/**
* Extracts the column of A and copies it into u while computing the magnitude of the
* largest element and returning it.
*
* <pre>
* u[ (offsetU+row0+i)*2 ] = A.getReal(row0+i,col)
* u[ (offsetU+row0+i)*2 + 1] = A.getImag(row0+i,col)
* </pre>
*
* @param A Complex matrix
* @param row0 First row in A to be copied
* @param row1 Last row in A + 1 to be copied
* @param col Column in A
* @param u Output array storage
* @param offsetU first index in U
* @return magnitude of largest element
*/
public static double extractColumnAndMax(ZMatrixRMaj A,
int row0, int row1,
int col, double[] u, int offsetU)
{
int indexU = (offsetU + row0) * 2;
// find the largest value in this column
// this is used to normalize the column and mitigate overflow/underflow
double max = 0;
int indexA = A.getIndex(row0, col);
double[] h = A.data;
for (int i = row0; i < row1; i++, indexA += A.numCols * 2)
{
// copy the householder vector to an array to reduce cache misses
// big improvement on larger matrices and a relatively small performance hit on small matrices.
double realVal = u[indexU++] = h[indexA];
double imagVal = u[indexU++] = h[indexA + 1];
double magVal = realVal * realVal + imagVal * imagVal;
if (max < magVal)
{
max = magVal;
}
}
return(Math.Sqrt(max));
}
/**
* Extracts a house holder vector from the column of A and stores it in u
* @param A Complex matrix with householder vectors stored in the lower left triangle
* @param row0 first row in A (implicitly assumed to be r + i0)
* @param row1 last row + 1 in A
* @param col Column in A
* @param u Output array storage
* @param offsetU first index in U
*/
public static void extractHouseholderColumn(ZMatrixRMaj A,
int row0, int row1,
int col, double[] u, int offsetU)
{
int indexU = (row0 + offsetU) * 2;
u[indexU++] = 1;
u[indexU++] = 0;
for (int row = row0 + 1; row < row1; row++)
{
int indexA = A.getIndex(row, col);
u[indexU++] = A.data[indexA];
u[indexU++] = A.data[indexA + 1];
}
}
/**
* <p>
* Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.
* </p>
* <p>
* s<sub>i-y0 , j-x0</sub> = o<sub>ij</sub> for all y0 ≤ i < y1 and x0 ≤ j < x1 <br>
* <br>
* where 's<sub>ij</sub>' is an element in the submatrix and 'o<sub>ij</sub>' is an element in the
* original matrix.
* </p>
*
* @param src The original matrix which is to be copied. Not modified.
* @param srcX0 Start column.
* @param srcX1 Stop column+1.
* @param srcY0 Start row.
* @param srcY1 Stop row+1.
* @param dst Where the submatrix are stored. Modified.
* @param dstY0 Start row in dst.
* @param dstX0 start column in dst.
*/
public static void extract(ZMatrixRMaj src,
int srcY0, int srcY1,
int srcX0, int srcX1,
ZMatrixRMaj dst,
int dstY0, int dstX0)
{
int numRows = srcY1 - srcY0;
int stride = (srcX1 - srcX0) * 2;
for (int y = 0; y < numRows; y++)
{
int indexSrc = src.getIndex(y + srcY0, srcX0);
int indexDst = dst.getIndex(y + dstY0, dstX0);
System.Array.Copy(src.data, indexSrc, dst.data, indexDst, stride);
}
}
/**
* <p>
* Extracts the diagonal elements 'src' write it to the 'dst' vector. 'dst'
* can either be a row or column vector.
* <p>
*
* @param src Matrix whose diagonal elements are being extracted. Not modified.
* @param dst A vector the results will be written into. Modified.
*/
public static void extractDiag(ZMatrixRMaj src, ZMatrixRMaj dst)
{
int N = Math.Min(src.numRows, src.numCols);
// reshape if it's not the right size
if (!MatrixFeatures_ZDRM.isVector(dst) || dst.numCols * dst.numCols != N)
{
dst.reshape(N, 1);
}
for (int i = 0; i < N; i++)
{
int index = src.getIndex(i, i);
dst.data[i * 2] = src.data[index];
dst.data[i * 2 + 1] = src.data[index + 1];
}
}
public override /**/ double quality()
{
return(SpecializedOps_ZDRM.qualityTriangular(R));
}
/**
* Solves for X using the QR decomposition.
*
* @param B A matrix that is n by m. Not modified.
* @param X An n by m matrix where the solution is written to. Modified.
*/
//@Override
public override void solve(ZMatrixRMaj B, ZMatrixRMaj X)
{
if (X.numRows != numCols)
{
throw new ArgumentException("Unexpected dimensions for X");
}
else if (B.numRows != numRows || B.numCols != X.numCols)
{
throw new ArgumentException("Unexpected dimensions for B");
}
int BnumCols = B.numCols;
Y.reshape(numRows, 1);
Z.reshape(numRows, 1);
// solve each column one by one
for (int colB = 0; colB < BnumCols; colB++)
{
// make a copy of this column in the vector
for (int i = 0; i < numRows; i++)
{
int indexB = B.getIndex(i, colB);
Y.data[i * 2] = B.data[indexB];
Y.data[i * 2 + 1] = B.data[indexB + 1];
}
// Solve Qa=b
// a = Q'b
CommonOps_ZDRM.mult(Qt, Y, Z);
// solve for Rx = b using the standard upper triangular solver
TriangularSolver_ZDRM.solveU(R.data, Z.data, numCols);
// save the results
for (int i = 0; i < numCols; i++)
{
X.set(i, colB, Z.data[i * 2], Z.data[i * 2 + 1]);
}
}
}
/**
* Finds the magnitude of the largest element in the row
* @param A Complex matrix
* @param row Row in A
* @param col0 First column in A to be copied
* @param col1 Last column in A + 1 to be copied
* @return magnitude of largest element
*/
public static double computeRowMax(ZMatrixRMaj A,
int row, int col0, int col1)
{
double max = 0;
int indexA = A.getIndex(row, col0);
double[] h = A.data;
for (int i = col0; i < col1; i++)
{
double realVal = h[indexA++];
double imagVal = h[indexA++];
double magVal = realVal * realVal + imagVal * imagVal;
if (max < magVal)
{
max = magVal;
}
}
return(Math.Sqrt(max));
}
/**
* Converts the columns in a matrix into a set of vectors.
*
* @param A Matrix. Not modified.
* @param v Optional storage for columns.
* @return An array of vectors.
*/
public static ZMatrixRMaj[] columnsToVector(ZMatrixRMaj A, ZMatrixRMaj[] v)
{
ZMatrixRMaj[] ret;
if (v == null || v.Count() < A.numCols)
{
ret = new ZMatrixRMaj[A.numCols];
}
else
{
ret = v;
}
for (int i = 0; i < ret.Count(); i++)
{
if (ret[i] == null)
{
ret[i] = new ZMatrixRMaj(A.numRows, 1);
}
else
{
ret[i].reshape(A.numRows, 1);
}
ZMatrixRMaj u = ret[i];
int indexU = 0;
for (int j = 0; j < A.numRows; j++)
{
int indexA = A.getIndex(j, i);
u.data[indexU++] = A.data[indexA++];
u.data[indexU++] = A.data[indexA];
}
}
return(ret);
}