/**
* Performs matrix addition:<br>
* C = αA + βB
*
* @param alpha scalar value multiplied against A
* @param A Matrix
* @param beta scalar value multiplied against B
* @param B Matrix
* @param C Output matrix.
* @param gw (Optional) Storage for internal workspace. Can be null.
* @param gx (Optional) Storage for internal workspace. Can be null.
*/
public static void add(double alpha, DMatrixSparseCSC A, double beta, DMatrixSparseCSC B, DMatrixSparseCSC C,
IGrowArray gw, DGrowArray gx)
{
double[] x = TriangularSolver_DSCC.adjust(gx, A.numRows);
int[] w = TriangularSolver_DSCC.adjust(gw, A.numRows, A.numRows);
C.indicesSorted = false;
C.nz_length = 0;
for (int col = 0; col < A.numCols; col++)
{
C.col_idx[col] = C.nz_length;
ImplSparseSparseMult_DSCC.multAddColA(A, col, alpha, C, col + 1, x, w);
ImplSparseSparseMult_DSCC.multAddColA(B, col, beta, C, col + 1, x, w);
// take the values in the dense vector 'x' and put them into 'C'
int idxC0 = C.col_idx[col];
int idxC1 = C.col_idx[col + 1];
for (int i = idxC0; i < idxC1; i++)
{
C.nz_values[i] = x[C.nz_rows[i]];
}
}
}
/**
* <p>
* Checks to see if a matrix is orthogonal or isometric.
* </p>
*
* @param Q The matrix being tested. Not modified.
* @param tol Tolerance.
* @return True if it passes the test.
*/
public static bool isOrthogonal(DMatrixSparseCSC Q, double tol)
{
if (Q.numRows < Q.numCols)
{
throw new ArgumentException("The number of rows must be more than or equal to the number of columns");
}
IGrowArray gw = new IGrowArray();
DGrowArray gx = new DGrowArray();
for (int i = 0; i < Q.numRows; i++)
{
for (int j = i + 1; j < Q.numCols; j++)
{
double val = CommonOps_DSCC.dotInnerColumns(Q, i, Q, j, gw, gx);
if (!(Math.Abs(val) <= tol))
{
return(false);
}
}
}
return(true);
}
/**
* Computes the solution to the triangular system.
*
* @param G (Input) Lower or upper triangular matrix. diagonal elements must be non-zero. Not modified.
* @param lower true for lower triangular and false for upper
* @param B (Input) Matrix. Not modified.
* @param X (Output) Solution
* @param g_x (Optional) Storage for workspace.
* @param g_xi (Optional) Storage for workspace.
* @param g_w (Optional) Storage for workspace.
*/
public static void solve(DMatrixSparseCSC G, bool lower,
DMatrixSparseCSC B, DMatrixSparseCSC X,
DGrowArray g_x, IGrowArray g_xi, IGrowArray g_w)
{
double[] x = adjust(g_x, G.numRows);
if (g_xi == null)
{
g_xi = new IGrowArray();
}
int[] xi = adjust(g_xi, G.numRows);
X.nz_length = 0;
X.col_idx[0] = 0;
X.indicesSorted = false;
for (int colB = 0; colB < B.numCols; colB++)
{
int top = solve(G, lower, B, colB, x, null, g_xi, g_w);
int nz_count = X.numRows - top;
if (X.nz_values.Length < X.nz_length + nz_count)
{
X.growMaxLength(X.nz_length * 2 + nz_count, true);
}
for (int p = top; p < X.numRows; p++, X.nz_length++)
{
X.nz_rows[X.nz_length] = xi[p];
X.nz_values[X.nz_length] = x[xi[p]];
}
X.col_idx[colB + 1] = X.nz_length;
}
}
/**
* Resizes the array to ensure that it is at least of length desired and returns its internal array
*/
public static double[] adjust(DGrowArray gwork, int desired)
{
if (gwork == null)
{
gwork = new DGrowArray();
}
gwork.reshape(desired);
return(gwork.data);
}
/**
* Performs an element-wise multiplication.<br>
* C[i,j] = A[i,j]*B[i,j]<br>
* All matrices must have the same shape.
*
* @param A (Input) Matrix.
* @param B (Input) Matrix
* @param C (Ouptut) Matrix.
* @param gw (Optional) Storage for internal workspace. Can be null.
* @param gx (Optional) Storage for internal workspace. Can be null.
*/
public static void elementMult(DMatrixSparseCSC A, DMatrixSparseCSC B, DMatrixSparseCSC C,
IGrowArray gw, DGrowArray gx)
{
if (A.numCols != B.numCols || A.numRows != B.numRows || A.numCols != C.numCols || A.numRows != C.numRows)
{
throw new ArgumentException("All inputs must have the same number of rows and columns");
}
ImplCommonOps_DSCC.elementMult(A, B, C, gw, gx);
}
/**
* Performs matrix addition:<br>
* C = αA + βB
*
* @param alpha scalar value multiplied against A
* @param A Matrix
* @param beta scalar value multiplied against B
* @param B Matrix
* @param C Output matrix.
* @param gw (Optional) Storage for internal workspace. Can be null.
* @param gx (Optional) Storage for internal workspace. Can be null.
*/
public static void add(double alpha, DMatrixSparseCSC A, double beta, DMatrixSparseCSC B, DMatrixSparseCSC C,
IGrowArray gw, DGrowArray gx)
{
if (A.numRows != B.numRows || A.numCols != B.numCols || A.numRows != C.numRows || A.numCols != C.numCols)
{
throw new ArgumentException("Inconsistent matrix shapes");
}
ImplCommonOps_DSCC.add(alpha, A, beta, B, C, gw, gx);
}
public static void multTransA(DMatrixSparseCSC A, DMatrixSparseCSC B, DMatrixSparseCSC C,
IGrowArray gw, DGrowArray gx)
{
if (A.numCols != C.numRows || B.numCols != C.numCols)
{
throw new ArgumentException("Inconsistent matrix shapes");
}
ImplSparseSparseMult_DSCC.multTransA(A, B, C, gw, gx);
}
/**
* Performs matrix multiplication. C = A*B<sup>T</sup></sup>
*
* @param A Matrix
* @param B Matrix
* @param C Storage for results. Data length is increased if increased if insufficient.
* @param gw (Optional) Storage for internal workspace. Can be null.
* @param gx (Optional) Storage for internal workspace. Can be null.
*/
public static void multTransB(DMatrixSparseCSC A, DMatrixSparseCSC B, DMatrixSparseCSC C,
IGrowArray gw, DGrowArray gx)
{
if (!B.isIndicesSorted())
{
throw new ArgumentException("B must have its indices sorted.");
}
else if (!CommonOps_DSCC.checkIndicesSorted(B))
{
throw new ArgumentException("Crap. Not really sorted");
}
double[] x = TriangularSolver_DSCC.adjust(gx, A.numRows);
int[] w = TriangularSolver_DSCC.adjust(gw, A.numRows + B.numCols, A.numRows);
C.growMaxLength(A.nz_length + B.nz_length, false);
C.indicesSorted = false;
C.nz_length = 0;
C.col_idx[0] = 0;
// initialize w is the first index in each column of B
int locationB = A.numRows;
Array.Copy(B.col_idx, 0, w, locationB, B.numCols);
for (int colC = 0; colC < B.numRows; colC++)
{
C.col_idx[colC + 1] = C.nz_length; // needs a value of B has nothing in the row
// find the column in the transposed B
int mark = colC + 1;
for (int colB = 0; colB < B.numCols; colB++)
{
int bi = w[locationB + colB];
if (bi < B.col_idx[colB + 1])
{
int row = B.nz_rows[bi];
if (row == colC)
{
multAddColA(A, colB, B.nz_values[bi], C, mark, x, w);
w[locationB + colB]++;
}
}
}
// take the values in the dense vector 'x' and put them into 'C'
int idxC0 = C.col_idx[colC];
int idxC1 = C.col_idx[colC + 1];
for (int i = idxC0; i < idxC1; i++)
{
C.nz_values[i] = x[C.nz_rows[i]];
}
}
}
/**
* Performs element-wise multiplication:<br>
* C_ij = A_ij * B_ij
*
* @param A (Input) Matrix
* @param B (Input) Matrix
* @param C (Output) matrix.
* @param gw (Optional) Storage for internal workspace. Can be null.
* @param gx (Optional) Storage for internal workspace. Can be null.
*/
public static void elementMult(DMatrixSparseCSC A, DMatrixSparseCSC B, DMatrixSparseCSC C,
IGrowArray gw, DGrowArray gx)
{
double[] x = TriangularSolver_DSCC.adjust(gx, A.numRows);
int[] w = TriangularSolver_DSCC.adjust(gw, A.numRows);
//Arrays.fill(w, 0, A.numRows, -1); // fill with -1. This will be a value less than column
for (var i = 0; i < A.numRows; i++)
{
w[i] = -1;
}
C.indicesSorted = false; // Hmm I think if B is storted then C will be sorted...
C.nz_length = 0;
for (int col = 0; col < A.numCols; col++)
{
int idxA0 = A.col_idx[col];
int idxA1 = A.col_idx[col + 1];
int idxB0 = B.col_idx[col];
int idxB1 = B.col_idx[col + 1];
// compute the maximum number of elements that there can be in this row
int maxInRow = Math.Min(idxA1 - idxA0, idxB1 - idxB0);
// make sure there are enough non-zero elements in C
if (C.nz_length + maxInRow > C.nz_values.Length)
{
C.growMaxLength(C.nz_values.Length + maxInRow, true);
}
// update the structure of C
C.col_idx[col] = C.nz_length;
// mark the rows that appear in A and save their value
for (int i = idxA0; i < idxA1; i++)
{
int row = A.nz_rows[i];
w[row] = col;
x[row] = A.nz_values[i];
}
// If a row appears in A and B, multiply and set as an element in C
for (int i = idxB0; i < idxB1; i++)
{
int row = B.nz_rows[i];
if (w[row] == col)
{
C.nz_values[C.nz_length] = x[row] * B.nz_values[i];
C.nz_rows[C.nz_length++] = row;
}
}
}
C.col_idx[C.numCols] = C.nz_length;
}
/**
* Performs matrix multiplication. C = A*B<sup>T</sup>. B needs to be sorted and will be sorted if it
* has not already been sorted.
*
* @param A (Input) Matrix. Not modified.
* @param B (Input) Matrix. Value not modified but indicies will be sorted if not sorted already.
* @param C (Output) Storage for results. Data length is increased if increased if insufficient.
* @param gw (Optional) Storage for internal workspace. Can be null.
* @param gx (Optional) Storage for internal workspace. Can be null.
*/
public static void multTransB(DMatrixSparseCSC A, DMatrixSparseCSC B, DMatrixSparseCSC C,
IGrowArray gw, DGrowArray gx)
{
if (A.numRows != C.numRows || B.numRows != C.numCols)
{
throw new ArgumentException("Inconsistent matrix shapes");
}
if (!B.isIndicesSorted())
{
B.sortIndices(null);
}
ImplSparseSparseMult_DSCC.multTransB(A, B, C, gw, gx);
}
/**
* Performs matrix multiplication. C = A*B
*
* @param A Matrix
* @param B Matrix
* @param C Storage for results. Data length is increased if increased if insufficient.
* @param gw (Optional) Storage for internal workspace. Can be null.
* @param gx (Optional) Storage for internal workspace. Can be null.
*/
public static void mult(DMatrixSparseCSC A, DMatrixSparseCSC B, DMatrixSparseCSC C,
IGrowArray gw, DGrowArray gx)
{
double[] x = TriangularSolver_DSCC.adjust(gx, A.numRows);
int[] w = TriangularSolver_DSCC.adjust(gw, A.numRows, A.numRows);
C.growMaxLength(A.nz_length + B.nz_length, false);
C.indicesSorted = false;
C.nz_length = 0;
// C(i,j) = sum_k A(i,k) * B(k,j)
int idx0 = B.col_idx[0];
for (int bj = 1; bj <= B.numCols; bj++)
{
int colB = bj - 1;
int idx1 = B.col_idx[bj];
C.col_idx[bj] = C.nz_length;
if (idx0 == idx1)
{
continue;
}
// C(:,j) = sum_k A(:,k)*B(k,j)
for (int bi = idx0; bi < idx1; bi++)
{
int rowB = B.nz_rows[bi];
double valB = B.nz_values[bi]; // B(k,j) k=rowB j=colB
multAddColA(A, rowB, valB, C, colB + 1, x, w);
}
// take the values in the dense vector 'x' and put them into 'C'
int idxC0 = C.col_idx[colB];
int idxC1 = C.col_idx[colB + 1];
for (int i = idxC0; i < idxC1; i++)
{
C.nz_values[i] = x[C.nz_rows[i]];
}
idx0 = idx1;
}
}
/**
* Computes the inner product of two column vectors taken from the input matrices.
*
* <p>dot = A(:,colA)'*B(:,colB)</p>
*
* @param A Matrix
* @param colA Column in A
* @param B Matrix
* @param colB Column in B
* @return Dot product
*/
public static double dotInnerColumns(DMatrixSparseCSC A, int colA, DMatrixSparseCSC B, int colB,
IGrowArray gw, DGrowArray gx)
{
if (A.numRows != B.numRows)
{
throw new ArgumentException("Number of rows must match.");
}
int[] w = TriangularSolver_DSCC.adjust(gw, A.numRows);
//Arrays.fill(w,0,A.numRows,-1);
for (var i = 0; i < A.numRows; i++)
{
w[i] = -1;
}
double[] x = TriangularSolver_DSCC.adjust(gx, A.numRows);
int length = 0;
int idx0 = A.col_idx[colA];
int idx1 = A.col_idx[colA + 1];
for (int i = idx0; i < idx1; i++)
{
int row = A.nz_rows[i];
x[length] = A.nz_values[i];
w[row] = length++;
}
double dot = 0;
idx0 = B.col_idx[colB];
idx1 = B.col_idx[colB + 1];
for (int i = idx0; i < idx1; i++)
{
int row = B.nz_rows[i];
if (w[row] != -1)
{
dot += x[w[row]] * B.nz_values[i];
}
}
return(dot);
}
/**
* <p>
* Performs a rank-1 update operation on the submatrix specified by V with the multiply on the right.<br>
* <br>
* C = (I - γ*v*v<sup>T</sup>)*A<br>
* </p>
* <p>
* The order that matrix multiplies are performed has been carefully selected
* to minimize the number of operations.
* </p>
*
* <p>
* Before this can become a truly generic operation the submatrix specification needs
* to be made more generic.
* </p>
*/
public static void rank1UpdateMultR(DMatrixSparseCSC V, int colV, double gamma,
DMatrixSparseCSC A, DMatrixSparseCSC C,
IGrowArray gw, DGrowArray gx)
{
if (V.numRows != A.numRows)
{
throw new ArgumentException("Number of rows in V and A must match");
}
C.nz_length = 0;
C.numRows = V.numRows;
C.numCols = 0;
for (int i = 0; i < A.numCols; i++)
{
double tau = CommonOps_DSCC.dotInnerColumns(V, colV, A, i, gw, gx);
ImplCommonOps_DSCC.addColAppend(1.0, A, i, -gamma * tau, V, colV, C, gw);
}
}
/**
* Performs matrix multiplication. C = A<sup>T</sup></sup>*B
*
* @param A Matrix
* @param B Matrix
* @param C Storage for results. Data length is increased if increased if insufficient.
* @param gw (Optional) Storage for internal workspace. Can be null.
* @param gx (Optional) Storage for internal workspace. Can be null.
*/
public static void multTransA(DMatrixSparseCSC A, DMatrixSparseCSC B, DMatrixSparseCSC C,
IGrowArray gw, DGrowArray gx)
{
double[] x = TriangularSolver_DSCC.adjust(gx, A.numRows);
int[] w = TriangularSolver_DSCC.adjust(gw, A.numRows, A.numRows);
C.growMaxLength(A.nz_length + B.nz_length, false);
C.indicesSorted = true;
C.nz_length = 0;
C.col_idx[0] = 0;
int idxB0 = B.col_idx[0];
for (int bj = 1; bj <= B.numCols; bj++)
{
int idxB1 = B.col_idx[bj];
C.col_idx[bj] = C.nz_length;
if (idxB0 == idxB1)
{
continue;
}
// convert the column of B into a dense format and mark which rows are used
for (int bi = idxB0; bi < idxB1; bi++)
{
int rowB = B.nz_rows[bi];
x[rowB] = B.nz_values[bi];
w[rowB] = bj;
}
// C(colA,colB) = A(:,colA)*B(:,colB)
for (int colA = 0; colA < A.numCols; colA++)
{
int idxA0 = A.col_idx[colA];
int idxA1 = A.col_idx[colA + 1];
double sum = 0;
for (int ai = idxA0; ai < idxA1; ai++)
{
int rowA = A.nz_rows[ai];
if (w[rowA] == bj)
{
sum += x[rowA] * A.nz_values[ai];
}
}
if (sum != 0)
{
if (C.nz_length == C.nz_values.Length)
{
C.growMaxLength(C.nz_length * 2 + 1, true);
}
C.nz_values[C.nz_length] = sum;
C.nz_rows[C.nz_length++] = colA;
}
}
C.col_idx[bj] = C.nz_length;
idxB0 = idxB1;
}
}
/**
* Computes the inner product of two column vectors taken from the input matrices.
*
* <p>dot = A(:,colA)'*B(:,colB)</p>
*
* @param A Matrix
* @param colA Column in A
* @param B Matrix
* @param colB Column in B
* @return Dot product
*/
public static double dotInnerColumns(DMatrixSparseCSC A, int colA, DMatrixSparseCSC B, int colB,
IGrowArray gw, DGrowArray gx)
{
return(ImplSparseSparseMult_DSCC.dotInnerColumns(A, colA, B, colB, gw, gx));
}
public static void main(String[] args)
{
IMersenneTwister rand = new MersenneTwisterFast(234);
// easy to work with sparse format, but hard to do computations with
DMatrixSparseTriplet work = new DMatrixSparseTriplet(5, 4, 5);
work.addItem(0, 1, 1.2);
work.addItem(3, 0, 3);
work.addItem(1, 1, 22.21234);
work.addItem(2, 3, 6);
// convert into a format that's easier to perform math with
DMatrixSparseCSC Z = ConvertDMatrixStruct.convert(work, (DMatrixSparseCSC)null);
// print the matrix to standard out in two different formats
Z.print();
Console.WriteLine();
Z.printNonZero();
Console.WriteLine();
// Create a large matrix that is 5% filled
DMatrixSparseCSC A = RandomMatrices_DSCC.rectangle(ROWS, COLS, (int)(ROWS * COLS * 0.05), rand);
// large vector that is 70% filled
DMatrixSparseCSC x = RandomMatrices_DSCC.rectangle(COLS, XCOLS, (int)(XCOLS * COLS * 0.7), rand);
Console.WriteLine("Done generating random matrices");
// storage for the initial solution
DMatrixSparseCSC y = new DMatrixSparseCSC(ROWS, XCOLS, 0);
DMatrixSparseCSC z = new DMatrixSparseCSC(ROWS, XCOLS, 0);
// To demonstration how to perform sparse math let's multiply:
// y=A*x
// Optional storage is set to null so that it will declare it internally
long before = DateTimeHelper.CurrentTimeMilliseconds;
IGrowArray workA = new IGrowArray(A.numRows);
DGrowArray workB = new DGrowArray(A.numRows);
for (int i = 0; i < 100; i++)
{
CommonOps_DSCC.mult(A, x, y, workA, workB);
CommonOps_DSCC.add(1.5, y, 0.75, y, z, workA, workB);
}
long after = DateTimeHelper.CurrentTimeMilliseconds;
Console.WriteLine("norm = " + NormOps_DSCC.fastNormF(y) + " sparse time = " + (after - before) + " ms");
DMatrixRMaj Ad = ConvertDMatrixStruct.convert(A, (DMatrixRMaj)null);
DMatrixRMaj xd = ConvertDMatrixStruct.convert(x, (DMatrixRMaj)null);
DMatrixRMaj yd = new DMatrixRMaj(y.numRows, y.numCols);
DMatrixRMaj zd = new DMatrixRMaj(y.numRows, y.numCols);
before = DateTimeHelper.CurrentTimeMilliseconds;
for (int i = 0; i < 100; i++)
{
CommonOps_DDRM.mult(Ad, xd, yd);
CommonOps_DDRM.add(1.5, yd, 0.75, yd, zd);
}
after = DateTimeHelper.CurrentTimeMilliseconds;
Console.WriteLine("norm = " + NormOps_DDRM.fastNormF(yd) + " dense time = " + (after - before) + " ms");
}
