/** * <p> * Performs a matrix multiplication on {@link DMatrixRBlock} submatrices.<br> * <br> * c = c + a * b <br> * <br> * </p> * * <p> * It is assumed that all submatrices start at the beginning of a block and end at the end of a block. * </p> * * @param blockLength Size of the blocks in the submatrix. * @param A A submatrix. Not modified. * @param B A submatrix. Not modified. * @param C Result of the operation. Modified, */ public static void multPlus(int blockLength, DSubmatrixD1 A, DSubmatrixD1 B, DSubmatrixD1 C) { // checkInput( blockLength,A,B,C); for (int i = A.row0; i < A.row1; i += blockLength) { int heightA = Math.Min(blockLength, A.row1 - i); for (int j = B.col0; j < B.col1; j += blockLength) { int widthB = Math.Min(blockLength, B.col1 - j); int indexC = (i - A.row0 + C.row0) * C.original.numCols + (j - B.col0 + C.col0) * heightA; for (int k = A.col0; k < A.col1; k += blockLength) { int widthA = Math.Min(blockLength, A.col1 - k); int indexA = i * A.original.numCols + k * heightA; int indexB = (k - A.col0 + B.row0) * B.original.numCols + j * widthA; InnerMultiplication_DDRB.blockMultPlus(A.original.data, B.original.data, C.original.data, indexA, indexB, indexC, heightA, widthA, widthB); } } } }
/** * <p> * Performs a matrix multiplication with a transpose on {@link DMatrixRBlock} submatrices.<br> * <br> * c = a * b <sup>T</sup> <br> * <br> * </p> * * <p> * It is assumed that all submatrices start at the beginning of a block and end at the end of a block. * </p> * * @param blockLength Length of the blocks in the submatrix. * @param A A submatrix. Not modified. * @param B A submatrix. Not modified. * @param C Result of the operation. Modified, */ public static void multTransB(int blockLength, DSubmatrixD1 A, DSubmatrixD1 B, DSubmatrixD1 C) { for (int i = A.row0; i < A.row1; i += blockLength) { int heightA = Math.Min(blockLength, A.row1 - i); for (int j = B.row0; j < B.row1; j += blockLength) { int widthC = Math.Min(blockLength, B.row1 - j); int indexC = (i - A.row0 + C.row0) * C.original.numCols + (j - B.row0 + C.col0) * heightA; for (int k = A.col0; k < A.col1; k += blockLength) { int widthA = Math.Min(blockLength, A.col1 - k); int indexA = i * A.original.numCols + k * heightA; int indexB = j * B.original.numCols + (k - A.col0 + B.col0) * widthC; if (k == A.col0) { InnerMultiplication_DDRB.blockMultSetTransB(A.original.data, B.original.data, C.original.data, indexA, indexB, indexC, heightA, widthA, widthC); } else { InnerMultiplication_DDRB.blockMultPlusTransB(A.original.data, B.original.data, C.original.data, indexA, indexB, indexC, heightA, widthA, widthC); } } } } }
/** * Inverts an upper or lower triangular block submatrix. * * @param blockLength * @param upper Is it upper or lower triangular. * @param T Triangular matrix that is to be inverted. Overwritten with solution. Modified. * @param temp Work space variable that is size blockLength*blockLength. */ public static void invert(int blockLength, bool upper, DSubmatrixD1 T, double[] temp) { if (upper) { throw new ArgumentException("Upper triangular matrices not supported yet"); } if (temp.Length < blockLength * blockLength) { throw new ArgumentException("Temp must be at least blockLength*blockLength long."); } int M = T.row1 - T.row0; double[] dataT = T.original.data; int offsetT = T.row0 * T.original.numCols + M * T.col0; for (int i = 0; i < M; i += blockLength) { int heightT = Math.Min(T.row1 - (i + T.row0), blockLength); int indexII = offsetT + T.original.numCols * (i + T.row0) + heightT * (i + T.col0); for (int j = 0; j < i; j += blockLength) { int widthX = Math.Min(T.col1 - (j + T.col0), blockLength); for (int w = 0; w < temp.Length; w++) { temp[w] = 0; } for (int k = j; k < i; k += blockLength) { int widthT = Math.Min(T.col1 - (k + T.col0), blockLength); int indL = offsetT + T.original.numCols * (i + T.row0) + heightT * (k + T.col0); int indX = offsetT + T.original.numCols * (k + T.row0) + widthT * (j + T.col0); InnerMultiplication_DDRB.blockMultMinus(dataT, dataT, temp, indL, indX, 0, heightT, widthT, widthX); } int indexX = offsetT + T.original.numCols * (i + T.row0) + heightT * (j + T.col0); InnerTriangularSolver_DDRB.solveL(dataT, temp, heightT, widthX, heightT, indexII, 0); Array.Copy(temp, 0, dataT, indexX, widthX * heightT); } InnerTriangularSolver_DDRB.invertLower(dataT, heightT, indexII); } }
/** * <p> * Performs:<br> * <br> * A = A + α B <sup>T</sup>B * </p> * * @param blockLength Size of the block in the block matrix. * @param alpha scaling factor for right hand side. * @param A Block aligned submatrix. * @param B Block aligned submatrix. */ public static void rankNUpdate(int blockLength, double alpha, DSubmatrixD1 A, DSubmatrixD1 B) { int heightB = B.row1 - B.row0; if (heightB > blockLength) { throw new ArgumentException("Height of B cannot be greater than the block length"); } int N = B.col1 - B.col0; if (A.col1 - A.col0 != N) { throw new ArgumentException("A does not have the expected number of columns based on B's width"); } if (A.row1 - A.row0 != N) { throw new ArgumentException("A does not have the expected number of rows based on B's width"); } for (int i = B.col0; i < B.col1; i += blockLength) { int indexB_i = B.row0 * B.original.numCols + i * heightB; int widthB_i = Math.Min(blockLength, B.col1 - i); int rowA = i - B.col0 + A.row0; int heightA = Math.Min(blockLength, A.row1 - rowA); for (int j = B.col0; j < B.col1; j += blockLength) { int widthB_j = Math.Min(blockLength, B.col1 - j); int indexA = rowA * A.original.numCols + (j - B.col0 + A.col0) * heightA; int indexB_j = B.row0 * B.original.numCols + j * heightB; InnerMultiplication_DDRB.blockMultPlusTransA(alpha, B.original.data, B.original.data, A.original.data, indexB_i, indexB_j, indexA, heightB, widthB_i, widthB_j); } } }