/** * Specialized version of applyQ() that allows the zeros in an identity matrix * to be taken advantage of depending on if isIdentity is true or not. * * @param B * @param isIdentity If B is an identity matrix. */ public void applyQ(DMatrixRBlock B, bool isIdentity) { int minDimen = Math.Min(dataA.numCols, dataA.numRows); DSubmatrixD1 subB = new DSubmatrixD1(B); W.col0 = W.row0 = 0; Y.row1 = W.row1 = dataA.numRows; WTA.row0 = WTA.col0 = 0; int start = minDimen - minDimen % blockLength; if (start == minDimen) { start -= blockLength; } if (start < 0) { start = 0; } // (Q1^T * (Q2^T * (Q3^t * A))) for (int i = start; i >= 0; i -= blockLength) { Y.col0 = i; Y.col1 = Math.Min(Y.col0 + blockLength, dataA.numCols); Y.row0 = i; if (isIdentity) { subB.col0 = i; } subB.row0 = i; setW(); WTA.row1 = Y.col1 - Y.col0; WTA.col1 = subB.col1 - subB.col0; WTA.original.reshape(WTA.row1, WTA.col1, false); // Compute W matrix from reflectors stored in Y if (!saveW) { BlockHouseHolder_DDRB.computeW_Column(blockLength, Y, W, temp, gammas, Y.col0); } // Apply the Qi to Q BlockHouseHolder_DDRB.multTransA_vecCol(blockLength, Y, subB, WTA); MatrixMult_DDRB.multPlus(blockLength, W, WTA, subB); } }
public virtual DMatrixRBlock getQ(DMatrixRBlock Q, bool transposed) { Q = QRDecompositionHouseholder_DDRB.initializeQ(Q, A.numRows, A.numCols, A.blockLength, false); int height = Math.Min(A.blockLength, A.numRows); V.reshape(height, A.numCols, false); this.tmp.reshape(height, A.numCols, false); DSubmatrixD1 subQ = new DSubmatrixD1(Q); DSubmatrixD1 subU = new DSubmatrixD1(A); DSubmatrixD1 subW = new DSubmatrixD1(V); DSubmatrixD1 temp = new DSubmatrixD1(this.tmp); int N = A.numRows; int start = N - N % A.blockLength; if (start == N) { start -= A.blockLength; } if (start < 0) { start = 0; } // (Q1^T * (Q2^T * (Q3^t * A))) for (int i = start; i >= 0; i -= A.blockLength) { int blockSize = Math.Min(A.blockLength, N - i); subW.col0 = i; subW.row1 = blockSize; subW.original.reshape(subW.row1, subW.col1, false); if (transposed) { temp.row0 = i; temp.row1 = A.numCols; temp.col0 = 0; temp.col1 = blockSize; } else { temp.col0 = i; temp.row1 = blockSize; } temp.original.reshape(temp.row1, temp.col1, false); subU.col0 = i; subU.row0 = i; subU.row1 = subU.row0 + blockSize; // zeros and ones are saved and overwritten in U so that standard matrix multiplication can be used copyZeros(subU); // compute W for Q(i) = ( I + W*Y^T) TridiagonalHelper_DDRB.computeW_row(A.blockLength, subU, subW, gammas, i); subQ.col0 = i; subQ.row0 = i; // Apply the Qi to Q // Qi = I + W*U^T // Note that U and V are really row vectors. but standard notation assumed they are column vectors. // which is why the functions called don't match the math above // (I + W*U^T)*Q // F=U^T*Q(i) if (transposed) { MatrixMult_DDRB.multTransB(A.blockLength, subQ, subU, temp); } else { MatrixMult_DDRB.mult(A.blockLength, subU, subQ, temp); } // Q(i+1) = Q(i) + W*F if (transposed) { MatrixMult_DDRB.multPlus(A.blockLength, temp, subW, subQ); } else { MatrixMult_DDRB.multPlusTransA(A.blockLength, subW, temp, subQ); } replaceZeros(subU); } return(Q); }