//! QR Solve
/*! This implementation is based on MINPACK
* (<http://www.netlib.org/minpack>,
* <http://www.netlib.org/cephes/linalg.tgz>)
*
* Given an m by n matrix A, an n by n diagonal matrix d,
* and an m-vector b, the problem is to determine an x which
* solves the system
*
* A*x = b , d*x = 0 ,
*
* in the least squares sense.
*
* d is an input array of length n which must contain the
* diagonal elements of the matrix d.
*
* See lmdiff.cpp for further details.
*/
public static Vector qrSolve(Matrix a, Vector b, bool pivot = true, Vector d = null)
{
int m = a.rows();
int n = a.columns();
if (d == null)
{
d = new Vector();
}
Utils.QL_REQUIRE(b.Count == m, () => "dimensions of A and b don't match");
Utils.QL_REQUIRE(d.Count == n || d.empty(), () => "dimensions of A and d don't match");
Matrix q = new Matrix(m, n), r = new Matrix(n, n);
List <int> lipvt = MatrixUtilities.qrDecomposition(a, ref q, ref r, pivot);
List <int> ipvt = new List <int>(n);
ipvt = lipvt;
//std::copy(lipvt.begin(), lipvt.end(), ipvt.get());
Matrix aT = Matrix.transpose(a);
Matrix rT = Matrix.transpose(r);
Vector sdiag = new Vector(n);
Vector wa = new Vector(n);
Vector ld = new Vector(n, 0.0);
if (!d.empty())
{
ld = d;
//std::copy(d.begin(), d.end(), ld.begin());
}
Vector x = new Vector(n);
Vector qtb = Matrix.transpose(q) * b;
MINPACK.qrsolv(n, rT, n, ipvt, ld, qtb, x, sdiag, wa);
return(x);
}
//! QR decompoisition
/*! This implementation is based on MINPACK
* (<http://www.netlib.org/minpack>,
* <http://www.netlib.org/cephes/linalg.tgz>)
*
* This subroutine uses householder transformations with column
* pivoting (optional) to compute a qr factorization of the
* m by n matrix A. That is, qrfac determines an orthogonal
* matrix q, a permutation matrix p, and an upper trapezoidal
* matrix r with diagonal elements of nonincreasing magnitude,
* such that A*p = q*r.
*
* Return value ipvt is an integer array of length n, which
* defines the permutation matrix p such that A*p = q*r.
* Column j of p is column ipvt(j) of the identity matrix.
*
* See lmdiff.cpp for further details.
*/
//public static List<int> qrDecomposition(Matrix A, Matrix q, Matrix r, bool pivot = true) {
public static List <int> qrDecomposition(Matrix M, Matrix q, Matrix r, bool pivot)
{
Matrix mT = Matrix.transpose(M);
int m = M.rows();
int n = M.columns();
List <int> lipvt = new InitializedList <int>(n);
Vector rdiag = new Vector(n);
Vector wa = new Vector(n);
MINPACK.qrfac(m, n, mT, 0, (pivot)?1:0, ref lipvt, n, ref rdiag, ref rdiag, wa);
if (r.columns() != n || r.rows() != n)
{
r = new Matrix(n, n);
}
for (int i = 0; i < n; ++i)
{
// std::fill(r.row_begin(i), r.row_begin(i)+i, 0.0);
r[i, i] = rdiag[i];
if (i < m)
{
// std::copy(mT.column_begin(i)+i+1, mT.column_end(i),
// r.row_begin(i)+i+1);
}
else
{
// std::fill(r.row_begin(i)+i+1, r.row_end(i), 0.0);
}
}
if (q.rows() != m || q.columns() != n)
{
q = new Matrix(m, n);
}
Vector w = new Vector(m);
//for (int k=0; k < m; ++k) {
// std::fill(w.begin(), w.end(), 0.0);
// w[k] = 1.0;
// for (int j=0; j < Math.Min(n, m); ++j) {
// double t3 = mT[j,j];
// if (t3 != 0.0) {
// double t
// = std::inner_product(mT.row_begin(j)+j, mT.row_end(j),
// w.begin()+j, 0.0)/t3;
// for (int i=j; i<m; ++i) {
// w[i]-=mT[j,i]*t;
// }
// }
// q[k,j] = w[j];
// }
// std::fill(q.row_begin(k) + Math.Min(n, m), q.row_end(k), 0.0);
//}
List <int> ipvt = new InitializedList <int>(n);
//if (pivot) {
// std::copy(lipvt.get(), lipvt.get()+n, ipvt.begin());
//}
//else {
// for (int i=0; i < n; ++i)
// ipvt[i] = i;
//}
return(ipvt);
}
//! QR decompoisition
/*! This implementation is based on MINPACK
* (<http://www.netlib.org/minpack>,
* <http://www.netlib.org/cephes/linalg.tgz>)
*
* This subroutine uses householder transformations with column
* pivoting (optional) to compute a qr factorization of the
* m by n matrix A. That is, qrfac determines an orthogonal
* matrix q, a permutation matrix p, and an upper trapezoidal
* matrix r with diagonal elements of nonincreasing magnitude,
* such that A*p = q*r.
*
* Return value ipvt is an integer array of length n, which
* defines the permutation matrix p such that A*p = q*r.
* Column j of p is column ipvt(j) of the identity matrix.
*
* See lmdiff.cpp for further details.
*/
//public static List<int> qrDecomposition(Matrix A, Matrix q, Matrix r, bool pivot = true) {
public static List <int> qrDecomposition(Matrix M, ref Matrix q, ref Matrix r, bool pivot)
{
Matrix mT = Matrix.transpose(M);
int m = M.rows();
int n = M.columns();
List <int> lipvt = new InitializedList <int>(n);
Vector rdiag = new Vector(n);
Vector wa = new Vector(n);
MINPACK.qrfac(m, n, mT, 0, (pivot)?1:0, ref lipvt, n, ref rdiag, ref rdiag, wa);
if (r.columns() != n || r.rows() != n)
{
r = new Matrix(n, n);
}
for (int i = 0; i < n; ++i)
{
r[i, i] = rdiag[i];
if (i < m)
{
for (int j = i; j < mT.rows() - 1; j++)
{
r[i, j + 1] = mT[j + 1, i];
}
}
}
if (q.rows() != m || q.columns() != n)
{
q = new Matrix(m, n);
}
Vector w = new Vector(m);
for (int k = 0; k < m; ++k)
{
w.Erase();
w[k] = 1.0;
for (int j = 0; j < Math.Min(n, m); ++j)
{
double t3 = mT[j, j];
if (t3 != 0.0)
{
double t = 0;
for (int kk = j; kk < mT.columns(); kk++)
{
t += (mT[j, kk] * w[kk]) / t3;
}
for (int i = j; i < m; ++i)
{
w[i] -= mT[j, i] * t;
}
}
q[k, j] = w[j];
}
}
List <int> ipvt = new InitializedList <int>(n);
if (pivot)
{
for (int i = 0; i < n; ++i)
{
ipvt[i] = lipvt[i];
}
}
else
{
for (int i = 0; i < n; ++i)
{
ipvt[i] = i;
}
}
return(ipvt);
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
currentProblem_ = P;
initCostValues_ = P.costFunction().values(x_);
int m = initCostValues_.size();
int n = x_.size();
if (useCostFunctionsJacobian_)
{
initJacobian_ = new Matrix(m, n);
P.costFunction().jacobian(initJacobian_, x_);
}
Vector xx = new Vector(x_);
Vector fvec = new Vector(m), diag = new Vector(n);
int mode = 1;
double factor = 1;
int nprint = 0;
int info = 0;
int nfev = 0;
Matrix fjac = new Matrix(m, n);
int ldfjac = m;
List <int> ipvt = new InitializedList <int>(n);
Vector qtf = new Vector(n), wa1 = new Vector(n), wa2 = new Vector(n), wa3 = new Vector(n), wa4 = new Vector(m);
// call lmdif to minimize the sum of the squares of m functions
// in n variables by the Levenberg-Marquardt algorithm.
Func <int, int, Vector, int, Matrix> j = null;
if (useCostFunctionsJacobian_)
{
j = jacFcn;
}
// requirements; check here to get more detailed error messages.
Utils.QL_REQUIRE(n > 0, () => "no variables given");
Utils.QL_REQUIRE(m >= n, () => $"less functions ({m}) than available variables ({n})");
Utils.QL_REQUIRE(endCriteria.functionEpsilon() >= 0.0, () => "negative f tolerance");
Utils.QL_REQUIRE(xtol_ >= 0.0, () => "negative x tolerance");
Utils.QL_REQUIRE(gtol_ >= 0.0, () => "negative g tolerance");
Utils.QL_REQUIRE(endCriteria.maxIterations() > 0, () => "null number of evaluations");
MINPACK.lmdif(m, n, xx, ref fvec,
endCriteria.functionEpsilon(),
xtol_,
gtol_,
endCriteria.maxIterations(),
epsfcn_,
diag, mode, factor,
nprint, ref info, ref nfev, ref fjac,
ldfjac, ref ipvt, ref qtf,
wa1, wa2, wa3, wa4,
fcn, j);
info_ = info;
// check requirements & endCriteria evaluation
Utils.QL_REQUIRE(info != 0, () => "MINPACK: improper input parameters");
if (info != 6)
{
ecType = EndCriteria.Type.StationaryFunctionValue;
}
endCriteria.checkMaxIterations(nfev, ref ecType);
Utils.QL_REQUIRE(info != 7, () => "MINPACK: xtol is too small. no further " +
"improvement in the approximate " +
"solution x is possible.");
Utils.QL_REQUIRE(info != 8, () => "MINPACK: gtol is too small. fvec is " +
"orthogonal to the columns of the " +
"jacobian to machine precision.");
// set problem
x_ = new Vector(xx.GetRange(0, n));
P.setCurrentValue(x_);
P.setFunctionValue(P.costFunction().value(x_));
return(ecType);
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
currentProblem_ = P;
initCostValues_ = P.costFunction().values(x_);
int m = initCostValues_.size();
int n = x_.size();
if (useCostFunctionsJacobian_)
{
initJacobian_ = new Matrix(m, n);
P.costFunction().jacobian(initJacobian_, x_);
}
Vector xx = new Vector(x_);
Vector fvec = new Vector(m), diag = new Vector(n);
int mode = 1;
double factor = 1;
int nprint = 0;
int info = 0;
int nfev = 0;
Matrix fjac = new Matrix(m, n);
int ldfjac = m;
List <int> ipvt = new InitializedList <int>(n);
Vector qtf = new Vector(n), wa1 = new Vector(n), wa2 = new Vector(n), wa3 = new Vector(n), wa4 = new Vector(m);
// call lmdif to minimize the sum of the squares of m functions
// in n variables by the Levenberg-Marquardt algorithm.
Func <int, int, Vector, int, Matrix> j = null;
if (useCostFunctionsJacobian_)
{
j = jacFcn;
}
MINPACK.lmdif(m, n, xx, ref fvec,
endCriteria.functionEpsilon(),
xtol_,
gtol_,
endCriteria.maxIterations(),
epsfcn_,
diag, mode, factor,
nprint, ref info, ref nfev, ref fjac,
ldfjac, ref ipvt, ref qtf,
wa1, wa2, wa3, wa4,
fcn, j);
info_ = info;
// check requirements & endCriteria evaluation
if (info == 0)
{
throw new ApplicationException("MINPACK: improper input parameters");
}
//if(info == 6) throw new ApplicationException("MINPACK: ftol is too small. no further " +
// "reduction in the sum of squares is possible.");
if (info != 6)
{
ecType = EndCriteria.Type.StationaryFunctionValue;
}
//QL_REQUIRE(info != 5, "MINPACK: number of calls to fcn has reached or exceeded maxfev.");
endCriteria.checkMaxIterations(nfev, ref ecType);
if (info == 7)
{
throw new ApplicationException("MINPACK: xtol is too small. no further " +
"improvement in the approximate " +
"solution x is possible.");
}
if (info == 8)
{
throw new ApplicationException("MINPACK: gtol is too small. fvec is " +
"orthogonal to the columns of the " +
"jacobian to machine precision.");
}
// set problem
x_ = new Vector(xx.GetRange(0, n));
P.setCurrentValue(x_);
P.setFunctionValue(P.costFunction().value(x_));
return(ecType);
}