Beispiel #1
0
// SolveCholesky finds the matrix m that solves A * m = b where A = L * L^T or
// A = U^T * U, and U or L are represented by t, placing the result in the
// receiver.
func (m *Dense) SolveCholesky(t Triangular, b Matrix) {
	_, n := t.Dims()
	bm, bn := b.Dims()
	if n != bm {
		panic(ErrShape)
	}

	m.reuseAs(bm, bn)
	if b != m {
		m.Copy(b)
	}

	// TODO(btracey): Implement an algorithm that doesn't require a copy into
	// a blas64.Triangular.
	ta := getBlasTriangular(t)

	switch ta.Uplo {
	case blas.Upper:
		blas64.Trsm(blas.Left, blas.Trans, 1, ta, m.mat)
		blas64.Trsm(blas.Left, blas.NoTrans, 1, ta, m.mat)
	case blas.Lower:
		blas64.Trsm(blas.Left, blas.NoTrans, 1, ta, m.mat)
		blas64.Trsm(blas.Left, blas.Trans, 1, ta, m.mat)
	default:
		panic(badTriangle)
	}
}
Beispiel #2
0
// SolveTri finds the matrix x that solves op(A) * X = B where A is a triangular
// matrix and op is specified by trans.
func (m *Dense) SolveTri(a Triangular, trans bool, b Matrix) {
	n, _ := a.Triangle()
	bm, bn := b.Dims()
	if n != bm {
		panic(ErrShape)
	}

	m.reuseAs(bm, bn)
	if b != m {
		m.Copy(b)
	}

	// TODO(btracey): Implement an algorithm that doesn't require a copy into
	// a blas64.Triangular.
	ta := getBlasTriangular(a)

	t := blas.NoTrans
	if trans {
		t = blas.Trans
	}
	switch ta.Uplo {
	case blas.Upper, blas.Lower:
		blas64.Trsm(blas.Left, t, 1, ta, m.mat)
	default:
		panic(badTriangle)
	}
}
Beispiel #3
0
// Solve computes minimum norm least squares solution of a.x = b where b has as many rows as a.
// A matrix x is returned that minimizes the two norm of Q*R*X-B. Solve will panic
// if a is not full rank.
func (f LQFactor) Solve(b *Dense) (x *Dense) {
	lq := f.LQ
	lDiag := f.lDiag
	m, n := lq.Dims()
	bm, bn := b.Dims()
	if bm != m {
		panic(ErrShape)
	}
	if !f.IsFullRank() {
		panic(ErrSingular)
	}

	x = NewDense(n, bn, nil)
	x.Copy(b)

	tau := make([]float64, m)
	for i := range tau {
		tau[i] = lq.at(i, i)
		lq.set(i, i, lDiag[i])
	}
	lqT := blas64.Triangular{
		// N omitted since it is not used by Trsm.
		Stride: lq.mat.Stride,
		Data:   lq.mat.Data,
		Uplo:   blas.Lower,
		Diag:   blas.NonUnit,
	}
	x.mat.Rows = bm
	blas64.Trsm(blas.Left, blas.NoTrans, 1, lqT, x.mat)
	x.mat.Rows = n
	for i := range tau {
		lq.set(i, i, tau[i])
	}

	f.applyQTo(x, true)

	return x
}