Golang FloatMatrix.SetAt方法代碼示例

// 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
}

func setDiagonal(M *matrix.FloatMatrix, srow, scol, erow, ecol int, val float64) {
	for i := srow; i < erow; i++ {
		if i < ecol {
			M.SetAt(i, i, val)
		}
	}
}

// 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
}

/*
 * 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 unblkQRBlockReflector(T, A, tau *matrix.FloatMatrix) {
	var ATL, ATR, ABL, ABR matrix.FloatMatrix
	var A00, a10, a11, A20, a21, A22 matrix.FloatMatrix
	var TTL, TTR, TBL, TBR matrix.FloatMatrix
	var T00, t01, T02, t11, t12, T22 matrix.FloatMatrix
	var tT, tB matrix.FloatMatrix
	var t0, tau1, t2 matrix.FloatMatrix

	partition2x2(
		&ATL, &ATR,
		&ABL, &ABR, A, 0, 0, pTOPLEFT)
	partition2x2(
		&TTL, &TTR,
		&TBL, &TBR, T, 0, 0, pTOPLEFT)
	partition2x1(
		&tT,
		&tB, tau, 0, pTOP)

	for ABR.Rows() > 0 && ABR.Cols() > 0 {
		repartition2x2to3x3(&ATL,
			&A00, nil, nil,
			&a10, &a11, nil,
			&A20, &a21, &A22, A, 1, pBOTTOMRIGHT)
		repartition2x2to3x3(&TTL,
			&T00, &t01, &T02,
			nil, &t11, &t12,
			nil, nil, &T22, T, 1, pBOTTOMRIGHT)
		repartition2x1to3x1(&tT,
			&t0,
			&tau1,
			&t2, tau, 1, pBOTTOM)
		// --------------------------------------------------

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

			// t01 := a10.T + &A20.T*a21
			a10.CopyTo(&t01)
			MVMult(&t01, &A20, &a21, -tauval, -tauval, TRANSA)
			// t01 := T00*t01
			MVMultTrm(&t01, &T00, UPPER)
			//t01.Scale(-tauval)
		}

		// --------------------------------------------------
		continue3x3to2x2(
			&ATL, &ATR,
			&ABL, &ABR, &A00, &a11, &A22, A, pBOTTOMRIGHT)
		continue3x3to2x2(
			&TTL, &TTR,
			&TBL, &TBR, &T00, &t11, &T22, T, pBOTTOMRIGHT)
		continue3x1to2x1(
			&tT,
			&tB, &t0, &tau1, tau, pBOTTOM)
	}
}

// Make A tridiagonal, lower, unit matrix by clearing the strictly upper part
// of the matrix and setting diagonal elements to one.
func TriLU(A *matrix.FloatMatrix) *matrix.FloatMatrix {
	var Ac matrix.FloatMatrix
	mlen := imin(A.Rows(), A.Cols())
	A.SetAt(0, 0, 1.0)
	for k := 1; k < mlen; k++ {
		A.SetAt(k, k, 1.0)
		Ac.SubMatrixOf(A, 0, k, k, 1)
		Ac.SetIndexes(0.0)
	}
	if A.Cols() > A.Rows() {
		Ac.SubMatrixOf(A, 0, A.Rows())
		Ac.SetIndexes(0.0)
	}
	return A
}

// Make A tridiagonal, upper, unit matrix by clearing the strictly lower part
// of the matrix and setting diagonal elements to one.
func TriUU(A *matrix.FloatMatrix) *matrix.FloatMatrix {
	var Ac matrix.FloatMatrix
	var k int
	mlen := imin(A.Rows(), A.Cols())
	for k = 0; k < mlen; k++ {
		Ac.SubMatrixOf(A, k+1, k, A.Rows()-k-1, 1)
		Ac.SetIndexes(0.0)
		A.SetAt(k, k, 1.0)
	}
	// last element on diagonal
	A.SetAt(k, k, 1.0)
	if A.Cols() < A.Rows() {
		Ac.SubMatrixOf(A, A.Cols(), 0)
		Ac.SetIndexes(0.0)
	}
	return A
}

/* From LAPACK/dlarfg.f
 *
 * DLARFG generates a real elementary reflector H of order n, such
 * that
 *
 *       H * ( alpha ) = ( beta ),   H**T * H = I.
 *           (   x   )   (   0  )
 *
 * where alpha and beta are scalars, and x is an (n-1)-element real
 * vector. 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 (n-1)-element
 * vector.
 *
 * If the elements of x are all zero, then tau = 0 and H is taken to be
 * the unit matrix.
 *
 * Otherwise  1 <= tau <= 2.
 */
func computeHouseholder(a11, x, tau *matrix.FloatMatrix, flags Flags) {

	// norm_x2 = ||x||_2
	norm_x2 := Norm2(x)
	if norm_x2 == 0.0 {
		//a11.SetAt(0, 0, -a11.GetAt(0, 0))
		tau.SetAt(0, 0, 0.0)
		return
	}

	alpha := a11.GetAt(0, 0)
	sign := 1.0
	if math.Signbit(alpha) {
		sign = -1.0
	}
	// beta = -(alpha / |alpha|) * ||alpha x||
	//      = -sign(alpha) * sqrt(alpha**2, norm_x2**2)
	beta := -sign * sqrtX2Y2(alpha, norm_x2)

	// x = x /(a11 - beta)
	InvScale(x, alpha-beta)

	tau.SetAt(0, 0, (beta-alpha)/beta)
	a11.SetAt(0, 0, beta)
}

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
}

/*
 * Apply diagonal pivot (row and column swapped) to symmetric matrix blocks.
 *
 * LOWER triangular; moving from top-left to bottom-right
 *
 *    -----------------------
 *    | d
 *    | x P1 x  x  x  P2     -- current row/col 'srcix'
 *    | x S2 d  x  x  x
 *    | x S2 x  d  x  x
 *    | x S2 x  x  d  x
 *    | x P2 D2 D2 D2 P3     -- swap with row/col 'dstix'
 *    | x S3 x  x  x  D3 d
 *    | x S3 x  x  x  D3 x d
 *         (AR)
 *
 * UPPER triangular; moving from bottom-right to top-left
 *
 *    d x D3 x  x  x  S3 x |
 *      d D3 x  x  x  S3 x |
 *        P3 D2 D2 D2 P2 x |  -- dstinx
 *           d  x  x  S2 x |
 *              d  x  S2 x |
 *                 d  S2 x |
 *                    P1 x |  -- srcinx
 *                       d |
 *    ----------------------
 *               (ABR)
 */
func applyBKPivotSym(AR *matrix.FloatMatrix, srcix, dstix int, flags Flags) {
	var s, d matrix.FloatMatrix
	if flags&LOWER != 0 {
		// S2 -- D2
		AR.SubMatrix(&s, srcix+1, srcix, dstix-srcix-1, 1)
		AR.SubMatrix(&d, dstix, srcix+1, 1, dstix-srcix-1)
		Swap(&s, &d)
		// S3 -- D3
		AR.SubMatrix(&s, dstix+1, srcix, AR.Rows()-dstix-1, 1)
		AR.SubMatrix(&d, dstix+1, dstix, AR.Rows()-dstix-1, 1)
		Swap(&s, &d)
		// swap P1 and P3
		p1 := AR.GetAt(srcix, srcix)
		p3 := AR.GetAt(dstix, dstix)
		AR.SetAt(srcix, srcix, p3)
		AR.SetAt(dstix, dstix, p1)
		return
	}
	if flags&UPPER != 0 {
		// AL is ATL, AR is ATR; P1 is AL[srcix, srcix];
		// S2 -- D2
		AR.SubMatrix(&s, dstix+1, srcix, srcix-dstix-1, 1)
		AR.SubMatrix(&d, dstix, dstix+1, 1, srcix-dstix-1)
		Swap(&s, &d)
		// S3 -- D3
		AR.SubMatrix(&s, 0, srcix, dstix, 1)
		AR.SubMatrix(&d, 0, dstix, dstix, 1)
		Swap(&s, &d)
		//fmt.Printf("3, AR=%v\n", AR)
		// swap P1 and P3
		p1 := AR.GetAt(srcix, srcix)
		p3 := AR.GetAt(dstix, dstix)
		AR.SetAt(srcix, srcix, p3)
		AR.SetAt(dstix, dstix, p1)
		return
	}
}

/*
 * Apply diagonal pivot (row and column swapped) to symmetric matrix blocks.
 * AR[0,0] is on diagonal and AL is block to the left of diagonal and AR the
 * triangular diagonal block. Need to swap row and column.
 *
 * LOWER triangular; moving from top-left to bottom-right
 *
 *    d
 *    x  d
 *    x  x  d  |
 *    --------------------------
 *    S1 S1 S1 | P1 x  x  x  P2     -- current row
 *    x  x  x  | S2 d  x  x  x
 *    x  x  x  | S2 x  d  x  x
 *    x  x  x  | S2 x  x  d  x
 *    D1 D1 D1 | P2 D2 D2 D2 P3     -- swap with row 'index'
 *    x  x  x  | S3 x  x  x  D3 d
 *    x  x  x  | S3 x  x  x  D3 x d
 *       (ABL)          (ABR)
 *
 * UPPER triangular; moving from bottom-right to top-left
 *
 *         (ATL)             (ATR)
 *    d  x  x  D3 x  x  x | S3 x  x
 *       d  x  D3 x  x  x | S3 x  x
 *          d  D3 x  x  x | S3 x  x
 *             P3 D2 D2 D2| P2 D1 D1
 *                d  x  x | S2 x  x
 *                   d  x | S2 x  x
 *                      d | S2 x  x
 *    -----------------------------
 *                        | P1 S1 S1
 *                        |    d  x
 *                        |       d
 *                           (ABR)
 */
func applyPivotSym(AL, AR *matrix.FloatMatrix, index int, flags Flags) {
	var s, d matrix.FloatMatrix
	if flags&LOWER != 0 {
		// AL is [ABL]; AR is [ABR]; P1 is AR[0,0], P2 is AR[index, 0]
		// S1 -- D1
		AL.SubMatrix(&s, 0, 0, 1, AL.Cols())
		AL.SubMatrix(&d, index, 0, 1, AL.Cols())
		Swap(&s, &d)
		// S2 -- D2
		AR.SubMatrix(&s, 1, 0, index-1, 1)
		AR.SubMatrix(&d, index, 1, 1, index-1)
		Swap(&s, &d)
		// S3 -- D3
		AR.SubMatrix(&s, index+1, 0, AR.Rows()-index-1, 1)
		AR.SubMatrix(&d, index+1, index, AR.Rows()-index-1, 1)
		Swap(&s, &d)
		// swap P1 and P3
		p1 := AR.GetAt(0, 0)
		p3 := AR.GetAt(index, index)
		AR.SetAt(0, 0, p3)
		AR.SetAt(index, index, p1)
		return
	}
	if flags&UPPER != 0 {
		// AL is merged from [ATL, ATR], AR is [ABR]; P1 is AR[0, 0]; P2 is AL[index, -1]
		colno := AL.Cols() - AR.Cols()
		// S1 -- D1; S1 is on the first row of AR
		AR.SubMatrix(&s, 0, 1, 1, AR.Cols()-1)
		AL.SubMatrix(&d, index, colno+1, 1, s.Cols())
		Swap(&s, &d)
		// S2 -- D2
		AL.SubMatrix(&s, index+1, colno, AL.Rows()-index-2, 1)
		AL.SubMatrix(&d, index, index+1, 1, colno-index-1)
		Swap(&s, &d)
		// S3 -- D3
		AL.SubMatrix(&s, 0, index, index, 1)
		AL.SubMatrix(&d, 0, colno, index, 1)
		Swap(&s, &d)
		//fmt.Printf("3, AR=%v\n", AR)
		// swap P1 and P3
		p1 := AR.GetAt(0, 0)
		p3 := AL.GetAt(index, index)
		AR.SetAt(0, 0, p3)
		AL.SetAt(index, index, p1)
		return
	}
}

/*
 * Apply diagonal pivot (row and column swapped) to symmetric matrix blocks.
 * AR[0,0] is on diagonal and AL is block to the left of diagonal and AR the
 * triangular diagonal block. Need to swap row and column.
 *
 * LOWER triangular; moving from top-left to bottom-right
 *
 *    d
 *    x  d |
 *    --------------------------
 *    x  x | d
 *    S1 S1| S1 P1 x  x  x  P2     -- current row/col 'srcix'
 *    x  x | x  S2 d  x  x  x
 *    x  x | x  S2 x  d  x  x
 *    x  x | x  S2 x  x  d  x
 *    D1 D1| D1 P2 D2 D2 D2 P3     -- swap with row/col 'dstix'
 *    x  x | x  S3 x  x  x  D3 d
 *    x  x | x  S3 x  x  x  D3 x d
 *    (ABL)          (ABR)
 *
 * UPPER triangular; moving from bottom-right to top-left
 *
 *         (ATL)                  (ATR)
 *    d  x  x  D3 x  x  x  S3 x | x
 *       d  x  D3 x  x  x  S3 x | x
 *          d  D3 x  x  x  S3 x | x
 *             P3 D2 D2 D2 P2 D1| D1  -- dstinx
 *                d  x  x  S2 x | x
 *                   d  x  S2 x | x
 *                      d  S2 x | x
 *                         P1 S1| S1  -- srcinx
 *                            d | x
 *    -----------------------------
 *                              | d
 *                           (ABR)
 */
func applyPivotSym2(AL, AR *matrix.FloatMatrix, srcix, dstix int, flags Flags) {
	var s, d matrix.FloatMatrix
	if flags&LOWER != 0 {
		// AL is [ABL]; AR is [ABR]; P1 is AR[0,0], P2 is AR[index, 0]
		// S1 -- D1
		AL.SubMatrix(&s, srcix, 0, 1, AL.Cols())
		AL.SubMatrix(&d, dstix, 0, 1, AL.Cols())
		Swap(&s, &d)
		if srcix > 0 {
			AR.SubMatrix(&s, srcix, 0, 1, srcix)
			AR.SubMatrix(&d, dstix, 0, 1, srcix)
			Swap(&s, &d)
		}
		// S2 -- D2
		AR.SubMatrix(&s, srcix+1, srcix, dstix-srcix-1, 1)
		AR.SubMatrix(&d, dstix, srcix+1, 1, dstix-srcix-1)
		Swap(&s, &d)
		// S3 -- D3
		AR.SubMatrix(&s, dstix+1, srcix, AR.Rows()-dstix-1, 1)
		AR.SubMatrix(&d, dstix+1, dstix, AR.Rows()-dstix-1, 1)
		Swap(&s, &d)
		// swap P1 and P3
		p1 := AR.GetAt(srcix, srcix)
		p3 := AR.GetAt(dstix, dstix)
		AR.SetAt(srcix, srcix, p3)
		AR.SetAt(dstix, dstix, p1)
		return
	}
	if flags&UPPER != 0 {
		// AL is ATL, AR is ATR; P1 is AL[srcix, srcix];
		// S1 -- D1;
		AR.SubMatrix(&s, srcix, 0, 1, AR.Cols())
		AR.SubMatrix(&d, dstix, 0, 1, AR.Cols())
		Swap(&s, &d)
		if srcix < AL.Cols()-1 {
			// not the corner element
			AL.SubMatrix(&s, srcix, srcix+1, 1, srcix)
			AL.SubMatrix(&d, dstix, srcix+1, 1, srcix)
			Swap(&s, &d)
		}
		// S2 -- D2
		AL.SubMatrix(&s, dstix+1, srcix, srcix-dstix-1, 1)
		AL.SubMatrix(&d, dstix, dstix+1, 1, srcix-dstix-1)
		Swap(&s, &d)
		// S3 -- D3
		AL.SubMatrix(&s, 0, srcix, dstix, 1)
		AL.SubMatrix(&d, 0, dstix, dstix, 1)
		Swap(&s, &d)
		//fmt.Printf("3, AR=%v\n", AR)
		// swap P1 and P3
		p1 := AR.GetAt(0, 0)
		p3 := AL.GetAt(dstix, dstix)
		AR.SetAt(srcix, srcix, p3)
		AL.SetAt(dstix, dstix, p1)
		return
	}
}

func findAndBuildPivot(AL, AR, WL, WR *matrix.FloatMatrix, k int) int {
	var dg, acol, wcol, wrow matrix.FloatMatrix

	// updated diagonal values on last column of workspace
	WR.SubMatrix(&dg, 0, WR.Cols()-1, AR.Rows(), 1)

	// find on-diagonal maximun value
	dmax := IAMax(&dg)
	//fmt.Printf("dmax=%d, val=%e\n", dmax, dg.GetAt(dmax, 0))

	// copy to first column of WR and update with factorized columns
	WR.SubMatrix(&wcol, 0, 0, WR.Rows(), 1)
	if dmax == 0 {
		AR.SubMatrix(&acol, 0, 0, AR.Rows(), 1)
		acol.CopyTo(&wcol)
	} else {
		AR.SubMatrix(&acol, dmax, 0, 1, dmax+1)
		acol.CopyTo(&wcol)
		if dmax < AR.Rows()-1 {
			var wrst matrix.FloatMatrix
			WR.SubMatrix(&wrst, dmax, 0, wcol.Rows()-dmax, 1)
			AR.SubMatrix(&acol, dmax, dmax, AR.Rows()-dmax, 1)
			acol.CopyTo(&wrst)
		}
	}
	if k > 0 {
		WL.SubMatrix(&wrow, dmax, 0, 1, WL.Cols())
		//fmt.Printf("update with wrow:%v\n", &wrow)
		//fmt.Printf("update wcol\n%v\n", &wcol)
		MVMult(&wcol, AL, &wrow, -1.0, 1.0, NOTRANS)
		//fmt.Printf("updated wcol:\n%v\n", &wcol)
	}
	if dmax > 0 {
		// pivot column in workspace
		t0 := WR.GetAt(0, 0)
		WR.SetAt(0, 0, WR.GetAt(dmax, 0))
		WR.SetAt(dmax, 0, t0)
		// pivot on diagonal
		t0 = dg.GetAt(0, 0)
		dg.SetAt(0, 0, dg.GetAt(dmax, 0))
		dg.SetAt(dmax, 0, t0)
	}
	return dmax
}

/*
 * 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))
//.........這裏部分代碼省略.........

/*
 * Find diagonal pivot and build incrementaly updated block.
 *
 *  (AL)  (AR)                   (WL)  (WR)
 *  --------------------------   ----------    k'th row in W
 *  x x | c1                     w w | k kp1
 *  x x | c1 d                   w w | k kp1
 *  x x | c1 x  d                w w | k kp1
 *  x x | c1 x  x  d             w w | k kp1
 *  x x | c1 r2 r2 r2 r2         w w | k kp1
 *  x x | c1 x  x  x  r2 d       w w | k kp1
 *  x x | c1 x  x  x  r2 x d     w w | k kp1
 *
 * Matrix AR contains the unfactored part of the matrix and AL the already
 * factored columns. Matrix WL is updated values of factored part ie.
 * w(i) = l(i)d(i). Matrix WR will have updated values for next column.
 * Column WR(k) contains updated AR(c1) and WR(kp1) possible pivot row AR(r2).
 *
 *
 */
func findAndBuildBKPivotLower(AL, AR, WL, WR *matrix.FloatMatrix, k int) (int, int) {
	var r, q int
	var rcol, qrow, src, wk, wkp1, wrow matrix.FloatMatrix

	// Copy AR column 0 to WR column 0 and update with WL[0:]
	AR.SubMatrix(&src, 0, 0, AR.Rows(), 1)
	WR.SubMatrix(&wk, 0, 0, AR.Rows(), 1)
	src.CopyTo(&wk)
	if k > 0 {
		WL.SubMatrix(&wrow, 0, 0, 1, WL.Cols())
		MVMult(&wk, AL, &wrow, -1.0, 1.0, NOTRANS)
		//fmt.Printf("wk after update:\n%v\n", &wk)
	}
	if AR.Rows() == 1 {
		return 0, 1
	}
	amax := math.Abs(WR.GetAt(0, 0))

	// find max off-diagonal on first column.
	WR.SubMatrix(&rcol, 1, 0, AR.Rows()-1, 1)
	//fmt.Printf("rcol:\n%v\n", &rcol)
	// r is row index and rmax is its absolute value
	r = IAMax(&rcol) + 1
	rmax := math.Abs(rcol.GetAt(r-1, 0))
	//fmt.Printf("r=%d, amax=%e, rmax=%e\n", r, amax, rmax)
	if amax >= bkALPHA*rmax {
		// no pivoting, 1x1 diagonal
		return 0, 1
	}
	// Now we need to copy row r to WR[:,1] and update it
	WR.SubMatrix(&wkp1, 0, 1, AR.Rows(), 1)
	AR.SubMatrix(&qrow, r, 0, 1, r+1)
	qrow.CopyTo(&wkp1)
	//fmt.Printf("m(AR)=%d, r=%d, qrow: %v\n", AR.Rows(), r, &qrow)
	if r < AR.Rows()-1 {
		var wkr matrix.FloatMatrix
		AR.SubMatrix(&qrow, r, r, AR.Rows()-r, 1)
		wkp1.SubMatrix(&wkr, r, 0, wkp1.Rows()-r, 1)
		qrow.CopyTo(&wkr)
		//fmt.Printf("m(AR)=%d, r=%d, qrow: %v\n", AR.Rows(), r, &qrow)
	}
	if k > 0 {
		// update wkp1
		WL.SubMatrix(&wrow, r, 0, 1, WL.Cols())
		//fmt.Printf("initial wpk1:\n%v\n", &wkp1)
		MVMult(&wkp1, AL, &wrow, -1.0, 1.0, NOTRANS)
		//fmt.Printf("updated wpk1:\n%v\n", &wkp1)
	}

	// set on-diagonal entry to zero to avoid finding it
	p1 := wkp1.GetAt(r, 0)
	wkp1.SetAt(r, 0, 0.0)
	// max off-diagonal on r'th column/row at index q
	q = IAMax(&wkp1)
	qmax := math.Abs(wkp1.GetAt(q, 0))
	// restore on-diagonal entry
	wkp1.SetAt(r, 0, p1)
	//arr := math.Abs(WR.GetAt(r, 1))
	//fmt.Printf("blk: r=%d, q=%d, amax=%e, rmax=%e, qmax=%e, Arr=%e\n", r, q, amax, rmax, qmax, arr)

	if amax >= bkALPHA*rmax*(rmax/qmax) {
		// no pivoting, 1x1 diagonal
		return 0, 1
	}
	// if q == r then qmax is not off-diagonal, qmax == WR[r,1] and
	// we get 1x1 pivot as following is always true
	if math.Abs(WR.GetAt(r, 1)) >= bkALPHA*qmax {
		// 1x1 pivoting and interchange with k, r
		// pivot row in column WR[:,1] to W[:,0]
		//pr := WR.GetAt(r, 1)
		//_ = pr
		WR.SubMatrix(&src, 0, 1, AR.Rows(), 1)
		WR.SubMatrix(&wkp1, 0, 0, AR.Rows(), 1)
		src.CopyTo(&wkp1)
		wkp1.SetAt(0, 0, src.GetAt(r, 0))
		wkp1.SetAt(r, 0, src.GetAt(0, 0))
		return r, 1
	} else {
		// 2x2 pivoting and interchange with k+1, r
		return r, 2
//.........這裏部分代碼省略.........

/*
 * 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,
//.........這裏部分代碼省略.........