Golang FloatMatrix.Float方法代码示例

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

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)

	for ATL.Rows() < A.Rows() {
		repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			&a10, &a11, &a12,
			&A20, &a21, &A22, A, 1, pBOTTOMRIGHT)

		// a21 = a21/a11
		//a21.Scale(1.0/a11.Float())
		InvScale(&a21, a11.Float())
		// A22 = A22 - a21*a12
		err = MVRankUpdate(&A22, &a21, &a12, -1.0)

		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pBOTTOMRIGHT)
	}
	return
}

// Inverse NON-UNIT diagonal tridiagonal matrix
func unblockedInverseLower(A *matrix.FloatMatrix) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a10t, a11, A20, a21, A22 matrix.FloatMatrix

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)

	for ATL.Rows() < A.Rows() {
		repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			&a10t, &a11, nil,
			&A20, &a21, &A22, A, 1, pBOTTOMRIGHT)
		// -------------------------------------------------
		aval := a11.Float()

		// a21 = -a21/a11
		InvScale(&a21, -aval)
		// A20 = A20 + a21*a10.t
		MVRankUpdate(&A20, &a21, &a10t, 1.0)
		// a10 = a10/a11
		InvScale(&a10t, aval)
		// a11 = 1.0/a11
		a11.SetAt(0, 0, 1.0/aval)

		// -------------------------------------------------
		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pBOTTOMRIGHT)
	}
	return
}

// Inverse NON-UNIT diagonal tridiagonal matrix
func unblockedInverseUpper(A *matrix.FloatMatrix) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a01, A02, a11, a12t, A22 matrix.FloatMatrix

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)

	for ATL.Rows() < A.Rows() {
		repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			nil, &a11, &a12t,
			nil, nil, &A22, A, 1, pBOTTOMRIGHT)
		// -------------------------------------------------
		aval := a11.Float()

		// a12 = -a12/a11
		InvScale(&a12t, -aval)
		// A02 = A02 + a01*a12
		MVRankUpdate(&A02, &a01, &a12t, 1.0)
		// a01 = a01/a11
		InvScale(&a01, aval)
		// a11 = 1.0/a11
		a11.SetAt(0, 0, 1.0/aval)

		// -------------------------------------------------
		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pBOTTOMRIGHT)
	}
	return
}

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))
}

/*
 *  ( A11  a12 )   ( U11 u12 )( D1  0  )( U11.t 0 )
 *  ( a21  a22 )   (  0   1  )(  0  d2 )( u12.t 1 )
 *
 *   a22  =   d2
 *   a01  =   u12*d2                       => u12 = a12/d2
 *   A11  =   u12*d2*u12.t + U11*D1*U11.t  => U11 = A11 - u12*d2*u12.t
 */
func unblkUpperLDLnoPiv(A *matrix.FloatMatrix) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a01, A02, a11, a12, A22 matrix.FloatMatrix

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pBOTTOMRIGHT)

	for ATL.Rows() > 0 {
		repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			nil, &a11, &a12,
			nil, nil, &A22, A, 1, pTOPLEFT)

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

		// A00 = A00 - u01*d11*u01.T = A00 - a01*a01.T/a11; triangular update
		err = MVUpdateTrm(&A00, &a01, &a01, -1.0/a11.Float(), UPPER)

		// u01 = a01/a11
		InvScale(&a01, a11.Float())
		// ---------------------------------------------------------

		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pTOPLEFT)
	}
	return
}

/*
 *  ( a11  a12 )   ( 1   0   )( d1  0   )( l  l21.t )
 *  ( a21  A22 )   ( l21 L22 )(  0  A22 )( 0  L22.t )
 *
 *   a11  =   d1
 *   a21  =   l21*d1                       => l21 = a21/d1
 *   A22  =   l21*d1*l21.t + L22*D2*L22.t  => L22 = A22 - l21*d1*l21t
 */
func unblkLowerLDLnoPiv(A *matrix.FloatMatrix) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a10, a11, A20, a21, A22 matrix.FloatMatrix

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)

	for ATL.Rows() < A.Rows() {
		repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			&a10, &a11, nil,
			&A20, &a21, &A22, A, 1, pBOTTOMRIGHT)

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

		// d11 = a11; no-op

		// A22 = A22 - l21*d11*l21.T = A22 - a21*a21.T/a11; triangular update
		err = MVUpdateTrm(&A22, &a21, &a21, -1.0/a11.Float(), LOWER)

		// l21 = a21/a11
		InvScale(&a21, a11.Float())
		// ---------------------------------------------------------

		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pBOTTOMRIGHT)
	}
	return
}

func _TestPartition1Dh(t *testing.T) {
	var AL, AR, A0, a1, A2 matrix.FloatMatrix
	A := matrix.FloatZeros(1, 6)
	partition1x2(&AL, &AR, A, 0, pRIGHT)
	t.Logf("m(AL)=%d, m(AR)=%d\n", AL.Cols(), AR.Cols())
	for AL.Cols() < A.Cols() {
		AR.Add(1.0)
		t.Logf("m(AR)=%d; %v\n", AR.Cols(), AR)
		repartition1x2to1x3(&AL, &A0, &a1, &A2, A, 1, pRIGHT)
		t.Logf("m(A0)=%d, m(A2)=%d, a1=%.1f\n", A0.Cols(), A2.Cols(), a1.Float())
		continue1x3to1x2(&AL, &AR, &A0, &a1, A, pRIGHT)
	}
}

/*
 *  ( A11  a12 )   ( U11 u12 )( D1  0  )( U11.t 0 )
 *  ( a21  a22 )   (  0   1  )(  0  d2 )( u12.t 1 )
 *
 *   a22  =   d2
 *   a01  =   u12*d2                       => u12 = a12/d2
 *   A11  =   u12*d2*u12.t + U11*D1*U11.t  => U11 = A11 - u12*d2*u12.t
 */
func unblkUpperLDL(A *matrix.FloatMatrix, p *pPivots) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a01, A02, a11, a12, A22 matrix.FloatMatrix
	var AL, AR, acol matrix.FloatMatrix
	var pT, pB, p0, p1, p2 pPivots

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pBOTTOMRIGHT)
	partitionPivot2x1(
		&pT,
		&pB, p, 0, pBOTTOM)

	for ATL.Rows() > 0 {
		repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			nil, &a11, &a12,
			nil, nil, &A22, A, 1, pTOPLEFT)
		repartPivot2x1to3x1(&pT,
			&p0, &p1, &p2 /**/, p, 1, pTOP)

		// --------------------------------------------------------
		// search diagonal; diag(A00;a11)
		ATL.Diag(&acol)
		//merge2x1(&acol, &a01, &a11)
		imax := IAMax(&acol)
		if imax < ATL.Rows()-1 {
			merge1x2(&AL, &ATL, &ATR)
			merge1x2(&AR, &a11, &a12)
			// pivot diagonal in symmetric matrix; will swap a11 and [imax,imax]
			applyPivotSym(&AL, &AR, imax, UPPER)
			p1.pivots[0] = imax + 1
		} else {
			p1.pivots[0] = 0
		}

		if a11.Float() == 0.0 {
			err = onError("zero on diagonal.")
			return
		}
		// A00 = A00 - u01*d11*u01.T = A00 - a01*a01.T/a11; triangular update
		err = MVUpdateTrm(&A00, &a01, &a01, -1.0/a11.Float(), UPPER)

		// u01 = a01/a11
		InvScale(&a01, a11.Float())
		// ---------------------------------------------------------

		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pTOPLEFT)
		contPivot3x1to2x1(
			&pT,
			&pB, &p0, &p1, p, pTOP)
	}
	return
}

func unblockedCHOL(A *matrix.FloatMatrix, flags Flags, nr int) (err error) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a01, A02, a10, a11, a12, A20, a21, A22 matrix.FloatMatrix

	err = nil
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)

	for ATL.Rows() < A.Rows() {
		repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			&a10, &a11, &a12,
			&A20, &a21, &A22, A, 1, pBOTTOMRIGHT)

		// a11 = sqrt(a11)
		aval := math.Sqrt(a11.Float())
		if math.IsNaN(aval) {
			panic(fmt.Sprintf("illegal value at %d: %e", nr+ATL.Rows(), a11.Float()))
		}
		a11.SetAt(0, 0, aval)

		if flags&LOWER != 0 {
			// a21 = a21/a11
			InvScale(&a21, a11.Float())
			// A22 = A22 - a21*a21' (SYR)
			err = MVRankUpdateSym(&A22, &a21, -1.0, flags)
		} else {
			// a21 = a12/a11
			InvScale(&a12, a11.Float())
			// A22 = A22 - a12'*a12 (SYR)
			err = MVRankUpdateSym(&A22, &a12, -1.0, flags)
		}

		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pBOTTOMRIGHT)
	}
	return
}

func unblkBoundedBKUpper(A, wrk *matrix.FloatMatrix, p *pPivots, ncol int) (error, int) {
	var err error
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a01, A02, a11, a12t, A22, a11inv matrix.FloatMatrix
	var w00, w01, w11 matrix.FloatMatrix
	var cwrk matrix.FloatMatrix
	var wx, Ax, wz matrix.FloatMatrix
	var pT, pB, p0, p1, p2 pPivots

	err = nil
	nc := 0
	if ncol > A.Cols() {
		ncol = A.Cols()
	}

	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pBOTTOMRIGHT)
	partitionPivot2x1(
		&pT,
		&pB, p, 0, pBOTTOM)

	// permanent working space for symmetric inverse of a11
	wrk.SubMatrix(&a11inv, wrk.Rows()-2, 0, 2, 2)
	a11inv.SetAt(0, 1, -1.0)
	a11inv.SetAt(1, 0, -1.0)

	for ATL.Cols() > 0 && nc < ncol {

		partition2x2(
			&w00, &w01,
			nil, &w11, wrk, nc, nc, pBOTTOMRIGHT)
		merge1x2(&wx, &w00, &w01)
		merge1x2(&Ax, &ATL, &ATR)

		//fmt.Printf("ATL:\n%v\n", &ATL)
		r, np := findAndBuildBKPivotUpper(&ATL, &ATR, &w00, &w01, nc)
		//fmt.Printf("[w00;w01]:\n%v\n", &wx)
		//fmt.Printf("after find: r=%d, np=%d, ncol=%d, nc=%d\n", r, np, ncol, nc)
		w00.SubMatrix(&wz, 0, w00.Cols()-2, w00.Rows(), 2)
		if np > ncol-nc {
			// next pivot does not fit into ncol columns, restore last column,
			// return with number of factorized columns
			return err, nc
		}
		if r != -1 {
			// pivoting needed; np == 1, last row; np == 2; next to last rows
			nrow := ATL.Rows() - np
			applyBKPivotSym(&ATL, nrow, r, UPPER)
			// swap left hand rows to get correct updates
			swapRows(&ATR, nrow, r)
			swapRows(&w01, nrow, r)
			if np == 2 {
				/* pivot block on diagonal; -1,-1
				 * [r, r] | [r ,-1]
				 * ----------------  2-by-2 pivot, swapping [1,0] and [r,0]
				 * [r,-1] | [-1,-1]
				 */
				t0 := w00.GetAt(-2, -1)
				tr := w00.GetAt(r, -1)
				//fmt.Printf("nc=%d, t0=%e, tr=%e\n", nc, t0, tr)
				w00.SetAt(-2, -1, tr)
				w00.SetAt(r, -1, t0)
				// interchange diagonal entries on w11[:,1]
				t0 = w00.GetAt(-2, -2)
				tr = w00.GetAt(r, -2)
				w00.SetAt(-2, -2, tr)
				w00.SetAt(r, -2, t0)
				//fmt.Printf("wrk:\n%v\n", &wz)
			}
			//fmt.Printf("pivoted A:\n%v\n", &Ax)
			//fmt.Printf("pivoted wrk:\n%v\n", &wx)
		}

		// repartition according the pivot size
		repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			nil, &a11, &a12t,
			nil, nil, &A22 /**/, A, np, pTOPLEFT)
		repartPivot2x1to3x1(&pT,
			&p0,
			&p1,
			&p2 /**/, p, np, pTOP)
		// ------------------------------------------------------------

		wlc := w00.Cols() - np
		//wlr := w00.Rows() - 1
		w00.SubMatrix(&cwrk, 0, wlc, a01.Rows(), np)
		if np == 1 {
			//fmt.Printf("wz:\n%v\n", &wz)
			//fmt.Printf("a11 <-- %e\n", w00.GetAt(a01.Rows(), wlc))

			//w00.SubMatrix(&cwrk, 0, wlc-np+1, a01.Rows(), np)
			a11.SetAt(0, 0, w00.GetAt(a01.Rows(), wlc))
			// a21 = a21/a11
			//fmt.Printf("np == 1: pre-update a01\n%v\n", &a01)
			cwrk.CopyTo(&a01)
			InvScale(&a01, a11.Float())
			//fmt.Printf("np == 1: cwrk\n%v\na21\n%v\n", &cwrk, &a21)
			// store pivot point relative to original matrix
//.........这里部分代码省略.........

func unblkBoundedLowerLDL(A, W *matrix.FloatMatrix, p *pPivots, ncol int) (error, int) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a10, a11, A20, a21, A22, adiag, wcol matrix.FloatMatrix
	var w00, w10, w11 matrix.FloatMatrix
	var pT, pB, p0, p1, p2 pPivots
	var err error = nil

	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)
	partitionPivot2x1(
		&pT,
		&pB, p, 0, pTOP)

	// copy current diagonal to last column of workspace
	W.SubMatrix(&wcol, 0, W.Cols()-1, A.Rows(), 1)
	A.Diag(&adiag)
	adiag.CopyTo(&wcol)
	//fmt.Printf("initial diagonal:\n%v\n", &wcol)

	nc := 0
	for ABR.Cols() > 0 && nc < ncol {

		partition2x2(
			&w00, nil,
			&w10, &w11, W, nc, nc, pTOPLEFT)

		dmax := findAndBuildPivot(&ABL, &ABR, &w10, &w11, nc)
		//fmt.Printf("dmax=%d\n", dmax)
		if dmax > 0 {
			// pivot diagonal in symmetric matrix; will swap a11 [0,0] and [imax,imax]
			applyPivotSym(&ABL, &ABR, dmax, LOWER)
			swapRows(&w10, 0, dmax)
			pB.pivots[0] = dmax + ATL.Rows() + 1
		} else {
			pB.pivots[0] = 0
		}

		//fmt.Printf("blk pivoted %d, A:\n%v\nW:\n%v\n", dmax, A, W)
		repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			&a10, &a11, nil,
			&A20, &a21, &A22, A, 1, pBOTTOMRIGHT)
		repartPivot2x1to3x1(&pT,
			&p0, &p1, &p2 /**/, p, 1, pBOTTOM)

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

		// Copy updated column from working space
		w11.SubMatrix(&wcol, 1, 0, a21.Rows(), 1)
		wcol.CopyTo(&a21)
		a11.SetAt(0, 0, w11.GetAt(0, 0))
		// l21 = a21/a11
		InvScale(&a21, a11.Float())
		// here: wcol == l21*d11 == a21
		if ncol-nc > 1 {
			// update diagonal in workspace if not last column of block
			w11.SubMatrix(&adiag, 1, w11.Cols()-1, a21.Rows(), 1)
			MVUpdateDiag(&adiag, &wcol, &wcol, -1.0/a11.Float())
		}
		//fmt.Printf("nc=%d, a11=%e\n", nc, a11.Float())
		//fmt.Printf("l21\n%v\n", &a21)
		//fmt.Printf("a21\n%v\n", &wcol)
		//fmt.Printf("diag\n%v\n", &adiag)
		//var Ablk, wblk matrix.FloatMatrix
		//merge1x2(&Ablk, &ABL, &ABR)
		//merge1x2(&wblk, &w10, &w11)
		//fmt.Printf("unblk Ablk:\n%v\n", &Ablk)
		//fmt.Printf("unblk wblk:\n%v\n", &wblk)

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

		nc++
		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pBOTTOMRIGHT)
		contPivot3x1to2x1(
			&pT,
			&pB, &p0, &p1, p, pBOTTOM)
	}
	return err, nc
}

/*
 * Unblocked Bunch-Kauffman LDL factorization.
 *
 * Corresponds lapack.DSYTF2
 */
func unblkDecompBKUpper(A, wrk *matrix.FloatMatrix, p *pPivots) (error, int) {
	var err error
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a01, A02, a12t, a11, A22, a11inv matrix.FloatMatrix
	var cwrk matrix.FloatMatrix
	var pT, pB, p0, p1, p2 pPivots

	err = nil
	nc := 0

	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pBOTTOMRIGHT)
	partitionPivot2x1(
		&pT,
		&pB, p, 0, pBOTTOM)

	// permanent working space for symmetric inverse of a11
	wrk.SubMatrix(&a11inv, 0, wrk.Cols()-2, 2, 2)
	a11inv.SetAt(1, 0, -1.0)
	a11inv.SetAt(0, 1, -1.0)

	for ATL.Cols() > 0 {

		nr := ATL.Rows() - 1
		r, np := findBKPivot(&ATL, UPPER)
		if r != -1 /*&& r != np-1*/ {
			// pivoting needed; do swaping here
			//fmt.Printf("pre-pivot ATL [%d]:\n%v\n", ATL.Rows()-np, &ATL)
			applyBKPivotSym(&ATL, ATL.Rows()-np, r, UPPER)
			if np == 2 {
				/*
				 *         [r,r] | [r, nr]
				 * a11 ==  ---------------  2-by-2 pivot, swapping [nr-1,nr] and [r,nr]
				 *         [r,0] | [nr,nr]
				 */
				t := ATL.GetAt(nr-1, nr)
				ATL.SetAt(nr-1, nr, ATL.GetAt(r, nr))
				ATL.SetAt(r, nr, t)
			}
			//fmt.Printf("unblk: ATL after %d pivot [r=%d]:\n%v\n", np, r, &ATL)
		}

		// repartition according the pivot size
		repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			nil, &a11, &a12t,
			nil, nil, &A22 /**/, A, np, pTOPLEFT)
		repartPivot2x1to3x1(&pT,
			&p0,
			&p1,
			&p2 /**/, p, np, pTOP)
		// ------------------------------------------------------------

		if np == 1 {
			// A00 = A00 - a01*a01.T/a11
			MVUpdateTrm(&A00, &a01, &a01, -1.0/a11.Float(), UPPER)
			// a01 = a01/a11
			InvScale(&a01, a11.Float())
			if r == -1 {
				p1.pivots[0] = ATL.Rows()
			} else {
				p1.pivots[0] = r + 1
			}
		} else if np == 2 {
			/*
			 * See comments on unblkDecompBKLower().
			 */
			a := a11.GetAt(0, 0)
			b := a11.GetAt(0, 1)
			d := a11.GetAt(1, 1)
			a11inv.SetAt(0, 0, d/b)
			a11inv.SetAt(1, 1, a/b)
			// denominator: (a/b)*(d/b)-1.0 == (a*d - b^2)/b^2
			scale := 1.0 / ((a/b)*(d/b) - 1.0)
			scale /= b

			// cwrk = a21
			wrk.SubMatrix(&cwrk, 2, 0, a01.Rows(), a01.Cols())
			a01.CopyTo(&cwrk)
			//fmt.Printf("cwrk:\n%v\n", &cwrk)
			//fmt.Printf("a11inv:\n%v\n", &a11inv)
			// a01 = a01*a11.-1
			Mult(&a01, &cwrk, &a11inv, scale, 0.0, NOTRANS)
			// A00 = A00 - a01*a11.-1*a01.T = A00 - a01*cwrk.T
			UpdateTrm(&A00, &a01, &cwrk, -1.0, 1.0, UPPER|TRANSB)

			p1.pivots[0] = -(r + 1)
			p1.pivots[1] = p1.pivots[0]
		}

		// ------------------------------------------------------------
		nc += np
		continue3x3to2x2(
			&ATL, &ATR,
//.........这里部分代码省略.........

/*
 * Unblocked, bounded Bunch-Kauffman LDL factorization for at most ncol columns.
 * At most ncol columns are factorized and trailing matrix updates are restricted
 * to ncol columns. Also original columns are accumulated to working matrix, which
 * is used by calling blocked algorithm to update the trailing matrix with BLAS3
 * update.
 *
 * Corresponds lapack.DLASYF
 */
func unblkBoundedBKLower(A, wrk *matrix.FloatMatrix, p *pPivots, ncol int) (error, int) {
	var err error
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a10t, a11, A20, a21, A22, a11inv matrix.FloatMatrix
	var w00, w10, w11 matrix.FloatMatrix
	var cwrk matrix.FloatMatrix
	//var s, d matrix.FloatMatrix
	var pT, pB, p0, p1, p2 pPivots

	err = nil
	nc := 0
	if ncol > A.Cols() {
		ncol = A.Cols()
	}

	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)
	partitionPivot2x1(
		&pT,
		&pB, p, 0, pTOP)

	// permanent working space for symmetric inverse of a11
	wrk.SubMatrix(&a11inv, 0, wrk.Cols()-2, 2, 2)
	a11inv.SetAt(1, 0, -1.0)
	a11inv.SetAt(0, 1, -1.0)

	for ABR.Cols() > 0 && nc < ncol {

		partition2x2(
			&w00, nil,
			&w10, &w11, wrk, nc, nc, pTOPLEFT)

		//fmt.Printf("ABR:\n%v\n", &ABR)
		r, np := findAndBuildBKPivotLower(&ABL, &ABR, &w10, &w11, nc)
		//fmt.Printf("after find: r=%d, np=%d, ncol=%d, nc=%d\n", r, np, ncol, nc)
		if np > ncol-nc {
			// next pivot does not fit into ncol columns, restore last column,
			// return with number of factorized columns
			//fmt.Printf("np > ncol-nc: %d > %d\n", np, ncol-nc)
			return err, nc
			//goto undo
		}
		if r != 0 && r != np-1 {
			// pivoting needed; do swaping here
			applyBKPivotSym(&ABR, np-1, r, LOWER)
			// swap left hand rows to get correct updates
			swapRows(&ABL, np-1, r)
			swapRows(&w10, np-1, r)
			//ABL.SubMatrix(&s, np-1, 0, 1, ABL.Cols())
			//ABL.SubMatrix(&d, r,    0, 1, ABL.Cols())
			//Swap(&s, &d)
			//w10.SubMatrix(&s, np-1, 0, 1, w10.Cols())
			//w10.SubMatrix(&d, r,    0, 1, w10.Cols())
			//Swap(&s, &d)
			if np == 2 {
				/*
				 *          [0,0] | [r,0]
				 * a11 ==   -------------  2-by-2 pivot, swapping [1,0] and [r,0]
				 *          [r,0] | [r,r]
				 */
				t0 := w11.GetAt(1, 0)
				tr := w11.GetAt(r, 0)
				//fmt.Printf("nc=%d, t0=%e, tr=%e\n", nc, t0, tr)
				w11.SetAt(1, 0, tr)
				w11.SetAt(r, 0, t0)
				// interchange diagonal entries on w11[:,1]
				t0 = w11.GetAt(1, 1)
				tr = w11.GetAt(r, 1)
				w11.SetAt(1, 1, tr)
				w11.SetAt(r, 1, t0)
			}
			//fmt.Printf("pivoted A:\n%v\n", A)
			//fmt.Printf("pivoted wrk:\n%v\n", wrk)
		}

		// repartition according the pivot size
		repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			&a10t, &a11, nil,
			&A20, &a21, &A22 /**/, A, np, pBOTTOMRIGHT)
		repartPivot2x1to3x1(&pT,
			&p0,
			&p1,
			&p2 /**/, p, np, pBOTTOM)
		// ------------------------------------------------------------

		if np == 1 {
			//
			w11.SubMatrix(&cwrk, np, 0, a21.Rows(), np)
			a11.SetAt(0, 0, w11.GetAt(0, 0))
//.........这里部分代码省略.........

/*
 * Unblocked Bunch-Kauffman LDL factorization.
 *
 * Corresponds lapack.DSYTF2
 */
func unblkDecompBKLower(A, wrk *matrix.FloatMatrix, p *pPivots) (error, int) {
	var err error
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a10t, a11, A20, a21, A22, a11inv matrix.FloatMatrix
	var cwrk matrix.FloatMatrix
	var pT, pB, p0, p1, p2 pPivots

	err = nil
	nc := 0

	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)
	partitionPivot2x1(
		&pT,
		&pB, p, 0, pTOP)

	// permanent working space for symmetric inverse of a11
	wrk.SubMatrix(&a11inv, 0, wrk.Cols()-2, 2, 2)
	a11inv.SetAt(1, 0, -1.0)
	a11inv.SetAt(0, 1, -1.0)

	for ABR.Cols() > 0 {

		r, np := findBKPivot(&ABR, LOWER)
		if r != 0 && r != np-1 {
			// pivoting needed; do swaping here
			applyBKPivotSym(&ABR, np-1, r, LOWER)
			if np == 2 {
				/*
				 *          [0,0] | [r,0]
				 * a11 ==   -------------  2-by-2 pivot, swapping [1,0] and [r,0]
				 *          [r,0] | [r,r]
				 */
				t := ABR.GetAt(1, 0)
				ABR.SetAt(1, 0, ABR.GetAt(r, 0))
				ABR.SetAt(r, 0, t)
			}
			//fmt.Printf("unblk: ABR after %d pivot [r=%d]:\n%v\n", np, r, &ABR)
		}

		// repartition according the pivot size
		repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			&a10t, &a11, nil,
			&A20, &a21, &A22 /**/, A, np, pBOTTOMRIGHT)
		repartPivot2x1to3x1(&pT,
			&p0,
			&p1,
			&p2 /**/, p, np, pBOTTOM)
		// ------------------------------------------------------------

		if np == 1 {
			// A22 = A22 - a21*a21.T/a11
			MVUpdateTrm(&A22, &a21, &a21, -1.0/a11.Float(), LOWER)
			// a21 = a21/a11
			InvScale(&a21, a11.Float())
			// store pivot point relative to original matrix
			p1.pivots[0] = r + ATL.Rows() + 1
		} else if np == 2 {
			/* from Bunch-Kaufmann 1977:
			 *  (E2 C.T) = ( I2      0      )( E  0      )( I[n-2] E.-1*C.T )
			 *  (C  B  )   ( C*E.-1  I[n-2] )( 0  A[n-2] )( 0      I2       )
			 *
			 *  A[n-2] = B - C*E.-1*C.T
			 *
			 *  E.-1 is inverse of a symmetric matrix, cannot use
			 *  triangular solve. We calculate inverse of 2x2 matrix.
			 *  Following is inspired by lapack.SYTF2
			 *
			 *      a | b      1        d | -b         b         d/b | -1
			 *  inv ----- =  ------  * ------  =  ----------- * --------
			 *      b | d    (ad-b^2)  -b |  a    (a*d - b^2)     -1 | a/b
			 *
			 */
			a := a11.GetAt(0, 0)
			b := a11.GetAt(1, 0)
			d := a11.GetAt(1, 1)
			a11inv.SetAt(0, 0, d/b)
			a11inv.SetAt(1, 1, a/b)
			// denominator: (a/b)*(d/b)-1.0 == (a*d - b^2)/b^2
			scale := 1.0 / ((a/b)*(d/b) - 1.0)
			scale /= b

			// cwrk = a21
			wrk.SubMatrix(&cwrk, 2, 0, a21.Rows(), a21.Cols())
			a21.CopyTo(&cwrk)
			// a21 = a21*a11.-1
			Mult(&a21, &cwrk, &a11inv, scale, 0.0, NOTRANS)
			// A22 = A22 - a21*a11.-1*a21.T = A22 - a21*cwrk.T
			UpdateTrm(&A22, &a21, &cwrk, -1.0, 1.0, LOWER|TRANSB)

			// store pivot point relative to original matrix
			p1.pivots[0] = -(r + ATL.Rows() + 1)
			p1.pivots[1] = p1.pivots[0]
//.........这里部分代码省略.........

func unblkSolveBKUpper(B, A *matrix.FloatMatrix, p *pPivots, phase int) error {
	var err error
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a01, A02, a11, a12t, A22 matrix.FloatMatrix
	var Aref *matrix.FloatMatrix
	var BT, BB, B0, b1, B2, Bx matrix.FloatMatrix
	var pT, pB, p0, p1, p2 pPivots
	var aStart, aDir, bStart, bDir pDirection
	var nc int

	err = nil
	np := 0

	if phase == 2 {
		aStart = pTOPLEFT
		aDir = pBOTTOMRIGHT
		bStart = pTOP
		bDir = pBOTTOM
		nc = 1
		Aref = &ABR
	} else {
		aStart = pBOTTOMRIGHT
		aDir = pTOPLEFT
		bStart = pBOTTOM
		bDir = pTOP
		nc = A.Rows()
		Aref = &ATL
	}
	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, aStart)
	partition2x1(
		&BT,
		&BB, B, 0, bStart)
	partitionPivot2x1(
		&pT,
		&pB, p, 0, bStart)

	// ABR.Cols() == 0 is end of matrix,
	for Aref.Cols() > 0 {

		// see if next diagonal block is 1x1 or 2x2
		np = 1
		if p.pivots[nc-1] < 0 {
			np = 2
		}
		fmt.Printf("nc=%d, np=%d, m(ABR)=%d\n", nc, np, m(&ABR))

		// repartition according the pivot size
		repartition2x2to3x3(&ATL,
			&A00, &a01, &A02,
			nil, &a11, &a12t,
			nil, nil, &A22 /**/, A, np, aDir)
		repartition2x1to3x1(&BT,
			&B0,
			&b1,
			&B2 /**/, B, np, bDir)
		repartPivot2x1to3x1(&pT,
			&p0,
			&p1,
			&p2 /**/, p, np, bDir)
		// ------------------------------------------------------------

		switch phase {
		case 1:
			// computes D.-1*(L.-1*B)
			if np == 1 {
				if p1.pivots[0] != nc {
					// swap rows in top part of B
					//fmt.Printf("1x1 pivot top with %d [%d]\n", p1.pivots[0], p1.pivots[0]-BT.Rows())
					swapRows(&BT, BT.Rows()-1, p1.pivots[0]-1)
				}
				// B2 = B2 - a21*b1
				MVRankUpdate(&B2, &a01, &b1, -1.0)
				// b1 = b1/d1
				InvScale(&b1, a11.Float())
				nc += 1
			} else if np == 2 {
				if p1.pivots[0] != -nc {
					// swap rows on bottom part of B
					//fmt.Printf("2x2 pivot %d with %d [%d]\n", nc+1, -p1.pivots[0])
					//fmt.Printf("pre :\n%v\n", B)
					swapRows(&BT, BT.Rows()-2, -p1.pivots[0]-1)
					//fmt.Printf("post:\n%v\n", B)
				}
				b := a11.GetAt(0, 1)
				apb := a11.GetAt(0, 0) / b
				dpb := a11.GetAt(1, 1) / b
				// (a/b)*(d/b)-1.0 == (a*d - b^2)/b^2
				scale := apb*dpb - 1.0
				scale *= b

				// B2 = B2 - a21*b1
				Mult(&B2, &a01, &b1, -1.0, 1.0, NOTRANS)
				// b1 = a11.-1*b1.T
				//(2x2 block, no subroutine for doing this in-place)
				for k := 0; k < b1.Cols(); k++ {
					s0 := b1.GetAt(0, k)
					s1 := b1.GetAt(1, k)
					b1.SetAt(0, k, (dpb*s0-s1)/scale)
//.........这里部分代码省略.........