科学计算科学计算 (6).pdf

1.5 1.5 MMatrix atrix E Elements lements ReferenceReferenceThe methods of referring to matrix elementsUsing the colon expression to get submatricesUsing empty matrices to delete matrix elementsChange the shape of a matrix A(3,2)=2001.1.The Methods of Referring to Matrix ElementsThe Methods of Referring to Matrix ElementsA(3,2)represents the element in the 3rd row and 2nd column of matrix A.(1)To Refer to Elements of a Matrix by Subscripts A=1,2,3;4,5,6;A(4,5)=10A=1 2 3 0 04 5 6 0 00 0 0 0 00 0 0 0 10Note:if the given row subscript or column subscript is greater than the number of rows and columns of the original matrix,MATLAB will automatically expand the original matrix,and set the expanded matrix elements without assignment to 0.(2)Reference by IndexIn MATLAB,matrix elements are stored by the order of columns.That is,the elements of the first column are stored firstly,and then the elements ofthe second column,until those of the last column are stored.The index of matrix elements is the order in which matrix elements arearranged in the memory.A=1,2,3;4,5,6A=1 2 34 5 6 A(3)ans=2The index actually corresponds to the subscript.Take matrix A with m rows and n columns as an example,the index of matrix element A(i,j)is(j-1)m+i.D=sub2ind(S,I,J)A vector composed of the number of rows and columnsRow subscript of the matrix to be converted Column subscript of transformation matrixIndexThe sub2ind function converts row and column subscripts of specified elements in a matrix into stored index.A=1:3;4:6A=1 2 34 5 6 D=sub2ind(size(A),1,2;2,2,1,1;3,2)D=1 26 4An example of the sub2ind function.I,J=ind2sub(S,D)A vector composed of the number of rows and columnsindexRow subscriptColumn subscriptThe ind2sub function is used to convert the index of matrix elements into corresponding subscripts.I,J=ind2sub(3,3,1,3,5)I=1 3 2J=1 1 2An example of the ind2sub function.2.Using the Colon Expression to Get a S2.Using the Colon Expression to Get a SubmatrixubmatrixA submatrix refers to a matrix composed of some elements in a matrix.A(i,:)All the elements of row i in matrix A.A(:,j)All the elements of column j in matrix A.A(i:i+m,k:k+m)All the elements from row i to row i+m and from column k tocolumn k+m in matrix A.A(i:i+m,:)All the elements from row i to row i+m in matrix A.A=1,2,3,4,5;6,7,8,9,10;11,12,13,14,15A=1 2 3 4 56 7 8 9 1011 12 13 14 15 A(1:2,:)ans=1 2 3 4 56 7 8 9 10 A(2:3,1:2:5)ans=6 8 1011 13 15 A=1,2,3,4,5;6,7,8,9,10;11,12,13,14,15;16,17,18,19,20;A(end,:)ans=16 17 18 19 20 A(1,4,3:end)ans=3 4 518 19 20The end operator indicates the subscript of the last element of a dimension.x=x=3.3.UsUse e an Ean Empty mpty MMatrix to atrix to D Delete elete E Elements of lements of a Ma MatrixatrixAn empty matrix is a matrix with no elements.The x is an empty matrix.A=1,2,3,0,0;7,0,9,2,6;1,4,-1,1,8A=1 2 3 0 07 0 9 2 61 4 -1 1 8 A(:,2,4)=A=1 3 07 9 61 -1 84.4.Change the Change the S Shape of hape of a a MMatrixatrixreshape(A,m,n):rearranges matrix A into a two dimensional matrix with m rows and n columns when the total elements of the matrix remain unchanged.Note:the reshape function only changes the number of rows and columns of the original matrix,but it does not change the number of matrix elements and storing order of the original matrix.x=23,45,65,34,65,34,98,45,78,65,43,76;y=reshape(x,3,4)y=23 34 98 6545 65 45 4365 34 78 76 A=-45,65,71;27,35,91A=-45 65 7127 35 91 B=A(:)B=-452765357191Note:A(:)is equivalent to reshape(A,6,1).A(:)stack elements of each column in matrix A to finally form a column vector.