// 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)
}
}
// 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)
}
}
// 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
}