/// <summary>
/// JOB: ABCDE decimal
/// A B C D E
/// --- --- --- --- ---
/// Qb Q'b x norm(A*x - b) A*x
///
/// Solve equation M x = b for x using the computed decomposition.
/// </summary>
/// <param name="b"></param>
/// <returns></returns>
public unsafe Vector Solve(Vector b)
{
int n = qrdc_out_.Columns;
int p = qrdc_out_.Rows;
float[] b_data = b.Datablock();
Vector QtB = new Vector(n);
Vector x = new Vector(p);
// see comment above
int JOB = 100;
int info = 0;
fixed(float *data = qrdc_out_.Datablock())
{
fixed(float *data2 = qraux_.Datablock())
{
fixed(float *data3 = b_data)
{
fixed(float *data4 = QtB.Datablock())
{
fixed(float *data5 = x.Datablock())
{
Netlib.dqrsl_(data, &n, &n, &p, data2, data3,
(float *)0, data4, data5,
(float *)0, // residual*
(float *)0, // Ax*
&JOB,
&info);
}
}
}
}
}
if (info > 0)
{
Debug.WriteLine("__FILE__ : VNL::QR<T>::Solve() : matrix is rank-deficient by " + Convert.ToString(info));
}
return(x);
}
/// <summary>
/// Solve least squares problem M x = b.
/// The right-hand-side std::vector x may be b,
/// which will give a fractional increase in speed.
/// </summary>
/// <param name="b"></param>
/// <param name="x"></param>
public unsafe void Solve(Vector b, Vector x)
{
//assert(b.size() == A_.Columns());
x = b;
int n = A_.Columns;
fixed(float *data = A_.Datablock())
{
fixed(float *data2 = x.Datablock())
{
Netlib.dposl_(data, &n, &n, data2);
}
}
}
public unsafe QR(MatrixFixed M)
{
qrdc_out_ = new MatrixFixed(M.Columns, M.Rows);
qraux_ = new Vector(M.Columns);
jpvt_ = new int[M.Rows];
Q_ = null;
R_ = null;
// Fill transposed O/P matrix
int c = M.Columns;
int r = M.Rows;
for (int i = 0; i < r; ++i)
{
for (int j = 0; j < c; ++j)
{
qrdc_out_[j, i] = M[i, j];
}
}
int do_pivot = 0; // Enable[!=0]/disable[==0] pivoting.
for (int i = 0; i < jpvt_.Length; i++)
{
jpvt_[i] = 0;
}
Vector work = new Vector(M.Rows);
fixed(float *data = qrdc_out_.Datablock())
{
fixed(float *data2 = qraux_.Datablock())
{
fixed(int *data3 = jpvt_)
{
fixed(float *data4 = work.Datablock())
{
Netlib.dqrdc_(data, // On output, UT is R, below diag is mangled Q
&r, &r, &c,
data2, // Further information required to demangle Q
data3,
data4,
&do_pivot);
}
}
}
}
}
/// <summary>
/// Cholesky decomposition.
/// Make cholesky decomposition of M optionally computing
/// the reciprocal condition number. If mode is estimate_condition, the
/// condition number and an approximate nullspace are estimated, at a cost
/// of a factor of (1 + 18/n). Here's a table of 1 + 18/n:
///<pre>
/// n: 3 5 10 50 100 500 1000
/// slowdown: 7.0f 4.6 2.8 1.4 1.18 1.04 1.02
/// </summary>
/// <param name="M"></param>
/// <param name="mode"></param>
public unsafe void init(MatrixFixed M, Operation mode)
{
A_ = new MatrixFixed(M);
int n = M.Columns;
//assert(n == (int)(M.Rows()));
num_dims_rank_def_ = -1;
int num_dims_rank_def_temp = num_dims_rank_def_;
// BJT: This warning is pointless - it often doesn't detect non symmetry and
// if you know what you're doing you don't want to be slowed down
// by a cerr
/*
* if (Math.Abs(M[0,n-1] - M[n-1,0]) > 1e-8)
* {
* Debug.WriteLine("cholesky: WARNING: unsymmetric: " + M);
* }
*/
if (mode != Operation.estimate_condition)
{
// Quick factorization
fixed(float *data = A_.Datablock())
{
Netlib.dpofa_(data, &n, &n, &num_dims_rank_def_temp);
}
//if ((mode == Operation.verbose) && (num_dims_rank_def_temp != 0))
// Debug.WriteLine("cholesky:: " + Convert.ToString(num_dims_rank_def_temp) + " dimensions of non-posdeffness");
}
else
{
Vector nullvector = new Vector(n);
float rcond_temp = rcond_;
fixed(float *data = A_.Datablock())
{
fixed(float *data2 = nullvector.Datablock())
{
Netlib.dpoco_(data, &n, &n, &rcond_temp, data2, &num_dims_rank_def_temp);
}
}
rcond_ = rcond_temp;
}
num_dims_rank_def_ = num_dims_rank_def_temp;
}
/// <summary>
/// Solve least squares problem M x = b.
/// </summary>
/// <param name="b"></param>
/// <returns></returns>
public unsafe Vector Solve(Vector b)
{
//assert(b.size() == A_.Columns());
int n = A_.Columns;
Vector ret = new Vector(b);
fixed(float *data = A_.Datablock())
{
fixed(float *data2 = ret.Datablock())
{
Netlib.dposl_(data, &n, &n, data2);
}
}
return(ret);
}
/// <summary>
/// Returns new vector which is the multiplication of row vector v with matrix m.\ O(m*n).
/// </summary>
/// <param name="m"></param>
/// <param name="v"></param>
/// <returns></returns>
public static Vector operator *(Vector v, MatrixFixed m)
{
Vector result = new Vector(m.Columns); // Temporary
MatrixFixed mm = m; // Drop const for get()
float[] result_data = result.Datablock();
float[] v_data = v.Datablock();
float[,] mm_data = mm.Datablock();
for (int i = 0; i < m.Columns; i++)
{ // For each index
result_data[i] = 0; // Initialize element value
for (int k = 0; k < result_data.Length; k++) // Loop over column values
{
result_data[i] += (v_data[k] * mm_data[k, i]); // Multiply
}
}
return(result);
}
public static Vector operator*(MatrixFixed m, Vector v)
{
Vector result = new Vector(m.Rows); // Temporary
MatrixFixed mm = m; // Drop const for get()
float[] result_data = result.Datablock();
float[] v_data = v.Datablock();
float[,] mm_data = mm.Datablock();
int vsize = v.size();
for (int i = 0; i < m.Rows; i++)
{ // For each index
result_data[i] = 0; // Initialize element value
for (int k = 0; k < vsize; k++) // Loop over column values
{
result_data[i] += (mm_data[i, k] * v_data[k]); // Multiply
}
}
return(result);
}
/// <summary>
/// Return residual vector d of M x = b -> d = Q'b.
/// </summary>
/// <param name="b"></param>
/// <returns></returns>
public unsafe Vector QtB(Vector b)
{
int n = qrdc_out_.Columns;
int p = qrdc_out_.Rows;
float[] b_data = b.Datablock();
Vector QtB = new Vector(n);
// see comment above
int JOB = 1000;
int info = 0;
fixed(float *data = qrdc_out_.Datablock())
{
fixed(float *data2 = qraux_.Datablock())
{
fixed(float *data3 = b_data)
{
fixed(float *data4 = QtB.Datablock())
{
Netlib.dqrsl_(data, &n, &n, &p, data2, data3,
(float *)0, // A: Qb
data4, // B: Q'b
(float *)0, // C: x
(float *)0, // D: residual
(float *)0, // E: Ax
&JOB,
&info);
}
}
}
}
if (info > 0)
{
Debug.WriteLine(" __FILE__ : VNL::QR<T>::QtB() -- matrix is rank-def by " + Convert.ToString(info));
}
return(QtB);
}
public unsafe QR(MatrixFixed M)
{
qrdc_out_ = new MatrixFixed(M.Columns, M.Rows);
qraux_ = new Vector(M.Columns);
jpvt_ = new int[M.Rows];
Q_ = null;
R_ = null;
// Fill transposed O/P matrix
int c = M.Columns;
int r = M.Rows;
for (int i = 0; i < r; ++i)
for (int j = 0; j < c; ++j)
qrdc_out_[j,i] = M[i,j];
int do_pivot = 0; // Enable[!=0]/disable[==0] pivoting.
for (int i = 0; i < jpvt_.Length; i++) jpvt_[i] = 0;
Vector work = new Vector(M.Rows);
fixed (float* data = qrdc_out_.Datablock())
{
fixed (float* data2 = qraux_.Datablock())
{
fixed (int* data3 = jpvt_)
{
fixed (float* data4 = work.Datablock())
{
Netlib.dqrdc_(data, // On output, UT is R, below diag is mangled Q
&r, &r, &c,
data2, // Further information required to demangle Q
data3,
data4,
&do_pivot);
}
}
}
}
}
/// <summary>
/// Solve least squares problem M x = b.
/// </summary>
/// <param name="b"></param>
/// <returns></returns>
public unsafe Vector Solve(Vector b)
{
//assert(b.size() == A_.Columns());
int n = A_.Columns;
Vector ret = new Vector(b);
fixed (float* data = A_.Datablock())
{
fixed (float* data2 = ret.Datablock())
{
Netlib.dposl_(data, &n, &n, data2);
}
}
return ret;
}
/// <summary>
/// Solve least squares problem M x = b.
/// The right-hand-side std::vector x may be b,
/// which will give a fractional increase in speed.
/// </summary>
/// <param name="b"></param>
/// <param name="x"></param>
public unsafe void Solve(Vector b, Vector x)
{
//assert(b.size() == A_.Columns());
x = b;
int n = A_.Columns;
fixed (float* data = A_.Datablock())
{
fixed (float* data2 = x.Datablock())
{
Netlib.dposl_(data, &n, &n, data2);
}
}
}
private unsafe void init(MatrixFixed M, float zero_out_tol)
{
m_ = M.Rows;
n_ = M.Columns;
U_ = new MatrixFixed(m_, n_);
W_ = new DiagMatrix(n_);
Winverse_ = new DiagMatrix(n_);
V_ = new MatrixFixed(n_, n_);
//assert(m_ > 0);
//assert(n_ > 0);
int n = M.Rows;
int p = M.Columns;
int mm = Netlib.min(n + 1, p);
// Copy source matrix into fortran storage
// SVD is slow, don't worry about the cost of this transpose.
Vector X = Vector.fortran_copy(M);
// Make workspace vectors
Vector work = new Vector(n);
work.Fill(0);
Vector uspace = new Vector(n * p);
uspace.Fill(0);
Vector vspace = new Vector(p * p);
vspace.Fill(0);
Vector wspace = new Vector(mm);
wspace.Fill(0); // complex fortran routine actually _wants_ complex W!
Vector espace = new Vector(p);
espace.Fill(0);
// Call Linpack SVD
int info = 0;
int job = 21;
fixed(float *data = X.Datablock())
{
fixed(float *data2 = wspace.Datablock())
{
fixed(float *data3 = espace.Datablock())
{
fixed(float *data4 = uspace.Datablock())
{
fixed(float *data5 = vspace.Datablock())
{
fixed(float *data6 = work.Datablock())
{
Netlib.dsvdc_(data, &n, &n, &p,
data2,
data3,
data4, &n,
data5, &p,
data6,
&job, &info);
}
}
}
}
}
}
// Error return?
if (info != 0)
{
// If info is non-zero, it contains the number of singular values
// for this the SVD algorithm failed to converge. The condition is
// not bogus. Even if the returned singular values are sensible,
// the singular vectors can be utterly wrong.
// It is possible the failure was due to NaNs or infinities in the
// matrix. Check for that now.
M.assert_finite();
// If we get here it might be because
// 1. The scalar type has such
// extreme precision that too few iterations were performed to
// converge to within machine precision (that is the svdc criterion).
// One solution to that is to increase the maximum number of
// iterations in the netlib code.
//
// 2. The LINPACK dsvdc_ code expects correct IEEE rounding behaviour,
// which some platforms (notably x86 processors)
// have trouble doing. For example, gcc can output
// code in -O2 and static-linked code that causes this problem.
// One solution to this is to persuade gcc to output slightly different code
// by adding and -fPIC option to the command line for v3p\netlib\dsvdc.c. If
// that doesn't work try adding -ffloat-store, which should fix the problem
// at the expense of being significantly slower for big problems. Note that
// if this is the cause, vxl/vnl/tests/test_svd should have failed.
//
// You may be able to diagnose the problem here by printing a warning message.
Debug.WriteLine("__FILE__ : suspicious return value (" + Convert.ToString(info) + ") from SVDC" +
"__FILE__ : M is " + Convert.ToString(M.Rows) + "x" + Convert.ToString(M.Columns));
valid_ = false;
}
else
{
valid_ = true;
}
// Copy fortran outputs into our storage
int ctr = 0;
for (int j = 0; j < p; ++j)
{
for (int i = 0; i < n; ++i)
{
U_[i, j] = uspace[ctr];
ctr++;
}
}
for (int j = 0; j < mm; ++j)
{
W_[j, j] = Math.Abs(wspace[j]); // we get rid of complexness here.
}
for (int j = mm; j < n_; ++j)
{
W_[j, j] = 0;
}
ctr = 0;
for (int j = 0; j < p; ++j)
{
for (int i = 0; i < p; ++i)
{
V_[i, j] = vspace[ctr];
ctr++;
}
}
//if (test_heavily)
{
// Test that recomposed matrix == M
//float recomposition_residual = Math.Abs((Recompose() - M).FrobeniusNorm());
//float n2 = Math.Abs(M.FrobeniusNorm());
//float thresh = m_ * (float)(eps) * n2;
//if (recomposition_residual > thresh)
{
//std::cerr << "VNL::SVD<T>::SVD<T>() -- Warning, recomposition_residual = "
//<< recomposition_residual << std::endl
//<< "FrobeniusNorm(M) = " << n << std::endl
//<< "eps*FrobeniusNorm(M) = " << thresh << std::endl
//<< "Press return to continue\n";
//char x;
//std::cin.get(&x, 1, '\n');
}
}
if (zero_out_tol >= 0)
{
// Zero out small sv's and update rank count.
ZeroOutAbsolute((float)(+zero_out_tol));
}
else
{
// negative tolerance implies relative to max elt.
ZeroOutRelative((float)(-zero_out_tol));
}
}
/// <summary>
/// Return residual vector d of M x = b -> d = Q'b.
/// </summary>
/// <param name="b"></param>
/// <returns></returns>
public unsafe Vector QtB(Vector b)
{
int n = qrdc_out_.Columns;
int p = qrdc_out_.Rows;
float[] b_data = b.Datablock();
Vector QtB = new Vector(n);
// see comment above
int JOB = 1000;
int info = 0;
fixed (float* data = qrdc_out_.Datablock())
{
fixed (float* data2 = qraux_.Datablock())
{
fixed (float* data3 = b_data)
{
fixed (float* data4 = QtB.Datablock())
{
Netlib.dqrsl_(data, &n, &n, &p, data2, data3,
(float*)0, // A: Qb
data4, // B: Q'b
(float*)0, // C: x
(float*)0, // D: residual
(float*)0, // E: Ax
&JOB,
&info);
}
}
}
}
if (info > 0)
Debug.WriteLine(" __FILE__ : VNL::QR<T>::QtB() -- matrix is rank-def by " + Convert.ToString(info));
return QtB;
}
public static Vector operator* (MatrixFixed m, Vector v)
{
Vector result = new Vector(m.Rows); // Temporary
MatrixFixed mm = m; // Drop const for get()
float[] result_data = result.Datablock();
float[] v_data = v.Datablock();
float[,] mm_data = mm.Datablock();
int vsize = v.size();
for (int i = 0; i < m.Rows; i++)
{ // For each index
result_data[i] = 0; // Initialize element value
for (int k = 0; k < vsize; k++) // Loop over column values
result_data[i] += (mm_data[i,k] * v_data[k]); // Multiply
}
return result;
}
/// <summary>
/// Returns new vector which is the multiplication of row vector v with matrix m.\ O(m*n).
/// </summary>
/// <param name="m"></param>
/// <param name="v"></param>
/// <returns></returns>
public static Vector operator *(Vector v, MatrixFixed m)
{
Vector result = new Vector(m.Columns); // Temporary
MatrixFixed mm = m; // Drop const for get()
float[] result_data = result.Datablock();
float[] v_data = v.Datablock();
float[,] mm_data = mm.Datablock();
for (int i = 0; i < m.Columns; i++)
{ // For each index
result_data[i] = 0; // Initialize element value
for (int k = 0; k < result_data.Length; k++) // Loop over column values
result_data[i] += (v_data[k] * mm_data[k, i]); // Multiply
}
return result;
}
/// <summary>
/// Cholesky decomposition.
/// Make cholesky decomposition of M optionally computing
/// the reciprocal condition number. If mode is estimate_condition, the
/// condition number and an approximate nullspace are estimated, at a cost
/// of a factor of (1 + 18/n). Here's a table of 1 + 18/n:
///<pre>
/// n: 3 5 10 50 100 500 1000
/// slowdown: 7.0f 4.6 2.8 1.4 1.18 1.04 1.02
/// </summary>
/// <param name="M"></param>
/// <param name="mode"></param>
public unsafe void init(MatrixFixed M, Operation mode)
{
A_ = new MatrixFixed(M);
int n = M.Columns;
//assert(n == (int)(M.Rows()));
num_dims_rank_def_ = -1;
int num_dims_rank_def_temp = num_dims_rank_def_;
// BJT: This warning is pointless - it often doesn't detect non symmetry and
// if you know what you're doing you don't want to be slowed down
// by a cerr
/*
if (Math.Abs(M[0,n-1] - M[n-1,0]) > 1e-8)
{
Debug.WriteLine("cholesky: WARNING: unsymmetric: " + M);
}
*/
if (mode != Operation.estimate_condition)
{
// Quick factorization
fixed (float* data = A_.Datablock())
{
Netlib.dpofa_(data, &n, &n, &num_dims_rank_def_temp);
}
//if ((mode == Operation.verbose) && (num_dims_rank_def_temp != 0))
// Debug.WriteLine("cholesky:: " + Convert.ToString(num_dims_rank_def_temp) + " dimensions of non-posdeffness");
}
else
{
Vector nullvector = new Vector(n);
float rcond_temp = rcond_;
fixed (float* data = A_.Datablock())
{
fixed (float* data2 = nullvector.Datablock())
{
Netlib.dpoco_(data, &n, &n, &rcond_temp, data2, &num_dims_rank_def_temp);
}
}
rcond_ = rcond_temp;
}
num_dims_rank_def_ = num_dims_rank_def_temp;
}
private unsafe void init(MatrixFixed M, float zero_out_tol)
{
m_ = M.Rows;
n_ = M.Columns;
U_ = new MatrixFixed(m_, n_);
W_ = new DiagMatrix(n_);
Winverse_ = new DiagMatrix(n_);
V_ = new MatrixFixed(n_, n_);
//assert(m_ > 0);
//assert(n_ > 0);
int n = M.Rows;
int p = M.Columns;
int mm = Netlib.min(n+1,p);
// Copy source matrix into fortran storage
// SVD is slow, don't worry about the cost of this transpose.
Vector X = Vector.fortran_copy(M);
// Make workspace vectors
Vector work = new Vector(n);
work.Fill(0);
Vector uspace = new Vector(n*p);
uspace.Fill(0);
Vector vspace = new Vector(p*p);
vspace.Fill(0);
Vector wspace = new Vector(mm);
wspace.Fill(0); // complex fortran routine actually _wants_ complex W!
Vector espace = new Vector(p);
espace.Fill(0);
// Call Linpack SVD
int info = 0;
int job = 21;
fixed (float* data = X.Datablock())
{
fixed (float* data2 = wspace.Datablock())
{
fixed (float* data3 = espace.Datablock())
{
fixed (float* data4 = uspace.Datablock())
{
fixed (float* data5 = vspace.Datablock())
{
fixed (float* data6 = work.Datablock())
{
Netlib.dsvdc_(data, &n, &n, &p,
data2,
data3,
data4, &n,
data5, &p,
data6,
&job, &info);
}
}
}
}
}
}
// Error return?
if (info != 0)
{
// If info is non-zero, it contains the number of singular values
// for this the SVD algorithm failed to converge. The condition is
// not bogus. Even if the returned singular values are sensible,
// the singular vectors can be utterly wrong.
// It is possible the failure was due to NaNs or infinities in the
// matrix. Check for that now.
M.assert_finite();
// If we get here it might be because
// 1. The scalar type has such
// extreme precision that too few iterations were performed to
// converge to within machine precision (that is the svdc criterion).
// One solution to that is to increase the maximum number of
// iterations in the netlib code.
//
// 2. The LINPACK dsvdc_ code expects correct IEEE rounding behaviour,
// which some platforms (notably x86 processors)
// have trouble doing. For example, gcc can output
// code in -O2 and static-linked code that causes this problem.
// One solution to this is to persuade gcc to output slightly different code
// by adding and -fPIC option to the command line for v3p\netlib\dsvdc.c. If
// that doesn't work try adding -ffloat-store, which should fix the problem
// at the expense of being significantly slower for big problems. Note that
// if this is the cause, vxl/vnl/tests/test_svd should have failed.
//
// You may be able to diagnose the problem here by printing a warning message.
Debug.WriteLine("__FILE__ : suspicious return value (" + Convert.ToString(info) + ") from SVDC" +
"__FILE__ : M is " + Convert.ToString(M.Rows) + "x" + Convert.ToString(M.Columns));
valid_ = false;
}
else
valid_ = true;
// Copy fortran outputs into our storage
int ctr = 0;
for (int j = 0; j < p; ++j)
for (int i = 0; i < n; ++i)
{
U_[i, j] = uspace[ctr];
ctr++;
}
for (int j = 0; j < mm; ++j)
W_[j, j] = Math.Abs(wspace[j]); // we get rid of complexness here.
for (int j = mm; j < n_; ++j)
W_[j, j] = 0;
ctr = 0;
for (int j = 0; j < p; ++j)
for (int i = 0; i < p; ++i)
{
V_[i, j] = vspace[ctr];
ctr++;
}
//if (test_heavily)
{
// Test that recomposed matrix == M
//float recomposition_residual = Math.Abs((Recompose() - M).FrobeniusNorm());
//float n2 = Math.Abs(M.FrobeniusNorm());
//float thresh = m_ * (float)(eps) * n2;
//if (recomposition_residual > thresh)
{
//std::cerr << "VNL::SVD<T>::SVD<T>() -- Warning, recomposition_residual = "
//<< recomposition_residual << std::endl
//<< "FrobeniusNorm(M) = " << n << std::endl
//<< "eps*FrobeniusNorm(M) = " << thresh << std::endl
//<< "Press return to continue\n";
//char x;
//std::cin.get(&x, 1, '\n');
}
}
if (zero_out_tol >= 0)
// Zero out small sv's and update rank count.
ZeroOutAbsolute((float)(+zero_out_tol));
else
// negative tolerance implies relative to max elt.
ZeroOutRelative((float)(-zero_out_tol));
}
/// <summary>
/// JOB: ABCDE decimal
/// A B C D E
/// --- --- --- --- ---
/// Qb Q'b x norm(A*x - b) A*x
///
/// Solve equation M x = b for x using the computed decomposition.
/// </summary>
/// <param name="b"></param>
/// <returns></returns>
public unsafe Vector Solve(Vector b)
{
int n = qrdc_out_.Columns;
int p = qrdc_out_.Rows;
float[] b_data = b.Datablock();
Vector QtB = new Vector(n);
Vector x = new Vector(p);
// see comment above
int JOB = 100;
int info = 0;
fixed (float* data = qrdc_out_.Datablock())
{
fixed (float* data2 = qraux_.Datablock())
{
fixed (float* data3 = b_data)
{
fixed (float* data4 = QtB.Datablock())
{
fixed (float* data5 = x.Datablock())
{
Netlib.dqrsl_(data, &n, &n, &p, data2, data3,
(float*)0, data4, data5,
(float*)0, // residual*
(float*)0, // Ax*
&JOB,
&info);
}
}
}
}
}
if (info > 0)
Debug.WriteLine("__FILE__ : VNL::QR<T>::Solve() : matrix is rank-deficient by " + Convert.ToString(info));
return x;
}