// Cholesky calculates the Cholesky decomposition of the matrix A and returns
// whether the matrix is positive definite. The returned matrix is either a
// lower triangular matrix such that A = L * L^T or an upper triangular matrix
// such that A = U^T * U depending on the upper parameter.
func (t *TriDense) Cholesky(a Symmetric, upper bool) (ok bool) {
n := a.Symmetric()
if t.isZero() {
t.mat = blas64.Triangular{
N: n,
Stride: n,
Diag: blas.NonUnit,
Data: use(t.mat.Data, n*n),
}
if upper {
t.mat.Uplo = blas.Upper
} else {
t.mat.Uplo = blas.Lower
}
} else {
if n != t.mat.N {
panic(ErrShape)
}
if (upper && t.mat.Uplo != blas.Upper) || (!upper && t.mat.Uplo != blas.Lower) {
panic(ErrTriangle)
}
}
copySymIntoTriangle(t, a)
// Potrf modifies the data in place
_, ok = lapack64.Potrf(
blas64.Symmetric{
N: t.mat.N,
Stride: t.mat.Stride,
Data: t.mat.Data,
Uplo: t.mat.Uplo,
})
return ok
}
// Factorize calculates the Cholesky decomposition of the matrix A and returns
// whether the matrix is positive definite.
func (c *Cholesky) Factorize(a Symmetric) (ok bool) {
n := a.Symmetric()
if c.chol == nil {
c.chol = NewTriDense(n, true, nil)
} else {
c.chol = NewTriDense(n, true, use(c.chol.mat.Data, n*n))
}
copySymIntoTriangle(c.chol, a)
sym := c.chol.asSymBlas()
work := make([]float64, c.chol.mat.N)
norm := lapack64.Lansy(matrix.CondNorm, sym, work)
_, ok = lapack64.Potrf(sym)
if ok {
c.updateCond(norm)
} else {
c.cond = math.Inf(1)
}
return ok
}
