Golang FloatMatrix.FloatArray方法代碼示例

// Solve multiple right sides. If flags&UNIT then A diagonal is assumed to
// to unit and is not referenced. (blas.TRSM)
//      alpha*B = A.-1*B if flags&LEFT
//      alpha*B = A.-T*B if flags&(LEFT|TRANS)
//      alpha*B = B*A.-1 if flags&RIGHT
//      alpha*B = B*A.-T if flags&(RIGHT|TRANS)
//
// Matrix A is N*N triangular matrix defined with flags bits as follow
//  LOWER       non-unit lower triangular
//  LOWER|UNIT  unit lower triangular
//  UPPER       non-unit upper triangular
//  UPPER|UNIT  unit upper triangular
//
// Matrix B is N*P if flags&LEFT or P*N if flags&RIGHT.
//
func SolveTrm(B, A *matrix.FloatMatrix, alpha float64, flags Flags) error {

	ok := true
	empty := false
	br, bc := B.Size()
	ar, ac := A.Size()
	switch flags & (LEFT | RIGHT) {
	case LEFT:
		empty = br == 0
		ok = br == ac && ac == ar
	case RIGHT:
		empty = bc == 0
		ok = bc == ar && ac == ar
	}
	if empty {
		return nil
	}
	if !ok {
		return onError("A, B size mismatch")
	}

	Ar := A.FloatArray()
	ldA := A.LeadingIndex()
	Br := B.FloatArray()
	ldB := B.LeadingIndex()

	E := bc
	if flags&RIGHT != 0 {
		E = br
	}
	// if more workers available can divide to tasks by B columns if flags&LEFT or by
	// B rows if flags&RIGHT.
	calgo.DSolveBlk(Br, Ar, alpha, calgo.Flags(flags), ldB, ldA, ac, 0, E, nB)
	return nil
}

func solveMVTest(t *testing.T, A, X0 *matrix.FloatMatrix, flags Flags, bN, bNB int) {
	X1 := X0.Copy()

	uplo := linalg.OptUpper
	diag := linalg.OptNonUnit
	if flags&LOWER != 0 {
		uplo = linalg.OptLower
	}
	if flags&UNIT != 0 {
		diag = linalg.OptUnit
	}

	blas.TrsvFloat(A, X0, uplo, diag)

	Ar := A.FloatArray()
	Xr := X1.FloatArray()
	if bN == bNB {
		DSolveUnblkMV(Xr, Ar, flags, 1, A.LeadingIndex(), bN)
	} else {
		DSolveBlkMV(Xr, Ar, flags, 1, A.LeadingIndex(), bN, bNB)
	}
	ok := X1.AllClose(X0)
	t.Logf("X1 == X0: %v\n", ok)
	if !ok && bN < 8 {
		t.Logf("A=\n%v\n", A)
		t.Logf("X0=\n%v\n", X0)
		t.Logf("blas: X0\n%v\n", X0)
		t.Logf("X1:\n%v\n", X1)
	}
}

func trmvTest(t *testing.T, A *matrix.FloatMatrix, flags Flags, nb int) bool {
	N := A.Cols()
	//S := 0
	//E := A.Cols()
	X0 := matrix.FloatWithValue(A.Rows(), 1, 2.0)
	X1 := X0.Copy()

	trans := linalg.OptNoTrans
	if flags&TRANS != 0 {
		trans = linalg.OptTrans
	}
	diag := linalg.OptNonUnit
	if flags&UNIT != 0 {
		diag = linalg.OptUnit
	}
	uplo := linalg.OptUpper
	if flags&LOWER != 0 {
		uplo = linalg.OptLower
	}

	blas.TrmvFloat(A, X0, uplo, diag, trans)

	Ar := A.FloatArray()
	Xr := X1.FloatArray()
	if nb == 0 {
		DTrimvUnblkMV(Xr, Ar, flags, 1, A.LeadingIndex(), N)
	}
	result := X0.AllClose(X1)
	t.Logf("   X0 == X1: %v\n", result)
	if !result && A.Rows() < 8 {
		t.Logf("  BLAS TRMV X0:\n%v\n", X0)
		t.Logf("  DTrmv X1:\n%v\n", X1)
	}
	return result
}

// See function Trsm.
func TrsmFloat(A, B *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error) {

	params, e := linalg.GetParameters(opts...)
	if e != nil {
		err = e
		return
	}
	ind := linalg.GetIndexOpts(opts...)
	err = check_level3_func(ind, ftrsm, A, B, nil, params)
	if err != nil {
		return
	}
	if ind.N == 0 || ind.M == 0 {
		return
	}
	Aa := A.FloatArray()
	Ba := B.FloatArray()
	uplo := linalg.ParamString(params.Uplo)
	transA := linalg.ParamString(params.TransA)
	side := linalg.ParamString(params.Side)
	diag := linalg.ParamString(params.Diag)
	dtrsm(side, uplo, transA, diag, ind.M, ind.N, alpha,
		Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb)
	return
}

func syrkTest(t *testing.T, C, A *matrix.FloatMatrix, flags Flags, vlen, nb int) bool {
	//var B0 *matrix.FloatMatrix
	P := A.Cols()
	S := 0
	E := C.Rows()
	C0 := C.Copy()

	trans := linalg.OptNoTrans
	if flags&TRANSA != 0 {
		trans = linalg.OptTrans
		P = A.Rows()
	}
	uplo := linalg.OptUpper
	if flags&LOWER != 0 {
		uplo = linalg.OptLower
	}

	blas.SyrkFloat(A, C0, 1.0, 1.0, uplo, trans)
	if A.Rows() < 8 {
		//t.Logf("..A\n%v\n", A)
		t.Logf("  BLAS C0:\n%v\n", C0)
	}

	Ar := A.FloatArray()
	Cr := C.FloatArray()
	DSymmRankBlk(Cr, Ar, 1.0, 1.0, flags, C.LeadingIndex(), A.LeadingIndex(),
		P, S, E, vlen, nb)
	result := C0.AllClose(C)
	t.Logf("   C0 == C: %v\n", result)
	if A.Rows() < 8 {
		t.Logf("  DMRank C:\n%v\n", C)
	}
	return result
}

// See function Syrk.
func SyrkFloat(A, C *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error) {

	params, e := linalg.GetParameters(opts...)
	if e != nil {
		err = e
		return
	}
	ind := linalg.GetIndexOpts(opts...)
	err = check_level3_func(ind, fsyrk, A, nil, C, params)
	if e != nil || err != nil {
		return
	}
	if ind.N == 0 {
		return
	}
	Aa := A.FloatArray()
	Ca := C.FloatArray()
	uplo := linalg.ParamString(params.Uplo)
	trans := linalg.ParamString(params.Trans)
	//diag := linalg.ParamString(params.Diag)
	dsyrk(uplo, trans, ind.N, ind.K, alpha, Aa[ind.OffsetA:], ind.LDa, beta,
		Ca[ind.OffsetC:], ind.LDc)

	return
}

// Swap X and Y.
func Swap(X, Y *matrix.FloatMatrix) {
	if X == nil || Y == nil {
		return
	}
	if X.NumElements() == 0 || Y.NumElements() == 0 {
		return
	}
	if !isVector(X) {
		return
	}
	if !isVector(Y) {
		return
	}
	Xr := X.FloatArray()
	incX := 1
	if X.Cols() != 1 {
		// Row vector
		incX = X.LeadingIndex()
	}
	Yr := Y.FloatArray()
	incY := 1
	if Y.Cols() != 1 {
		// Row vector
		incY = Y.LeadingIndex()
	}
	calgo.DSwap(Xr, Yr, incX, incY, X.NumElements())
}

// Y := alpha * X + Y
func Axpy(Y, X *matrix.FloatMatrix, alpha float64) {
	if X == nil || Y == nil {
		return
	}
	if !isVector(X) {
		return
	}
	if !isVector(Y) {
		return
	}
	Xr := X.FloatArray()
	incX := 1
	if X.Cols() != 1 {
		// Row vector
		incX = X.LeadingIndex()
	}
	Yr := Y.FloatArray()
	incY := 1
	if Y.Cols() != 1 {
		// Row vector
		incY = Y.LeadingIndex()
	}
	calgo.DAxpy(Xr, Yr, alpha, incX, incY, X.NumElements())
	return
}

func sinv(x, y *matrix.FloatMatrix, dims *sets.DimensionSet, mnl int) (err error) {
	/*DEBUGGED*/

	err = nil

	// For the nonlinear and 'l' blocks:
	//
	//     yk o\ xk = yk .\ xk.

	ind := mnl + dims.At("l")[0]
	blas.Tbsv(y, x, &la_.IOpt{"n", ind}, &la_.IOpt{"k", 0}, &la_.IOpt{"ldA", 1})

	// For the 'q' blocks:
	//
	//                        [ l0   -l1'              ]
	//     yk o\ xk = 1/a^2 * [                        ] * xk
	//                        [ -l1  (a*I + l1*l1')/l0 ]
	//
	// where yk = (l0, l1) and a = l0^2 - l1'*l1.

	for _, m := range dims.At("q") {
		aa := blas.Nrm2Float(y, &la_.IOpt{"n", m - 1}, &la_.IOpt{"offset", ind + 1})
		ee := y.GetIndex(ind)
		aa = (ee + aa) * (ee - aa)
		cc := x.GetIndex(ind)
		dd := blas.DotFloat(x, y, &la_.IOpt{"n", m - 1}, &la_.IOpt{"offsetx", ind + 1},
			&la_.IOpt{"offsety", ind + 1})
		x.SetIndex(ind, cc*ee-dd)
		blas.ScalFloat(x, aa/ee, &la_.IOpt{"n", m - 1}, &la_.IOpt{"offset", ind + 1})
		blas.AxpyFloat(y, x, dd/ee-cc, &la_.IOpt{"n", m - 1},
			&la_.IOpt{"offsetx", ind + 1}, &la_.IOpt{"offsety", ind + 1})
		blas.ScalFloat(x, 1.0/aa, &la_.IOpt{"n", m}, &la_.IOpt{"offset", ind})
		ind += m
	}

	// For the 's' blocks:
	//
	//     yk o\ xk =  xk ./ gamma
	//
	// where gammaij = .5 * (yk_i + yk_j).

	ind2 := ind
	for _, m := range dims.At("s") {
		for j := 0; j < m; j++ {
			u := matrix.FloatVector(y.FloatArray()[ind2+j : ind2+m])
			u.Add(y.GetIndex(ind2 + j))
			u.Scale(0.5)
			blas.Tbsv(u, x, &la_.IOpt{"n", m - j}, &la_.IOpt{"k", 0}, &la_.IOpt{"lda", 1},
				&la_.IOpt{"offsetx", ind + j*(m+1)})
		}
		ind += m * m
		ind2 += m
	}
	return
}

// Returns min {t | x + t*e >= 0}, where e is defined as follows
//
//  - For the nonlinear and 'l' blocks: e is the vector of ones.
//  - For the 'q' blocks: e is the first unit vector.
//  - For the 's' blocks: e is the identity matrix.
//
// When called with the argument sigma, also returns the eigenvalues
// (in sigma) and the eigenvectors (in x) of the 's' components of x.
func maxStep(x *matrix.FloatMatrix, dims *sets.DimensionSet, mnl int, sigma *matrix.FloatMatrix) (rval float64, err error) {
	/*DEBUGGED*/

	rval = 0.0
	err = nil
	t := make([]float64, 0, 10)
	ind := mnl + dims.Sum("l")
	if ind > 0 {
		t = append(t, -minvec(x.FloatArray()[:ind]))
	}
	for _, m := range dims.At("q") {
		if m > 0 {
			v := blas.Nrm2Float(x, &la_.IOpt{"offset", ind + 1}, &la_.IOpt{"n", m - 1})
			v -= x.GetIndex(ind)
			t = append(t, v)
		}
		ind += m
	}

	//var Q *matrix.FloatMatrix
	//var w *matrix.FloatMatrix
	ind2 := 0
	//if sigma == nil && len(dims.At("s")) > 0 {
	//	mx := dims.Max("s")
	//	Q = matrix.FloatZeros(mx, mx)
	//	w = matrix.FloatZeros(mx, 1)
	//}
	for _, m := range dims.At("s") {
		if sigma == nil {
			Q := matrix.FloatZeros(m, m)
			w := matrix.FloatZeros(m, 1)
			blas.Copy(x, Q, &la_.IOpt{"offsetx", ind}, &la_.IOpt{"n", m * m})
			err = lapack.SyevrFloat(Q, w, nil, 0.0, nil, []int{1, 1}, la_.OptRangeInt,
				&la_.IOpt{"n", m}, &la_.IOpt{"lda", m})
			if m > 0 && err == nil {
				t = append(t, -w.GetIndex(0))
			}
		} else {
			err = lapack.SyevdFloat(x, sigma, la_.OptJobZValue, &la_.IOpt{"n", m},
				&la_.IOpt{"lda", m}, &la_.IOpt{"offseta", ind}, &la_.IOpt{"offsetw", ind2})
			if m > 0 {
				t = append(t, -sigma.GetIndex(ind2))
			}
		}
		ind += m * m
		ind2 += m
	}

	if len(t) > 0 {
		rval = maxvec(t)
	}
	return
}

// See function Scal.
func ScalFloat(X *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error) {
	ind := linalg.GetIndexOpts(opts...)
	err = check_level1_func(ind, fscal, X, nil)
	if err != nil {
		return
	}
	if ind.Nx == 0 {
		return
	}
	Xa := X.FloatArray()
	dscal(ind.Nx, alpha, Xa[ind.OffsetX:], ind.IncX)
	return
}

// A = alpha*A + beta*B
// A = alpha*A + beta*B.T  if flags&TRANSB
func ScalePlus(A, B *matrix.FloatMatrix, alpha, beta float64, flags Flags) error {

	Ar := A.FloatArray()
	ldA := A.LeadingIndex()
	Br := B.FloatArray()
	ldB := B.LeadingIndex()
	S := 0
	L := A.Cols()
	R := 0
	E := A.Rows()
	calgo.DScalePlus(Ar, Br, alpha, beta, calgo.Flags(flags), ldA, ldB, S, L, R, E)
	return nil
}

func trmmTest(t *testing.T, A *matrix.FloatMatrix, flags Flags, nb int) bool {
	var B0 *matrix.FloatMatrix
	N := A.Cols()
	S := 0
	E := A.Cols()
	side := linalg.OptLeft
	if flags&RIGHT != 0 {
		B0 = matrix.FloatWithValue(2, A.Rows(), 2.0)
		side = linalg.OptRight
		E = B0.Rows()
	} else {
		B0 = matrix.FloatWithValue(A.Rows(), 2, 2.0)
		E = B0.Cols()
	}
	B1 := B0.Copy()

	trans := linalg.OptNoTrans
	if flags&TRANSA != 0 {
		trans = linalg.OptTransA
	}
	diag := linalg.OptNonUnit
	if flags&UNIT != 0 {
		diag = linalg.OptUnit
	}
	uplo := linalg.OptUpper
	if flags&LOWER != 0 {
		uplo = linalg.OptLower
	}

	blas.TrmmFloat(A, B0, 1.0, uplo, diag, trans, side)
	if A.Rows() < 8 {
		//t.Logf("..A\n%v\n", A)
		t.Logf("  BLAS B0:\n%v\n", B0)
	}

	Ar := A.FloatArray()
	Br := B1.FloatArray()
	if nb != 0 {
		DTrmmBlk(Br, Ar, 1.0, flags, B1.LeadingIndex(), A.LeadingIndex(),
			N, S, E, nb)
	} else {
		DTrmmUnblk(Br, Ar, 1.0, flags, B1.LeadingIndex(), A.LeadingIndex(),
			N, S, E, 0)
	}
	result := B0.AllClose(B1)
	t.Logf("   B0 == B1: %v\n", result)
	if A.Rows() < 8 {
		t.Logf("  DTrmm B1:\n%v\n", B1)
	}
	return result
}

// See function Copy.
func CopyFloat(X, Y *matrix.FloatMatrix, opts ...linalg.Option) (err error) {
	ind := linalg.GetIndexOpts(opts...)
	err = check_level1_func(ind, fcopy, X, Y)
	if err != nil {
		return
	}
	if ind.Nx == 0 {
		return
	}
	Xa := X.FloatArray()
	Ya := Y.FloatArray()
	dcopy(ind.Nx, Xa[ind.OffsetX:], ind.IncX, Ya[ind.OffsetY:], ind.IncY)
	return
}

// index of max |x|
func IAMax(X *matrix.FloatMatrix) int {
	if X == nil {
		return -1
	}
	if !isVector(X) {
		return -1
	}
	Xr := X.FloatArray()
	incX := 1
	if X.Cols() != 1 {
		// Row vector
		incX = X.LeadingIndex()
	}
	return calgo.DIAMax(Xr, incX, X.NumElements())
}