Constructs the slope constraints
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Date: Nov. 19, 2008, ver01
By: Hooman Askari
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Inputs
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blocksOnTopCellArray:
numBlocks:
numOfPeriods:
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outputs
A_slope:
b_Uslope:
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Pseudo Code
--------------------------------------------------------------------------0001 % Constructs the slope constraints 0002 %-------------------------------------------------------------------------- 0003 % Date: Nov. 19, 2008, ver01 0004 % By: Hooman Askari 0005 %-------------------------------------------------------------------------- 0006 %Inputs 0007 %-------------------------------------------------------------------------- 0008 % blocksOnTopCellArray: 0009 % numBlocks: 0010 % numOfPeriods: 0011 % 0012 %-------------------------------------------------------------------------- 0013 % outputs 0014 % A_slope: 0015 % b_Uslope: 0016 % 0017 %-------------------------------------------------------------------------- 0018 % 0019 %-------------------------------------------------------------------------- 0020 % Pseudo Code 0021 % 0022 %-------------------------------------------------------------------------- 0023 function [A_slope b_Uslope] = slope_constraints( blocksOnTopCellArray,... 0024 numBlocks,... 0025 numOfPeriods) 0026 yA_slope = cell(numBlocks,1); 0027 xA_slope = cell(numBlocks,1); 0028 yA=[]; save yA yA; 0029 xA=[]; save xA xA; 0030 0031 % a blank template to preallocate memory space to the yVector 0032 % and xVector 0033 blankTemp = sparse(1, numBlocks); 0034 index = 0; 0035 0036 for iBlocks = 1 : numBlocks 0037 0038 if length(find(blocksOnTopCellArray{iBlocks})) ~= 0 0039 0040 % blocksOnTop is a (1*numOfBlocksOnTop) matrix holding the 0041 % indices of the blocks on top of the current block iBlocks 0042 [row col blocksOnTop] = find(blocksOnTopCellArray{iBlocks}); 0043 0044 for j = 1:length(blocksOnTop) 0045 0046 % one constraint per block per period. 0047 % the number of constraints for each block is equal to the 0048 % number of periods 0049 0050 % create the diagonal matrix, see documentation 0051 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0052 xVec = blankTemp; 0053 xVec(1, iBlocks)= 1; 0054 0055 % create the diagMatrix 0056 A = cell(1, numOfPeriods); 0057 [A{:}] = deal(xVec); 0058 xMatrix = blkdiag(A{:}); 0059 0060 % create the lower triangular matrix see documentation 0061 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0062 yVec = blankTemp; 0063 yVec(1, blocksOnTop(j))= -1; 0064 0065 % the case that all the blocks on top are added 0066 % need to re-adjust the for loop, omit the loop 0067 % for j = 1:length(blocksOnTop) 0068 0069 % yVec(1, blocksOnTop(1:end))= -1; 0070 0071 yMatrixCell = cell(numOfPeriods,numOfPeriods); 0072 [yMatrixCell{:}] = deal(blankTemp); 0073 0074 for i = 1:numOfPeriods 0075 [yMatrixCell{i,1:(i)}] = deal(yVec); 0076 end 0077 0078 yMatrix = cell2mat(yMatrixCell); 0079 yMatrix = sparse(yMatrix); 0080 0081 index = index + 1; 0082 yA_slope{index,1}= deal(yMatrix); 0083 xA_slope{index,1}= deal(xMatrix); 0084 0085 % the number controls how often the yA and xA array are 0086 % supposed to be written into file 0087 0088 if index >= 2000 0089 load yA; load xA; 0090 yA =[yA; cell2mat(yA_slope)]; 0091 xA =[xA; cell2mat(xA_slope)]; 0092 save yA yA; save xA xA; 0093 clear yA yA_slope xA xA_slope; 0094 index = 0; 0095 end 0096 0097 clear xMatrix yMatrix yVec xVec; 0098 0099 end % for j = 1:length(blocksOnTop) 0100 0101 iBlocks; 0102 0103 end % if numOfBlocksOnTop(iBlocks) ~= 0 0104 0105 end % end for iBlocks 0106 0107 % check to see if the size of the matirx is greater than 1 0108 0109 % the mulitplier vector in the constraints matrix have different sizes 0110 % and units. (some are tonnage some are grade....). It is necessary to 0111 % transform the constraints matrix in a way that it is unit less to be 0112 % solved by the MIP code. 0113 0114 % divide each row vector by its norm [A(i,:)* A(i,:)']^1/2 0115 % A_slope2NormVector(m,1) is vertical vector holding the respective 0116 % norm of each row of the A_slope2 matrix 0117 0118 % if there is any yA-slope not written to yA. it is going to be taken 0119 % care of here 0120 load yA; load xA; 0121 yA =[yA; cell2mat(yA_slope)]; 0122 xA =[xA; cell2mat(xA_slope)]; 0123 save yA yA; save xA xA; 0124 %xA = full(xA); 0125 %yA = full(yA); 0126 clear yA xA yA_slope xA_slope; 0127 0128 load yA; load xA 0129 [m n] = size(yA); 0130 b_Uslope = sparse(m,1); 0131 0132 % A_slope = [yA xA sparse(m, 2*n)]; 0133 A_slope = [xA sparse(m, numBlocks*numOfPeriods)... 0134 sparse(m, numBlocks*numOfPeriods) yA... 0135 sparse(m, numOfPeriods) sparse(m, numOfPeriods)... 0136 sparse(m, numOfPeriods) sparse(m, numOfPeriods)]; 0137 0138 save A_slope A_slope 0139 end