// Inverse computes the inverse of the matrix a, storing the result into the
// receiver. If a is ill-conditioned, a Condition error will be returned.
// Note that matrix inversion is numerically unstable, and should generally
// be avoided where possible, for example by using the Solve routines.
func (m *Dense) Inverse(a Matrix) error {
// TODO(btracey): Special case for RawTriangular, etc.
r, c := a.Dims()
if r != c {
panic(ErrSquare)
}
m.reuseAs(a.Dims())
aMat, aTrans := untranspose(a)
if m != aMat {
m.Copy(a)
} else if aTrans {
tmp := getWorkspace(r, c, false)
tmp.Copy(a)
m.Copy(tmp)
putWorkspace(tmp)
}
ipiv := make([]int, r)
lapack64.Getrf(m.mat, ipiv)
work := make([]float64, 1, 4*r) // must be at least 4*r for cond.
lapack64.Getri(m.mat, ipiv, work, -1)
if int(work[0]) > 4*r {
work = make([]float64, int(work[0]))
} else {
work = work[:4*r]
}
lapack64.Getri(m.mat, ipiv, work, len(work))
norm := lapack64.Lange(condNorm, m.mat, work)
cond := lapack64.Gecon(condNorm, m.mat, norm, work, ipiv) // reuse ipiv
if cond > condTol {
return Condition(cond)
}
return nil
}
// Inverse computes the inverse of the matrix a, storing the result into the
// receiver. If a is ill-conditioned, a Condition error will be returned.
// Note that matrix inversion is numerically unstable, and should generally
// be avoided where possible, for example by using the Solve routines.
func (m *Dense) Inverse(a Matrix) error {
// TODO(btracey): Special case for RawTriangular, etc.
r, c := a.Dims()
if r != c {
panic(matrix.ErrSquare)
}
m.reuseAs(a.Dims())
aU, aTrans := untranspose(a)
switch rm := aU.(type) {
case RawMatrixer:
if m != aU || aTrans {
if m == aU || m.checkOverlap(rm.RawMatrix()) {
tmp := getWorkspace(r, c, false)
tmp.Copy(a)
m.Copy(tmp)
putWorkspace(tmp)
break
}
m.Copy(a)
}
default:
if m != aU {
m.Copy(a)
} else if aTrans {
// m and a share data so Copy cannot be used directly.
tmp := getWorkspace(r, c, false)
tmp.Copy(a)
m.Copy(tmp)
putWorkspace(tmp)
}
}
ipiv := make([]int, r)
lapack64.Getrf(m.mat, ipiv)
work := make([]float64, 1, 4*r) // must be at least 4*r for cond.
lapack64.Getri(m.mat, ipiv, work, -1)
if int(work[0]) > 4*r {
work = make([]float64, int(work[0]))
} else {
work = work[:4*r]
}
lapack64.Getri(m.mat, ipiv, work, len(work))
norm := lapack64.Lange(matrix.CondNorm, m.mat, work)
cond := lapack64.Gecon(matrix.CondNorm, m.mat, norm, work, ipiv) // reuse ipiv
if cond > matrix.ConditionTolerance {
return matrix.Condition(cond)
}
return nil
}