/**
* <p>
* Performs the following operation:<br>
* <br>
* B = A + αI
* <p>
*
* @param A A square matrix. Not modified.
* @param B A square matrix that the results are saved to. Modified.
* @param alpha Scaling factor for the identity matrix.
*/
public static void addIdentity(DMatrix1Row A, DMatrix1Row B, double alpha)
{
if (A.numCols != A.numRows)
{
throw new ArgumentException("A must be square");
}
if (B.numCols != A.numCols || B.numRows != A.numRows)
{
throw new ArgumentException("B must be the same shape as A");
}
int n = A.numCols;
int index = 0;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++, index++)
{
if (i == j)
{
B.set(index, A.get(index) + alpha);
}
else
{
B.set(index, A.get(index));
}
}
}
}
/**
* An alternative implementation of {@link #multTransA_small} that performs well on large
* matrices. There is a relative performance hit when used on small matrices.
*
* @param A A matrix that is m by n. Not modified.
* @param B A Vector that has length m. Not modified.
* @param C A column vector that has length n. Modified.
*/
public static void multTransA_reorder(DMatrix1Row A, DMatrixD1 B, DMatrixD1 C)
{
if (C.numCols != 1)
{
throw new MatrixDimensionException("C is not a column vector");
}
else if (C.numRows != A.numCols)
{
throw new MatrixDimensionException("C is not the expected length");
}
if (B.numRows == 1)
{
if (A.numRows != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numRows != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
if (A.numRows == 0)
{
CommonOps_DDRM.fill(C, 0);
return;
}
double B_val = B.get(0);
for (int i = 0; i < A.numCols; i++)
{
C.set(i, A.get(i) * B_val);
}
int indexA = A.numCols;
for (int i = 1; i < A.numRows; i++)
{
B_val = B.get(i);
for (int j = 0; j < A.numCols; j++)
{
C.plus(j, A.get(indexA++) * B_val);
}
}
}
/**
* <p>
* Performs a matrix vector multiply.<br>
* <br>
* c = A * b <br>
* and<br>
* c = A * b<sup>T</sup> <br>
* <br>
* c<sub>i</sub> = Sum{ j=1:n, a<sub>ij</sub> * b<sub>j</sub>}<br>
* <br>
* where A is a matrix, b is a column or transposed row vector, and c is a column vector.
* </p>
*
* @param A A matrix that is m by n. Not modified.
* @param B A vector that has length n. Not modified.
* @param C A column vector that has length m. Modified.
*/
public static void mult(DMatrix1Row A, DMatrixD1 B, DMatrixD1 C)
{
if (C.numCols != 1)
{
throw new MatrixDimensionException("C is not a column vector");
}
else if (C.numRows != A.numRows)
{
throw new MatrixDimensionException("C is not the expected length");
}
if (B.numRows == 1)
{
if (A.numCols != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numCols != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
if (A.numCols == 0)
{
CommonOps_DDRM.fill(C, 0);
return;
}
int indexA = 0;
int cIndex = 0;
double b0 = B.get(0);
for (int i = 0; i < A.numRows; i++)
{
double total = A.get(indexA++) * b0;
for (int j = 1; j < A.numCols; j++)
{
total += A.get(indexA++) * B.get(j);
}
C.set(cIndex++, total);
}
}
/**
* <p>
* Element wise p-norm:<br>
* <br>
* norm = {∑<sub>i=1:m</sub> ∑<sub>j=1:n</sub> { |a<sub>ij</sub>|<sup>p</sup>}}<sup>1/p</sup>
* </p>
*
* <p>
* This is not the same as the induced p-norm used on matrices, but is the same as the vector p-norm.
* </p>
*
* @param A Matrix. Not modified.
* @param p p value.
* @return The norm's value.
*/
public static double elementP(DMatrix1Row A, double p)
{
if (p == 1)
{
return(CommonOps_DDRM.elementSumAbs(A));
}
if (p == 2)
{
return(normF(A));
}
else
{
double max = CommonOps_DDRM.elementMaxAbs(A);
if (max == 0.0)
{
return(0.0);
}
double total = 0;
int size = A.getNumElements();
for (int i = 0; i < size; i++)
{
double a = A.get(i) / max;
total += Math.Pow(Math.Abs(a), p);
}
return(max * Math.Pow(total, 1.0 / p));
}
}
/**
* <p>
* Extracts a row or column vector from matrix A. The first element in the matrix is at element (rowA,colA).
* The next 'length' elements are extracted along a row or column. The results are put into vector 'v'
* start at its element v0.
* </p>
*
* @param A Matrix that the vector is being extracted from. Not modified.
* @param rowA Row of the first element that is extracted.
* @param colA Column of the first element that is extracted.
* @param length Length of the extracted vector.
* @param row If true a row vector is extracted, otherwise a column vector is extracted.
* @param offsetV First element in 'v' where the results are extracted to.
* @param v Vector where the results are written to. Modified.
*/
public static void subvector(DMatrix1Row A, int rowA, int colA, int length, bool row, int offsetV, DMatrix1Row v)
{
if (row)
{
for (int i = 0; i < length; i++)
{
v.set(offsetV + i, A.get(rowA, colA + i));
}
}
else
{
for (int i = 0; i < length; i++)
{
v.set(offsetV + i, A.get(rowA + i, colA));
}
}
}
/**
* <p>
* Performs a matrix vector multiply.<br>
* <br>
* C = C + A * B <br>
* or<br>
* C = C + A * B<sup>T</sup> <br>
* <br>
* c<sub>i</sub> = Sum{ j=1:n, c<sub>i</sub> + a<sub>ij</sub> * b<sub>j</sub>}<br>
* <br>
* where A is a matrix, B is a column or transposed row vector, and C is a column vector.
* </p>
*
* @param A A matrix that is m by n. Not modified.
* @param B A vector that has length n. Not modified.
* @param C A column vector that has length m. Modified.
*/
public static void multAdd(DMatrix1Row A, DMatrixD1 B, DMatrixD1 C)
{
if (B.numRows == 1)
{
if (A.numCols != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numCols != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
if (A.numRows != C.NumElements)
{
throw new MatrixDimensionException("C is not compatible with A");
}
if (A.numCols == 0)
{
return;
}
int indexA = 0;
int cIndex = 0;
for (int i = 0; i < A.numRows; i++)
{
double total = A.get(indexA++) * B.get(0);
for (int j = 1; j < A.numCols; j++)
{
total += A.get(indexA++) * B.get(j);
}
C.plus(cIndex++, total);
}
}
public static void setSubMatrix(DMatrix1Row src, DMatrix1Row dst,
int srcRow, int srcCol, int dstRow, int dstCol,
int numSubRows, int numSubCols)
{
for (int i = 0; i < numSubRows; i++)
{
for (int j = 0; j < numSubCols; j++)
{
double val = src.get(i + srcRow, j + srcCol);
dst.set(i + dstRow, j + dstCol, val);
}
}
}
/**
* <p>
* Performs a matrix vector multiply.<br>
* <br>
* C = C + A<sup>T</sup> * B <br>
* or<br>
* C = C<sup>T</sup> + A<sup>T</sup> * B<sup>T</sup> <br>
* <br>
* c<sub>i</sub> = Sum{ j=1:n, c<sub>i</sub> + a<sub>ji</sub> * b<sub>j</sub>}<br>
* <br>
* where A is a matrix, B is a column or transposed row vector, and C is a column vector.
* </p>
* <p>
* This implementation is optimal for small matrices. There is a huge performance hit when
* used on large matrices due to CPU cache issues.
* </p>
*
* @param A A matrix that is m by n. Not modified.
* @param B A vector that has length m. Not modified.
* @param C A column vector that has length n. Modified.
*/
public static void multAddTransA_small(DMatrix1Row A, DMatrixD1 B, DMatrixD1 C)
{
if (C.numCols != 1)
{
throw new MatrixDimensionException("C is not a column vector");
}
else if (C.numRows != A.numCols)
{
throw new MatrixDimensionException("C is not the expected length");
}
if (B.numRows == 1)
{
if (A.numRows != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numRows != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
int cIndex = 0;
for (int i = 0; i < A.numCols; i++)
{
double total = 0.0;
int indexA = i;
for (int j = 0; j < A.numRows; j++)
{
total += A.get(indexA) * B.get(j);
indexA += A.numCols;
}
C.plus(cIndex++, total);
}
}
private void createMinor(DMatrix1Row mat)
{
int w = minWidth - 1;
int firstRow = (width - w) * width;
for (int i = 0; i < numOpen; i++)
{
int col = open[i];
int srcIndex = firstRow + col;
int dstIndex = i;
for (int j = 0; j < w; j++)
{
tempMat.set(dstIndex, mat.get(srcIndex));
dstIndex += w;
srcIndex += width;
}
}
}
/**
* <p>
* Performs a matrix vector multiply.<br>
* <br>
* C = A<sup>T</sup> * B <br>
* where B is a column vector.<br>
* or<br>
* C = A<sup>T</sup> * B<sup>T</sup> <br>
* where B is a row vector. <br>
* <br>
* c<sub>i</sub> = Sum{ j=1:n, a<sub>ji</sub> * b<sub>j</sub>}<br>
* <br>
* where A is a matrix, B is a column or transposed row vector, and C is a column vector.
* </p>
* <p>
* This implementation is optimal for small matrices. There is a huge performance hit when
* used on large matrices due to CPU cache issues.
* </p>
*
* @param A A matrix that is m by n. Not modified.
* @param B A that has length m and is a column. Not modified.
* @param C A column vector that has length n. Modified.
*/
public static void multTransA_small(DMatrix1Row A, DMatrixD1 B, DMatrixD1 C)
{
if (B.numRows == 1)
{
if (A.numRows != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numRows != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
C.reshape(A.numCols, 1);
int cIndex = 0;
for (int i = 0; i < A.numCols; i++)
{
double total = 0.0;
int indexA = i;
for (int j = 0; j < A.numRows; j++)
{
total += A.get(indexA) * B.get(j);
indexA += A.numCols;
}
C.set(cIndex++, total);
}
}
/**
* An alternative implementation of {@link #multAddTransA_small} that performs well on large
* matrices. There is a relative performance hit when used on small matrices.
*
* @param A A matrix that is m by n. Not modified.
* @param B A vector that has length m. Not modified.
* @param C A column vector that has length n. Modified.
*/
public static void multAddTransA_reorder(DMatrix1Row A, DMatrixD1 B, DMatrixD1 C)
{
if (B.numRows == 1)
{
if (A.numRows != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numRows != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
if (A.numCols != C.NumElements)
{
throw new MatrixDimensionException("C is not compatible with A");
}
int indexA = 0;
for (int j = 0; j < A.numRows; j++)
{
double B_val = B.get(j);
for (int i = 0; i < A.numCols; i++)
{
C.plus(i, A.get(indexA++) * B_val);
}
}
}
/**
* Computes the determinant for the specified matrix. It must be square and have
* the same width and height as what was specified in the constructor.
*
* @param mat The matrix whose determinant is to be computed.
* @return The determinant.
*/
public double compute(DMatrix1Row mat)
{
if (width != mat.numCols || width != mat.numRows)
{
throw new InvalidOperationException("Unexpected matrix dimension");
}
// make sure everything is in the proper state before it starts
initStructures();
// Array.Copy(mat.data,0,minorMatrix[0],0,mat.data.Length);
int level = 0;
while (true)
{
int levelWidth = width - level;
int levelIndex = levelIndexes[level];
if (levelIndex == levelWidth)
{
if (level == 0)
{
return(levelResults[0]);
}
int prevLevelIndex = levelIndexes[level - 1]++;
double val = mat.get((level - 1) * width + levelRemoved[level - 1]);
if (prevLevelIndex % 2 == 0)
{
levelResults[level - 1] += val * levelResults[level];
}
else
{
levelResults[level - 1] -= val * levelResults[level];
}
putIntoOpen(level - 1);
levelResults[level] = 0;
levelIndexes[level] = 0;
level--;
}
else
{
int excluded = openRemove(levelIndex);
levelRemoved[level] = excluded;
if (levelWidth == minWidth)
{
createMinor(mat);
double subresult = mat.get(level * width + levelRemoved[level]);
subresult *= UnrolledDeterminantFromMinor_DDRM.det(tempMat);
if (levelIndex % 2 == 0)
{
levelResults[level] += subresult;
}
else
{
levelResults[level] -= subresult;
}
// put it back into the list
putIntoOpen(level);
levelIndexes[level]++;
}
else
{
level++;
}
}
}
}