// 1-norm
// t >= sum( |x_i| ), x is a vector Variable
public static void norm1(Model M, Variable t, Variable x)
{
Variable u = M.Variable(x.GetShape(), Domain.Unbounded());
abs(M, u, x);
M.Constraint(Expr.Sub(t, Expr.Sum(u)), Domain.GreaterThan(0.0));
}
private void FetchTest_Check(Variable v, int[] shape)
{
Assert.IsFalse(v.DataSet.HasChanges);
Assert.IsTrue(v.DataSet.IsAutocommitEnabled);
Assert.AreEqual(shape.Length, v.Rank);
for (int i = 0; i < v.Rank; i++)
{
Assert.AreEqual(shape[i], v.GetShape()[i]);
}
var data = v.GetData();
int[] index = new int[v.Rank];
for (int i = 0; i < data.Length; i++)
{
Assert.IsTrue(((double)data.GetValue(index)) > 0);
for (int j = v.Rank; --j >= 0;)
{
index[j]++;
if (index[j] < shape[j])
{
break;
}
index[j] = 0;
}
}
Assert.IsNotNull(v.MissingValue);
Assert.IsNotNull(v.Metadata["Units", SchemaVersion.Recent]);
Assert.IsNotNull(v.Metadata["Name", SchemaVersion.Recent]);
Assert.IsNotNull(v.Metadata["long_name", SchemaVersion.Recent]);
}
// Cardinality bound
// At most k of entries in x are nonzero, assuming in advance |x_i|<=1.
public static void card(Model M, Variable x, int k)
{
Variable t = M.Variable(x.GetShape(), Domain.Binary());
abs(M, t, x);
M.Constraint(Expr.Sum(t), Domain.LessThan(k));
}
// Semicontinuous variable
// x = 0 or a <= x <= b
public static void semicontinuous(Model M, Variable x, double a, double b)
{
Variable u = M.Variable(x.GetShape(), Domain.Binary());
M.Constraint(Expr.Sub(x, Expr.Mul(a, u)), Domain.GreaterThan(0.0));
M.Constraint(Expr.Sub(x, Expr.Mul(b, u)), Domain.LessThan(0.0));
}
/**
* Purpose: Models the hypograph of the n-th power of the
* determinant of a positive definite matrix.
*
* The convex set (a hypograph)
*
* C = { (X, t) \in S^n_+ x R | t <= det(X)^{1/n} },
*
* can be modeled as the intersection of a semidefinite cone
*
* [ X, Z; Z^T Diag(Z) ] >= 0
*
* and a number of rotated quadratic cones and affine hyperplanes,
*
* t <= (Z11*Z22*...*Znn)^{1/n} (see geometric_mean).
*
* References:
* [1] "Lectures on Modern Optimization", Ben-Tal and Nemirovski, 2000.
*/
public static void det_rootn(Model M, Variable X, Variable t)
{
int n = X.GetShape().Dim(0);
// Setup variables
Variable Y = M.Variable(Domain.InPSDCone(2 * n));
// Setup Y = [X, Z; Z^T diag(Z)]
Variable Y11 = Y.Slice(new int[] { 0, 0 }, new int[] { n, n });
Variable Y21 = Y.Slice(new int[] { n, 0 }, new int[] { 2 * n, n });
Variable Y22 = Y.Slice(new int[] { n, n }, new int[] { 2 * n, 2 * n });
M.Constraint(Expr.Sub(Expr.MulElm(Matrix.Eye(n), Y21), Y22), Domain.EqualsTo(0.0));
M.Constraint(Expr.Sub(X, Y11), Domain.EqualsTo(0.0));
// t^n <= (Z11*Z22*...*Znn)
Variable[] tmpv = new Variable[n];
for (int i = 0; i < n; ++i)
{
tmpv[i] = Y22.Index(i, i);
}
Variable z = Var.Reshape(Var.Vstack(tmpv), n);
geometric_mean(M, z, t);
}
public static long TotalLength(this Variable var)
{
if (var == null)
{
throw new ArgumentNullException("var");
}
return(var.GetShape().Select(i => (long)i).Aggregate((i, j) => i * j));
}
public static Point[][] SplitSecondDimension(Variable variable)
{
if (variable == null)
throw new ArgumentNullException("variable");
if (variable.Rank != 2)
throw new ArgumentException("Only 2d variables are supported");
int n = variable.GetShape()[1];
int m = variable.GetShape()[0];
Array d = variable.GetData();
Point[][] pts = new Point[n][];
for (int i = 0; i < n; i++)
{
List<Point> tmp = new List<Point>(m);
if (variable.TypeOfData == typeof(float))
{
float[,] dt = (float[,])d;
object mvObj = variable.GetMissingValue();
if (mvObj == null)
{
for (int j = 0; j < m; j++)
if (!Double.IsNaN(dt[j, i]))
tmp.Add(new Point(j, dt[j, i]));
}
else
{
float mv;
try
{
mv = Convert.ToSingle(mvObj);
}
catch (Exception exc)
{
Trace.WriteLine("PolyPolyline: cannot convert missing value attribute to float: " + exc.Message);
mv = float.NaN;
}
for (int j = 0; j < m; j++)
if (dt[j, i] != mv)
tmp.Add(new Point(j, dt[j, i]));
}
}
else if (variable.TypeOfData == typeof(double))
{
double[,] dt = (double[,])d;
object mvObj = variable.GetMissingValue();
if (mvObj == null)
{
for (int j = 0; j < m; j++)
if (!Double.IsNaN(dt[j, i]))
tmp.Add(new Point(j, dt[j, i]));
}
else
{
double mv;
try
{
mv = Convert.ToDouble(mvObj);
}
catch (Exception exc)
{
Trace.WriteLine("PolyPolyline: cannot convert missing value attribute to double: " + exc.Message);
mv = double.NaN;
}
for (int j = 0; j < m; j++)
if (dt[j, i] != mv)
tmp.Add(new Point(j, dt[j, i]));
}
}
else
{
object mv = variable.GetMissingValue();
for (int j = 0; j < m; j++)
{
object obj = d.GetValue(j, i);
if (!Object.Equals(obj, mv))
tmp.Add(new Point(j, Convert.ToDouble(obj)));
}
}
pts[i] = tmp.ToArray();
}
return pts;
}
static void PrintData(Variable v, string range, string format)
{
try
{
// Find out which data to take
int rank = v.Rank;
var shape = v.GetShape();
var origin = rank == 0 ? null : new int[rank];
var count = rank == 0 ? null : new int[rank];
var stride = rank == 0 ? null : new int[rank];
for (int i = 0; i < rank; i++)
{
origin[i] = 0;
count[i] = shape[i];
stride[i] = 1;
}
if (range != null)
{
// parse range specification 'from:to' or 'from:step:to'
var ranges = range.Split(',');
for (int i = 0; i < rank && i < ranges.Length; i++)
{
var fromto = ranges[i].Split(':');
if (!int.TryParse(fromto[0], out origin[i]))
{
origin[i] = 0;
}
if (origin[i] < 0)
{
origin[i] = 0;
}
if (origin[i] >= shape[i])
{
origin[i] = shape[i] - 1;
}
if (fromto.Length < 2)
{
count[i] = 1;
}
else
{
if (!int.TryParse(fromto[fromto.Length - 1], out count[i]))
{
count[i] = 0;
}
if (count[i] == 0 || count[i] >= shape[i])
{
count[i] = shape[i] - 1;
}
if (count[i] < origin[i])
{
count[i] = origin[i];
}
if (fromto.Length > 2)
{
if (!int.TryParse(fromto[1], out stride[i]))
{
stride[i] = 1;
}
if (stride[i] <= 0)
{
stride[i] = 1;
}
}
count[i] = 1 + (count[i] - origin[i]) / stride[i];
}
}
}
// Now get the data
Array data = v.GetData(origin, stride, count);
if (data == null || (rank > 0 && data.Rank != rank))
{
Console.Error.WriteLine("No data");
}
else
{
int prefix = string.Join(",", Array.ConvertAll(shape, i => i.ToString())).Length + 2;
// parse format
int cell = 8;
string frm = "{0,8}";
if (format != null)
{
int p = format.IndexOf(':');
if (p < 0)
{
if (!int.TryParse(format, out cell))
{
cell = 8;
}
frm = "{0," + cell + "}";
}
else
{
if (!int.TryParse(format.Substring(0, p), out cell))
{
cell = 8;
}
frm = "{0," + cell + format.Substring(p) + "}";
}
}
// Now print the data
if (rank == 0) // scalar variable
{
Console.WriteLine();
string item = string.Format(frm, data.GetValue(0));
// check that item fits a cell
if (item.Length > cell)
{
item = item.Substring(0, cell - 1) + "#";
}
Console.Write(" "); Console.Write(item);
}
else // has rank > 0 (array)
{
int[] indices = new int[data.Rank];
int[] varIndices = new int[rank];
int bufferWidth = Math.Max(80, Console.BufferWidth);
// .. to allow for non-console output
string lineSeparator = Environment.NewLine;
while (indices[0] < data.GetLength(0))
{
// print last dimension
Console.Write(lineSeparator);
lineSeparator = string.Empty;
int lastIndex = data.Rank - 1;
indices[lastIndex] = 0;
while (indices[lastIndex] < data.GetLength(lastIndex))
{
// print line of cells
// print prefix of current indices
for (int i = 0; i < rank; i++)
{
varIndices[i] = origin[i] + indices[i] * stride[i];
}
string item = ("[" + string.Join(",", Array.ConvertAll(varIndices, i => i.ToString())) + "]").PadRight(prefix);
Console.Write(item);
int left = bufferWidth - item.Length;
while (left > cell && indices[lastIndex] < data.GetLength(lastIndex))
{
item = string.Format(frm, data.GetValue(indices));
// check that item fits a cell
if (item.Length > cell)
{
item = item.Substring(0, cell - 1) + "#";
}
Console.Write(" "); Console.Write(item);
left -= item.Length + 1;
indices[lastIndex]++;
varIndices[lastIndex] += stride[lastIndex];
}
Console.WriteLine();
if (indices[lastIndex] < data.GetLength(lastIndex))
{
lineSeparator = Environment.NewLine;
}
}
lastIndex -= 1;
// increment recursively other dimensions
while (lastIndex >= 0 && ++indices[lastIndex] >= data.GetLength(lastIndex))
{
if (lastIndex > 0)
{
indices[lastIndex] = 0;
}
lastIndex -= 1;
}
}
}
}
Console.WriteLine();
}
catch (Exception e)
{
Console.Error.WriteLine("Error while printing data: " + e.Message);
}
}
static void PrintData(Variable v, string range, string format)
{
try
{
// Find out which data to take
int rank = v.Rank;
var shape = v.GetShape();
var origin = rank == 0 ? null : new int[rank];
var count = rank == 0 ? null : new int[rank];
var stride = rank == 0 ? null : new int[rank];
for (int i = 0; i < rank; i++)
{
origin[i] = 0;
count[i] = shape[i];
stride[i] = 1;
}
if (range != null)
{
// parse range specification 'from:to' or 'from:step:to'
var ranges = range.Split(',');
for (int i = 0; i < rank && i < ranges.Length; i++)
{
var fromto = ranges[i].Split(':');
if (!int.TryParse(fromto[0], out origin[i])) origin[i] = 0;
if (origin[i] < 0) origin[i] = 0;
if (origin[i] >= shape[i]) origin[i] = shape[i] - 1;
if (fromto.Length < 2) count[i] = 1;
else
{
if (!int.TryParse(fromto[fromto.Length - 1], out count[i])) count[i] = 0;
if (count[i] == 0 || count[i] >= shape[i]) count[i] = shape[i] - 1;
if (count[i] < origin[i]) count[i] = origin[i];
if (fromto.Length > 2)
{
if (!int.TryParse(fromto[1], out stride[i])) stride[i] = 1;
if (stride[i] <= 0) stride[i] = 1;
}
count[i] = 1 + (count[i] - origin[i]) / stride[i];
}
}
}
// Now get the data
Array data = v.GetData(origin, stride, count);
if (data == null || (rank > 0 && data.Rank != rank))
Console.Error.WriteLine("No data");
else
{
int prefix = string.Join(",", Array.ConvertAll(shape, i => i.ToString())).Length + 2;
// parse format
int cell = 8;
string frm = "{0,8}";
if (format != null)
{
int p = format.IndexOf(':');
if (p < 0)
{
if (!int.TryParse(format, out cell)) cell = 8;
frm = "{0," + cell + "}";
}
else
{
if (!int.TryParse(format.Substring(0, p), out cell)) cell = 8;
frm = "{0," + cell + format.Substring(p) + "}";
}
}
// Now print the data
if (rank == 0) // scalar variable
{
Console.WriteLine();
string item = string.Format(frm, data.GetValue(0));
// check that item fits a cell
if (item.Length > cell) item = item.Substring(0, cell - 1) + "#";
Console.Write(" "); Console.Write(item);
}
else // has rank > 0 (array)
{
int[] indices = new int[data.Rank];
int[] varIndices = new int[rank];
int bufferWidth = Math.Max(80, Console.BufferWidth);
// .. to allow for non-console output
string lineSeparator = Environment.NewLine;
while (indices[0] < data.GetLength(0))
{
// print last dimension
Console.Write(lineSeparator);
lineSeparator = string.Empty;
int lastIndex = data.Rank - 1;
indices[lastIndex] = 0;
while (indices[lastIndex] < data.GetLength(lastIndex))
{
// print line of cells
// print prefix of current indices
for (int i = 0; i < rank; i++)
varIndices[i] = origin[i] + indices[i] * stride[i];
string item = ("[" + string.Join(",", Array.ConvertAll(varIndices, i => i.ToString())) + "]").PadRight(prefix);
Console.Write(item);
int left = bufferWidth - item.Length;
while (left > cell && indices[lastIndex] < data.GetLength(lastIndex))
{
item = string.Format(frm, data.GetValue(indices));
// check that item fits a cell
if (item.Length > cell) item = item.Substring(0, cell - 1) + "#";
Console.Write(" "); Console.Write(item);
left -= item.Length + 1;
indices[lastIndex]++;
varIndices[lastIndex] += stride[lastIndex];
}
Console.WriteLine();
if (indices[lastIndex] < data.GetLength(lastIndex))
lineSeparator = Environment.NewLine;
}
lastIndex -= 1;
// increment recursively other dimensions
while (lastIndex >= 0 && ++indices[lastIndex] >= data.GetLength(lastIndex))
{
if (lastIndex > 0) indices[lastIndex] = 0;
lastIndex -= 1;
}
}
}
}
Console.WriteLine();
}
catch (Exception e)
{
Console.Error.WriteLine("Error while printing data: " + e.Message);
}
}
public static Point[][] SplitFirstDimension(Variable variable)
{
if (variable == null)
{
throw new ArgumentNullException("variable");
}
if (variable.Rank != 2)
{
throw new ArgumentException("Only 2d variables are supported");
}
int n = variable.GetShape()[0];
int m = variable.GetShape()[1];
Array d = variable.GetData();
Point[][] pts = new Point[n][];
for (int i = 0; i < n; i++)
{
List <Point> tmp = new List <Point>(m);
if (variable.TypeOfData == typeof(float))
{
float[,] dt = (float[, ])d;
object mvObj = variable.GetMissingValue();
if (mvObj == null)
{
for (int j = 0; j < m; j++)
{
if (!Double.IsNaN(dt[i, j]))
{
tmp.Add(new Point(j, dt[i, j]));
}
}
}
else
{
float mv;
try
{
mv = Convert.ToSingle(mvObj);
}
catch (Exception exc)
{
Trace.WriteLine("PolyPolyline: cannot convert missing value attribute to Double: " + exc.Message);
mv = float.NaN;
}
for (int j = 0; j < m; j++)
{
if (dt[i, j] != mv)
{
tmp.Add(new Point(j, dt[i, j]));
}
}
}
}
else if (variable.TypeOfData == typeof(double))
{
double[,] dt = (double[, ])d;
object mvObj = variable.GetMissingValue();
if (mvObj == null)
{
for (int j = 0; j < m; j++)
{
if (!Double.IsNaN(dt[i, j]))
{
tmp.Add(new Point(j, dt[i, j]));
}
}
}
else
{
double mv = Convert.ToDouble(mvObj);
try
{
mv = Convert.ToDouble(mvObj);
}
catch (Exception exc)
{
Trace.WriteLine("PolyPolyline: cannot convert missing value attribute to double: " + exc.Message);
mv = double.NaN;
}
for (int j = 0; j < m; j++)
{
if (dt[i, j] != mv)
{
tmp.Add(new Point(j, dt[i, j]));
}
}
}
}
else
{
object mv = variable.GetMissingValue();
for (int j = 0; j < m; j++)
{
object obj = d.GetValue(i, j);
if (!Object.Equals(obj, mv))
{
tmp.Add(new Point(j, Convert.ToDouble(obj)));
}
}
}
pts[i] = tmp.ToArray();
}
return(pts);
}
