public virtual FMatrixRBlock getQ(FMatrixRBlock Q, bool transposed) { Q = QRDecompositionHouseholder_FDRB.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); FSubmatrixD1 subQ = new FSubmatrixD1(Q); FSubmatrixD1 subU = new FSubmatrixD1(A); FSubmatrixD1 subW = new FSubmatrixD1(V); FSubmatrixD1 tmp = new FSubmatrixD1(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) { tmp.row0 = i; tmp.row1 = A.numCols; tmp.col0 = 0; tmp.col1 = blockSize; } else { tmp.col0 = i; tmp.row1 = blockSize; } tmp.original.reshape(tmp.row1, tmp.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_FDRB.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_FDRB.multTransB(A.blockLength, subQ, subU, tmp); } else { MatrixMult_FDRB.mult(A.blockLength, subU, subQ, tmp); } // Q(i+1) = Q(i) + W*F if (transposed) { MatrixMult_FDRB.multPlus(A.blockLength, tmp, subW, subQ); } else { MatrixMult_FDRB.multPlusTransA(A.blockLength, subW, tmp, subQ); } replaceZeros(subU); } return(Q); }