocation.
 */
func applyHouseholder2x1(tau, v, a1, A2, w1 *cmat.FloatMatrix, flags int) *gomas.Error {
	var err *gomas.Error = nil
	tval := tau.Get(0, 0)
	if tval == 0.0 {
		return err
	}

	// shape oblivious vector copy.
	blasd.Axpby(w1, a1, 1.0, 0.0)
	if flags&gomas.LEFT != 0 {
		// w1 = a1 + A2.T*v
		err = blasd.MVMult(w1, A2, v, 1.0, 1.0, gomas.TRANSA)
	} else {
		// w1 = a1 + A2*v
		err = blasd.MVMult(w1, A2, v, 1.0, 1.0, gomas.NONE)
	}
	// w1 = tau*w1
	blasd.Scale(w1, tval)

	// a1 = a1 - w1
	blasd.Axpy(a1, w1, -1.0)

	// A2 = A2 - v*w1
	if flags&gomas.LEFT != 0 {
		err = blasd.MVUpdate(A2, v, w1, -1.0)
	} else {
		err = blasd.MVUpdate(A2, w1, v, -1.0)
	}
	return err
}

func TestPartition2D(t *testing.T) {
	var ATL, ATR, ABL, ABR, As cmat.FloatMatrix
	var A00, a01, A02, a10, a11, a12, A20, a21, A22 cmat.FloatMatrix

	csource := cmat.NewFloatConstSource(1.0)
	A := cmat.NewMatrix(6, 6)
	As.SubMatrix(A, 1, 1, 4, 4)
	As.SetFrom(csource)

	Partition2x2(&ATL, &ATR, &ABL, &ABR, &As, 0, 0, PTOPLEFT)
	t.Logf("ATL:\n%v\n", &ATL)

	t.Logf("n(ATL)=%d, n(As)=%d\n", n(&ATL), n(&As))
	k := 0
	for n(&ATL) < n(&As) && k < n(&As) {
		Repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			&a10, &a11, &a12,
			&A20, &a21, &A22, &As, 1, PBOTTOMRIGHT)
		t.Logf("n(A00)=%d, n(a01)=%d, n(A02)=%d\n", n(&A00), n(&a01), n(&A02))
		t.Logf("n(a10)=%d, n(a11)=%d, n(a12)=%d\n", n(&a10), n(&a11), n(&a12))
		t.Logf("n(A20)=%d, n(a21)=%d, n(A22)=%d\n", n(&A20), n(&a21), n(&A22))
		//t.Logf("n(a12)=%d [%d], n(a11)=%d\n", n(&a12), a12.Len(), a11.Len())
		a11.Set(0, 0, a11.Get(0, 0)+1.0)
		addConst(&a21, -2.0)

		Continue3x3to2x2(&ATL, &ATR, &ABL, &ABR, &A00, &a11, &A22, &As, PBOTTOMRIGHT)
		t.Logf("n(ATL)=%d, n(As)=%d\n", n(&ATL), n(&As))
		k += 1
	}
	t.Logf("A:\n%v\n", A)
}

// unblocked LU decomposition w/o pivots, FLAME LU nopivots variant 5
func unblockedLUnoPiv(A *cmat.FloatMatrix, conf *gomas.Config) *gomas.Error {
	var ATL, ATR, ABL, ABR cmat.FloatMatrix
	var A00, a01, A02, a10, a11, a12, A20, a21, A22 cmat.FloatMatrix
	var err *gomas.Error = nil

	util.Partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, util.PTOPLEFT)

	for m(&ATL) < m(A) {
		util.Repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			&a10, &a11, &a12,
			&A20, &a21, &A22, A, 1, util.PBOTTOMRIGHT)

		// a21 = a21/a11
		blasd.InvScale(&a21, a11.Get(0, 0))
		// A22 = A22 - a21*a12
		blasd.MVUpdate(&A22, &a21, &a12, -1.0)

		util.Continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, util.PBOTTOMRIGHT)
	}
	return err
}

/*
 * 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)
	}
}

func blkReduceTridiagUpper(A, tauq, Y, W *cmat.FloatMatrix, lb int, conf *gomas.Config) {
	var ATL, ABR cmat.FloatMatrix
	var A00, A01, A11, A22 cmat.FloatMatrix
	var YT, YB, Y0, Y1, Y2 cmat.FloatMatrix
	var tqT, tqB, tq0, tauq1, tq2 cmat.FloatMatrix
	var v0 float64

	util.Partition2x2(
		&ATL, nil,
		nil, &ABR, A, 0, 0, util.PBOTTOMRIGHT)
	util.Partition2x1(
		&YT,
		&YB, Y, 0, util.PBOTTOM)
	util.Partition2x1(
		&tqT,
		&tqB, tauq, 1, util.PBOTTOM)

	for m(&ATL)-lb > 0 {
		util.Repartition2x2to3x3(&ATL,
			&A00, &A01, nil,
			nil, &A11, nil,
			nil, nil, &A22, A, lb, util.PTOPLEFT)
		util.Repartition2x1to3x1(&YT,
			&Y0,
			&Y1,
			&Y2, Y, lb, util.PTOP)
		util.Repartition2x1to3x1(&tqT,
			&tq0,
			&tauq1,
			&tq2, tauq, lb, util.PTOP)
		// ------------------------------------------------------
		unblkBuildTridiagUpper(&ATL, &tauq1, &YT, W)

		// set subdiagonal entry to unit
		v0 = A01.Get(-1, 0)
		A01.Set(-1, 0, 1.0)

		// A22 := A22 - A01*Y0.T - Y0*A01.T
		blasd.Update2Sym(&A00, &A01, &Y0, -1.0, 1.0, gomas.UPPER, conf)

		// restore subdiagonal entry
		A01.Set(-1, 0, v0)
		// ------------------------------------------------------
		util.Continue3x3to2x2(
			&ATL, nil,
			nil, &ABR, &A00, &A11, &A22, A, util.PTOPLEFT)
		util.Continue3x1to2x1(
			&YT,
			&YB, &Y0, &Y1, Y, util.PTOP)
		util.Continue3x1to2x1(
			&tqT,
			&tqB, &tq0, &tauq1, tauq, util.PTOP)
	}

	if m(&ATL) > 0 {
		unblkReduceTridiagUpper(&ATL, &tqT, W, true)
	}
}

/*
 * like LAPACK/dlafrt.f
 *
 * Build block reflector T from HH reflector stored in TriLU(A) and coefficients
 * in tau.
 *
 * Q = I - Y*T*Y.T; Householder H = I - tau*v*v.T
 *
 * T = | T  z |   z = -tau*T*Y.T*v
 *     | 0  c |   c = tau
 *
 * Q = H(1)H(2)...H(k) building forward here.
 */
func unblkQLBlockReflector(T, A, tau *cmat.FloatMatrix) {
	var ATL, ABR cmat.FloatMatrix
	var A00, a01, a11, A02, a12, A22 cmat.FloatMatrix
	var TTL, TBR cmat.FloatMatrix
	var T00, t11, t21, T22 cmat.FloatMatrix
	var tT, tB cmat.FloatMatrix
	var t0, tau1, t2 cmat.FloatMatrix

	util.Partition2x2(
		&ATL, nil,
		nil, &ABR, A, 0, 0, util.PBOTTOMRIGHT)
	util.Partition2x2(
		&TTL, nil,
		nil, &TBR, T, 0, 0, util.PBOTTOMRIGHT)
	util.Partition2x1(
		&tT,
		&tB, tau, 0, util.PBOTTOM)

	for m(&ATL) > 0 && n(&ATL) > 0 {
		util.Repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			nil, &a11, &a12,
			nil, nil, &A22, A, 1, util.PTOPLEFT)
		util.Repartition2x2to3x3(&TTL,
			&T00, nil, nil,
			nil, &t11, nil,
			nil, &t21, &T22, T, 1, util.PTOPLEFT)
		util.Repartition2x1to3x1(&tT,
			&t0,
			&tau1,
			&t2, tau, 1, util.PTOP)
		// --------------------------------------------------

		// t11 := tau
		tauval := tau1.Get(0, 0)
		if tauval != 0.0 {
			t11.Set(0, 0, tauval)

			// t21 := -tauval*(a12.T + &A02.T*a12)
			blasd.Axpby(&t21, &a12, 1.0, 0.0)
			blasd.MVMult(&t21, &A02, &a01, -tauval, -tauval, gomas.TRANSA)
			// t21 := T22*t01
			blasd.MVMultTrm(&t21, &T22, 1.0, gomas.LOWER)
		}

		// --------------------------------------------------
		util.Continue3x3to2x2(
			&ATL, nil,
			nil, &ABR, &A00, &a11, &A22, A, util.PTOPLEFT)
		util.Continue3x3to2x2(
			&TTL, nil,
			nil, &TBR, &T00, &t11, &T22, T, util.PTOPLEFT)
		util.Continue3x1to2x1(
			&tT,
			&tB, &t0, &tau1, tau, util.PTOP)
	}
}

/*
 * like LAPACK/dlafrt.f
 *
 * Build block reflector T from HH reflector stored in TriLU(A) and coefficients
 * in tau.
 *
 * Q = I - Y*T*Y.T; Householder H = I - tau*v*v.T
 *
 * T = | T  0 |   z = -tau*T*Y.T*v
 *     | z  c |   c = tau
 *
 * Q = H(1)H(2)...H(k) building forward here.
 */
func unblkBlockReflectorRQ(T, A, tau *cmat.FloatMatrix) {
	var ATL, ABR cmat.FloatMatrix
	var A00, a10, A20, a11, a21, A22 cmat.FloatMatrix
	var TTL, TBR cmat.FloatMatrix
	var T00, t11, t21, T22 cmat.FloatMatrix
	var tT, tB cmat.FloatMatrix
	var t0, tau1, t2 cmat.FloatMatrix

	util.Partition2x2(
		&ATL, nil,
		nil, &ABR /**/, A, 0, 0, util.PBOTTOMRIGHT)
	util.Partition2x2(
		&TTL, nil,
		nil, &TBR /**/, T, 0, 0, util.PBOTTOMRIGHT)
	util.Partition2x1(
		&tT,
		&tB /**/, tau, 0, util.PBOTTOM)

	for m(&ATL) > 0 && n(&ATL) > 0 {
		util.Repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			&a10, &a11, nil,
			&A20, &a21, &A22 /**/, A, 1, util.PTOPLEFT)
		util.Repartition2x2to3x3(&TTL,
			&T00, nil, nil,
			nil, &t11, nil,
			nil, &t21, &T22 /**/, T, 1, util.PTOPLEFT)
		util.Repartition2x1to3x1(&tT,
			&t0,
			&tau1,
			&t2 /**/, tau, 1, util.PTOP)
		// --------------------------------------------------

		// t11 := tau
		tauval := tau1.Get(0, 0)
		if tauval != 0.0 {
			t11.Set(0, 0, tauval)

			// t21 := -tauval*(a21 + A20*a10)
			blasd.Axpby(&t21, &a21, 1.0, 0.0)
			blasd.MVMult(&t21, &A20, &a10, -tauval, -tauval, gomas.NONE)
			// t21 := T22*t21
			blasd.MVMultTrm(&t21, &T22, 1.0, gomas.LOWER)
		}

		// --------------------------------------------------
		util.Continue3x3to2x2(
			&ATL, nil,
			nil, &ABR /**/, &A00, &a11, &A22, A, util.PTOPLEFT)
		util.Continue3x3to2x2(
			&TTL, nil,
			nil, &TBR /**/, &T00, &t11, &T22, T, util.PTOPLEFT)
		util.Continue3x1to2x1(
			&tT,
			&tB /**/, &t0, &tau1, tau, util.PTOP)
	}
}

/*
 * like LAPACK/dlafrt.f
 *
 * Build block reflector T from HH reflector stored in TriLU(A) and coefficients
 * in tau.
 *
 * Q = I - Y*T*Y.T; Householder H = I - tau*v*v.T
 *
 * T = | T  z |   z = -tau*T*Y.T*v
 *     | 0  c |   c = tau
 *
 * Q = H(1)H(2)...H(k) building forward here.
 */
func unblkBlockReflectorLQ(T, A, tau *cmat.FloatMatrix) {
	var ATL, ATR, ABL, ABR cmat.FloatMatrix
	var A00, a01, A02, a11, a12, A22 cmat.FloatMatrix
	var TTL, TTR, TBL, TBR cmat.FloatMatrix
	var T00, t01, T02, t11, t12, T22 cmat.FloatMatrix
	var tT, tB cmat.FloatMatrix
	var t0, tau1, t2 cmat.FloatMatrix

	util.Partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, util.PTOPLEFT)
	util.Partition2x2(
		&TTL, &TTR,
		&TBL, &TBR, T, 0, 0, util.PTOPLEFT)
	util.Partition2x1(
		&tT,
		&tB, tau, 0, util.PTOP)

	for m(&ABR) > 0 && n(&ABR) > 0 {
		util.Repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			nil, &a11, &a12,
			nil, nil, &A22, A, 1, util.PBOTTOMRIGHT)
		util.Repartition2x2to3x3(&TTL,
			&T00, &t01, &T02,
			nil, &t11, &t12,
			nil, nil, &T22, T, 1, util.PBOTTOMRIGHT)
		util.Repartition2x1to3x1(&tT,
			&t0,
			&tau1,
			&t2, tau, 1, util.PBOTTOM)
		// --------------------------------------------------

		// t11 := tau
		tauval := tau1.Get(0, 0)
		if tauval != 0.0 {
			t11.Set(0, 0, tauval)

			// t01 := -tauval*(a01 + A02*a12)
			blasd.Axpby(&t01, &a01, 1.0, 0.0)
			blasd.MVMult(&t01, &A02, &a12, -tauval, -tauval, gomas.NONE)
			// t01 := T00*t01
			blasd.MVMultTrm(&t01, &T00, 1.0, gomas.UPPER)
		}

		// --------------------------------------------------
		util.Continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, util.PBOTTOMRIGHT)
		util.Continue3x3to2x2(
			&TTL, &TTR,
			&TBL, &TBR, &T00, &t11, &T22, T, util.PBOTTOMRIGHT)
		util.Continue3x1to2x1(
			&tT,
			&tB, &t0, &tau1, tau, util.PBOTTOM)
	}
}

/*
 * 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)
	}
}

/*
 * Unblocked QR decomposition with block reflector T.
 */
func unblockedQRT(A, T, W *cmat.FloatMatrix) *gomas.Error {
	var err *gomas.Error = nil
	var ATL, ATR, ABL, ABR cmat.FloatMatrix
	var A00, a10, a11, a12, A20, a21, A22 cmat.FloatMatrix
	var TTL, TTR, TBL, TBR cmat.FloatMatrix
	var T00, t01, T02, t11, t12, T22, w12 cmat.FloatMatrix

	util.Partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, util.PTOPLEFT)
	util.Partition2x2(
		&TTL, &TTR,
		&TBL, &TBR, T, 0, 0, util.PTOPLEFT)

	for m(&ABR) > 0 && n(&ABR) > 0 {
		util.Repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			&a10, &a11, &a12,
			&A20, &a21, &A22, A, 1, util.PBOTTOMRIGHT)
		util.Repartition2x2to3x3(&TTL,
			&T00, &t01, &T02,
			nil, &t11, &t12,
			nil, nil, &T22, T, 1, util.PBOTTOMRIGHT)

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

		computeHouseholder(&a11, &a21, &t11)

		// H*[a12 A22].T
		w12.SubMatrix(W, 0, 0, a12.Len(), 1)
		applyHouseholder2x1(&t11, &a21, &a12, &A22, &w12, gomas.LEFT)

		// update T
		tauval := t11.Get(0, 0)
		if tauval != 0.0 {
			// t01 := -tauval*(a10.T + &A20.T*a21)
			//a10.CopyTo(&t01)
			blasd.Axpby(&t01, &a10, 1.0, 0.0)
			blasd.MVMult(&t01, &A20, &a21, -tauval, -tauval, gomas.TRANSA)
			// t01 := T00*t01
			blasd.MVMultTrm(&t01, &T00, 1.0, gomas.UPPER)
		}

		// ------------------------------------------------------
		util.Continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, util.PBOTTOMRIGHT)
		util.Continue3x3to2x2(
			&TTL, &TTR,
			&TBL, &TBR, &T00, &t11, &T22, T, util.PBOTTOMRIGHT)
	}
	return err
}

func Amax(X *cmat.FloatMatrix, confs ...*gomas.Config) float64 {
	switch X.Len() {
	case 0:
		return 0.0
	case 1:
		return X.Get(0, 0)
	}
	ix := IAmax(X, confs...)
	if ix == -1 {
		return 0.0
	}
	return X.Get(ix, 0)
}

func TestPartition1H(t *testing.T) {
	var AL, AR, A0, a1, A2 cmat.FloatMatrix
	A := cmat.NewMatrix(1, 6)
	Partition1x2(&AL, &AR, A, 0, PLEFT)
	t.Logf("n(AL)=%d, n(AR)=%d\n", n(&AL), n(&AR))
	for n(&AL) < n(A) {
		addConst(&AR, 1.0)
		t.Logf("n(AR)=%d; %v\n", n(&AR), &AR)
		Repartition1x2to1x3(&AL, &A0, &a1, &A2, A, 1, PRIGHT)
		t.Logf("n(A0)=%d, n(A2)=%d, a1=%.1f\n", n(&A0), n(&A2), a1.Get(0, 0))
		Continue1x3to1x2(&AL, &AR, &A0, &a1, A, PRIGHT)
	}
	t.Logf("A:%v\n", A)
}

/*
 * Unblocked code for generating M by N matrix Q with orthogonal columns which
 * are defined as the last N columns of the product of K first elementary
 * reflectors.
 *
 * Parameter nk is last nk elementary reflectors that are not used in computing
 * the matrix Q. Parameter mk length of the first unused elementary reflectors
 * First nk columns are zeroed and subdiagonal mk-nk is set to unit.
 *
 * Compatible with lapack.DORG2L subroutine.
 */
func unblkBuildQL(A, Tvec, W *cmat.FloatMatrix, mk, nk int, mayClear bool) {
	var ATL, ATR, ABL, ABR cmat.FloatMatrix
	var A00, a01, a10, a11, a21, A22 cmat.FloatMatrix
	var tT, tB cmat.FloatMatrix
	var t0, tau1, t2, w12, D cmat.FloatMatrix

	// (mk, nk) = (rows, columns) of upper left partition
	util.Partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, mk, nk, util.PTOPLEFT)
	util.Partition2x1(
		&tT,
		&tB, Tvec, nk, util.PTOP)

	// zero the left side
	if nk > 0 && mayClear {
		blasd.Scale(&ABL, 0.0)
		blasd.Scale(&ATL, 0.0)
		D.Diag(&ATL, nk-mk)
		blasd.Add(&D, 1.0)
	}

	for m(&ABR) > 0 && n(&ABR) > 0 {
		util.Repartition2x2to3x3(&ATL,
			&A00, &a01, nil,
			&a10, &a11, nil,
			nil, &a21, &A22, A, 1, util.PBOTTOMRIGHT)
		util.Repartition2x1to3x1(&tT,
			&t0,
			&tau1,
			&t2, Tvec, 1, util.PBOTTOM)
		// ------------------------------------------------------
		w12.SubMatrix(W, 0, 0, a10.Len(), 1)
		applyHouseholder2x1(&tau1, &a01, &a10, &A00, &w12, gomas.LEFT)

		blasd.Scale(&a01, -tau1.Get(0, 0))
		a11.Set(0, 0, 1.0-tau1.Get(0, 0))

		// zero bottom elements
		blasd.Scale(&a21, 0.0)
		// ------------------------------------------------------
		util.Continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, util.PBOTTOMRIGHT)
		util.Continue3x1to2x1(
			&tT,
			&tB, &t0, &tau1, Tvec, util.PBOTTOM)
	}
}

/*
 * Unblocked code for generating M by N matrix Q with orthogonal columns which
 * are defined as the first N columns of the product of K first elementary
 * reflectors.
 *
 * Parameters nk = n(A)-K, mk = m(A)-K define the initial partitioning of
 * matrix A.
 *
 *  Q = H(k)H(k-1)...H(1)  , 0 < k <= M, where H(i) = I - tau*v*v.T
 *
 * Computation is ordered as H(k)*H(k-1)...*H(1)*I ie. from bottom to top.
 *
 * If k < M rows k+1:M are cleared and diagonal entries [k+1:M,k+1:M] are
 * set to unit. Then the matrix Q is generated by right multiplying elements below
 * of i'th elementary reflector H(i).
 *
 * Compatible to lapack.xORG2L subroutine.
 */
func unblkBuildLQ(A, Tvec, W *cmat.FloatMatrix, mk, nk int, mayClear bool) {
	var ATL, ATR, ABL, ABR cmat.FloatMatrix
	var A00, a10, a11, a12, a21, A22 cmat.FloatMatrix
	var tT, tB cmat.FloatMatrix
	var t0, tau1, t2, w12, D cmat.FloatMatrix

	util.Partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, mk, nk, util.PBOTTOMRIGHT)
	util.Partition2x1(
		&tT,
		&tB, Tvec, mk, util.PBOTTOM)

	// zero the bottom part
	if mk > 0 && mayClear {
		blasd.Scale(&ABL, 0.0)
		blasd.Scale(&ABR, 0.0)
		D.Diag(&ABR)
		blasd.Add(&D, 1.0)
	}

	for m(&ATL) > 0 && n(&ATL) > 0 {
		util.Repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			&a10, &a11, &a12,
			nil, &a21, &A22, A, 1, util.PTOPLEFT)
		util.Repartition2x1to3x1(&tT,
			&t0,
			&tau1,
			&t2, Tvec, 1, util.PTOP)
		// ------------------------------------------------------

		w12.SubMatrix(W, 0, 0, a21.Len(), 1)
		applyHouseholder2x1(&tau1, &a12, &a21, &A22, &w12, gomas.RIGHT)

		blasd.Scale(&a12, -tau1.Get(0, 0))
		a11.Set(0, 0, 1.0-tau1.Get(0, 0))

		// zero
		blasd.Scale(&a10, 0.0)
		// ------------------------------------------------------
		util.Continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, util.PTOPLEFT)
		util.Continue3x1to2x1(
			&tT,
			&tB, &t0, &tau1, Tvec, util.PTOP)
	}
}

func findBKPivotUpper(A *cmat.FloatMatrix) (int, int) {
	var r, q int
	var rcol, qrow cmat.FloatMatrix
	if m(A) == 1 {
		return 0, 1
	}
	lastcol := m(A) - 1
	amax := math.Abs(A.Get(lastcol, lastcol))
	// column above [A.Rows()-1, A.Rows()-1]
	rcol.SubMatrix(A, 0, lastcol, lastcol, 1)

	r = blasd.IAmax(&rcol)
	// max off-diagonal on first column at index r
	rmax := math.Abs(A.Get(r, lastcol))

	if amax >= bkALPHA*rmax {
		// no pivoting, 1x1 diagonal
		return -1, 1
	}
	// max off-diagonal on r'th row at index q
	//  a) rest of the r'th row above diagonal
	qmax := 0.0
	if r > 0 {
		qrow.SubMatrix(A, 0, r, r, 1)
		q = blasd.IAmax(&qrow)
		qmax = math.Abs(A.Get(q, r /*+1*/))
	}
	//  b) elements right of diagonal
	qrow.SubMatrix(A, r, r+1, 1, lastcol-r)
	q = blasd.IAmax(&qrow)
	qmax2 := math.Abs(qrow.Get(0, q))
	if qmax2 > qmax {
		qmax = qmax2
	}

	if amax >= bkALPHA*rmax*(rmax/qmax) {
		// no pivoting, 1x1 diagonal
		return -1, 1
	}
	if math.Abs(A.Get(r, r)) >= bkALPHA*qmax {
		// 1x1 pivoting and interchange with k, r
		return r, 1
	} else {
		// 2x2 pivoting and interchange with k+1, r
		return r, 2
	}
	return 0, 1
}