public (NDArray, NDArray) qr()
{
var a = (double[])this.Storage.GetData <double>().Clone();
int m = this.Storage.Shape.Dimensions[0];
int n = this.Storage.Shape.Dimensions[1];
int lda = m;
double[] tau = new double[Math.Min(m, n)];
double[] work = new double[Math.Max(m, n)];
int lwork = m;
int info = 0;
LAPACK.dgeqrf_(ref m, ref n, a, ref lda, tau, work, ref lwork, ref info);
double[] RDouble = new double[n * n];
for (int idx = 0; idx < n; idx++)
{
for (int jdx = idx; jdx < n; jdx++)
{
RDouble[idx + jdx * n] = a[idx + jdx * n];
}
}
var R = new NDArray(typeof(double), new Shape(n, n));
R.Storage.SetData(RDouble);
int k = tau.Length;
LAPACK.dorgqr_(ref m, ref n, ref k, a, ref lda, tau, work, ref lwork, ref info);
var Q = new NDArray(typeof(double), new Shape(tau.Length, tau.Length));
Q.Storage.Allocate(Q.Storage.DType, Q.Storage.Shape);
Q.Storage.SetData(a);
return(Q, R);
}
public (NDArray, NDArray, NDArray) svd()
{
double[] A = Data <double>();
int m = this.shape[0];
int n = this.shape[1];
int lda = m;
int ldu = m;
int ldvt = n;
int info = 0;
int lwork = -1;
double[] work = new double[Math.Max(m, n)];
double[] s = new double[n];
double[] u = new double[m * m];
double[] vt = new double[n * n];
LAPACK.dgesvd_("ALL".ToCharArray(), "All".ToCharArray(), ref m, ref n, A, ref lda, s, u, ref ldu, vt, ref ldvt, work, ref lwork, ref info);
lwork = (int)work[0];
work = new double[lwork];
LAPACK.dgesvd_("ALL".ToCharArray(), "All".ToCharArray(), ref m, ref n, A, ref lda, s, u, ref ldu, vt, ref ldvt, work, ref lwork, ref info);
var uNDArr = new NDArray(typeof(double), new Shape(m, n));
var vtNDArr = new NDArray(typeof(double), new Shape(n, n));
var sNDArr = new NDArray(typeof(double), n);
// set variables
double[] uDouble = uNDArr.Storage.GetData <double>();
for (int idx = 0; idx < uNDArr.size; idx++)
{
uDouble[idx] = u[idx];
}
vtNDArr.Storage.ReplaceData(vt);
sNDArr.Storage.ReplaceData(s);
return(uNDArr, sNDArr, vtNDArr);
}
/// <summary>
/// Least Square method
///
/// Determines NDArray X which reduces least square error of Linear System A * X = B.
/// This NDArray is equal to A.
/// </summary>
/// <param name="nDArrayB">Result NDArray B</param>
/// <param name="rcon"></param>
/// <returns>NArray X</returns>
public NDArray lstqr(NDArray nDArrayB, double rcon = 0.0001)
{
var A = (double[])Data <double>();
var b = (double[])nDArrayB.Data <double>();
int m = this.shape[0];
int n = this.shape[1];
int nrhs = (nDArrayB.ndim > 1) ? nDArrayB.shape[1] : 1;
int lda = m;
int ldb = m;
int rank = 0;
double[] work = new double[1];
int lwork = -1;
int info = 0;
double[] singVal = new double[m];
LAPACK.dgelss_(ref m, ref n, ref nrhs, A, ref lda, b, ref ldb, singVal, ref rcon, ref rank, work, ref lwork, ref info);
lwork = (int)work[0];
work = new double[lwork];
LAPACK.dgelss_(ref m, ref n, ref nrhs, A, ref lda, b, ref ldb, singVal, ref rcon, ref rank, work, ref lwork, ref info);
double[] sln = new double[n * nrhs];
for (int idx = 0; idx < sln.Length; idx++)
{
sln[idx] = b[m * (idx % nrhs) + idx / nrhs];
}
var slnArr = new NDArray(typeof(double), new Shape(n, nrhs));
slnArr.Storage.ReplaceData(sln);
return(slnArr);
}