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Maximizing the area of a polygon using tokens based input - using a 'multimap' userfunction Description Demonstrates how to solve a nonlinear problem in C Further explanation of this example: 'Xpress NonLinear Reference Manual'
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Polygon_userfunc_multimap.c /*********************************************************************** Xpress Optimizer Examples ========================= file Polygon_multimap.c `````````````````````````` Maximize the area of polygon of N vertices and diameter of 1 The position of vertices is indicated as (rho,theta) coordinates where rho denotes the distance to the base point (vertex with number N) and theta the angle from the x-axis. The nonlinear expressions are described text based input. (c) 2021-2024 Fair Isaac Corporation *********************************************************************** Polygon example: maximise the area of an N sided polygon *** Demonstrating using a multi map (R^k->R^l) userfunction *** Variables: rho : 0..N-1 ! Distance of vertex from the base point theta : 0..N-1 ! Angle from x-axis Objective: (sum (i in 1..N-2) (rho(i)*rho(i-1)*sin(theta(i)-theta(i-1)))) * 0.5 Constraints: Vertices in increasing degree order: theta(i) >= theta(i-1) +.01 : i = 1..N-2 Boundary conditions: theta(N-1) <= Pi 0.1 <= rho(i) <= 1 : i = 0..N-2 Third side of all triangles <= 1 rho(i)^2 + rho(j)^2 - rho(i)*rho(j)*2*cos(theta(j)-theta(i)) <= 1 : i in 0..N-3, j in i..N-2 ***********************************************************************/ #include <stdio.h> #include <stdlib.h> #include <string.h> #include <math.h> #include "xprs.h" #define PI 3.14159 /* Perform the Xpress specified function call and check its return value. */ #define CHECK_XPRSCALL(call) \ do { \ int result_ = call; \ if ( result_ != 0 ) { \ fprintf(stderr, "Line %d: Failed call to `%s`.\n", \ __LINE__, #call); \ goto returnWithError; \ } \ } while (0) // userfunction of type "multimapdelta", implementing (x0,x1) -> (sin(x0-x1),cos(x0-x1)) int XPRS_CC myTrigonometrics(double* x, double* results, void* context) { (void)context; results[0] = sin(x[0] - x[1]); results[1] = cos(x[0] - x[1]); return (0); } // Message callback void XPRS_CC message(XPRSprob prob, void* my_object, const char* msg, int len, int msgtype) { (void)prob; (void)my_object; switch (msgtype) { case 4: /* error */ case 3: /* warning */ case 2: /* dialogue */ case 1: /* information */ if (len == 0) printf("\n"); else printf("%s\n", msg); break; default: /* exiting - buffers need flushing */ fflush(stdout); break; } } int main(void) { XPRSprob xprob = NULL; // Number of side of the Polygon int nSide = 5; int maxNameLength = 256; int ReturnValue = 0; int nameCursor = 0; int nameBufferSizeRows = 0; int nameBufferSizeCols = 0; double* RHS = NULL; char* RowType = NULL; char* RowNames = NULL; double* OBJ = NULL; double* Lower = NULL; double* Upper = NULL; int* ColStart = NULL; double* Element = NULL; int* RowIndex = NULL; char* ColNames = NULL; char* CoefBuffer = NULL; int coefBufferCursor = 0; int coefBufferSize = 0; int i, j; /* Initialisation */ CHECK_XPRSCALL(XPRSinit(NULL)); CHECK_XPRSCALL(XPRScreateprob(&xprob)); /* Messaging */ CHECK_XPRSCALL(XPRSaddcbmessage(xprob, message, NULL, 0)); printf("####################\n"); printf("# Polygon example #\n"); printf("####################\n"); /* Create rows */ int nRow = nSide - 2 + (nSide - 1) * (nSide - 2) / 2 + 1; RHS = (double*)malloc(nRow * sizeof(double)); if (!RHS) goto MemoryReturn; for (i = 0; i < nRow; i++) RHS[i] = 0; RowType = (char*)malloc((nRow + 1) * sizeof(char)); if (!RowType) goto MemoryReturn; nameBufferSizeRows = maxNameLength * (nRow + 1); RowNames = (char*)malloc(nameBufferSizeRows * sizeof(char)); if (!RowNames) goto MemoryReturn; nRow = 0; // Objective constraint RowType[nRow] = 'E'; /* OBJEQ */ nameCursor += snprintf(RowNames + nameCursor, nameBufferSizeRows - nameCursor, "OBJEQ"); nameCursor++; if (nameCursor + 1 > nameBufferSizeRows) goto BufferReturn; nRow++; // Vertices in increasing degree order for (i = 1; i < nSide - 1; i++) { RowType[nRow] = 'G'; /* T2T1 .. T4T3 */ nameCursor += snprintf(RowNames + nameCursor, nameBufferSizeRows - nameCursor, "T%iT%i", i + 1, i); nameCursor++; if (nameCursor + 1 > nameBufferSizeRows) goto BufferReturn; nRow++; RHS[i] = 0.001; } // Third side of all triangles <= 1 for (i = 1; i < nSide - 1; i++) { for (j = i + 1; j < nSide; j++) { RowType[nRow] = 'L'; RHS[nRow] = 1.0; nameCursor += snprintf(RowNames + nameCursor, nameBufferSizeRows - nameCursor, "V%iV%i", i, j); nameCursor++; if (nameCursor + 1 > nameBufferSizeRows) goto BufferReturn; nRow++; } } RowType[nRow] = '\0'; /* Columns and linear coefficients*/ int nCol = (nSide - 1) * 2 + 2; int nElement = 0; OBJ = (double*)malloc((nCol + 1) * sizeof(double)); if (!OBJ) goto MemoryReturn; Lower = (double*)malloc((nCol + 1) * sizeof(double)); if (!Lower) goto MemoryReturn; Upper = (double*)malloc((nCol + 1) * sizeof(double)); if (!Upper) goto MemoryReturn; for (i = 0; i < nCol; i++) { OBJ[i] = 0; /* objective function */ Lower[i] = 0; /* lower bound normally zero */ Upper[i] = XPRS_PLUSINFINITY; /* upper bound infinity */ } // Arrays to load linear coefficients ColStart = (int*)malloc((nRow + 1) * sizeof(int)); if (!ColStart) goto MemoryReturn; Element = (double*)malloc((10 * nCol) * sizeof(double)); if (!Element) goto MemoryReturn; RowIndex = (int*)malloc((10 * nCol) * sizeof(int)); if (!RowIndex) goto MemoryReturn; nameBufferSizeCols = maxNameLength * (nCol); ColNames = (char*)malloc(nameBufferSizeCols * sizeof(char)); if (!ColNames) goto MemoryReturn; nameCursor = 0; /* OBJX */ nCol = 0; ColStart[nCol] = nElement; OBJ[nCol] = 1.0; nameCursor += snprintf(ColNames + nameCursor, nameBufferSizeCols - nameCursor, "OBJX"); nameCursor++; if (nameCursor + 1 > nameBufferSizeCols) goto BufferReturn; Lower[nCol++] = XPRS_MINUSINFINITY; /* free column */ Element[nElement] = -1.0; RowIndex[nElement++] = 0; /* THETA1 - THETA 4 */ int iRow = 0; for (i = 1; i < nSide; i++) { nameCursor += snprintf(ColNames + nameCursor, nameBufferSizeCols - nameCursor, "THETA%i", i); nameCursor++; if (nameCursor + 1 > nameBufferSizeCols) goto BufferReturn; ColStart[nCol++] = nElement; if (i < nSide - 1) { Element[nElement] = -1; RowIndex[nElement++] = iRow + 1; } if (i > 1) { Element[nElement] = 1; RowIndex[nElement++] = iRow; } iRow++; } Upper[nCol - 1] = PI; /* Rho's */ for (i = 1; i < nSide; i++) { Lower[nCol] = 0.01; /* lower bound */ Upper[nCol] = 1; nameCursor += snprintf(ColNames + nameCursor, nameBufferSizeCols - nameCursor, "RHO%i", i); nameCursor++; if (nameCursor + 1 > nameBufferSizeCols) goto BufferReturn; ColStart[nCol++] = nElement; } ColStart[nCol] = nElement; CHECK_XPRSCALL(XPRSloadlp(xprob, "Polygon", nCol, nRow, RowType, RHS, NULL, OBJ, ColStart, NULL, RowIndex, Element, Lower, Upper)); CHECK_XPRSCALL(XPRSaddnames(xprob, 1, RowNames, 0, nRow - 1)); CHECK_XPRSCALL(XPRSaddnames(xprob, 2, ColNames, 0, nCol - 1)); /* Add the user function*/ CHECK_XPRSCALL(XPRSnlpadduserfunction(xprob, "myTrigonometrics", XPRS_USERFUNCTION_MULTIMAP, 2 /* #inputs arguments */, 2 /* #output arguments*/, 0, (XPRSfunctionptr)myTrigonometrics, NULL, NULL)); /* Build up nonlinear coefficients */ coefBufferSize = 1000 * maxNameLength; CoefBuffer = (char*)malloc(coefBufferSize); if (!CoefBuffer) goto MemoryReturn; /* Area */ coefBufferCursor += snprintf(CoefBuffer + coefBufferCursor, coefBufferSize - coefBufferCursor, "0.5 * ( "); if (coefBufferCursor + 1 > coefBufferSize) goto BufferReturn; for (i = 1; i < nSide - 1; i++) { if (i > 1) { coefBufferCursor += snprintf(CoefBuffer + coefBufferCursor, coefBufferSize - coefBufferCursor, " + "); if (coefBufferCursor + 1 > coefBufferSize) goto BufferReturn; } coefBufferCursor += snprintf(CoefBuffer + coefBufferCursor, coefBufferSize - coefBufferCursor, "RHO%i * RHO%i * myTrigonometrics ( THETA%i , THETA%i : 1 )", i + 1, i, i + 1, i); if (coefBufferCursor + 1 > coefBufferSize) goto BufferReturn; } coefBufferCursor += snprintf(CoefBuffer + coefBufferCursor, coefBufferSize - coefBufferCursor, " )"); if (coefBufferCursor + 1 > coefBufferSize) goto BufferReturn; CHECK_XPRSCALL(XPRSnlpchgformulastr(xprob, 0, CoefBuffer)); /* Distances */ for (i = 1; i < nSide - 1; i++) { for (j = i + 1; j < nSide; j++) { coefBufferCursor = 0; coefBufferCursor += snprintf(CoefBuffer + coefBufferCursor, coefBufferSize - coefBufferCursor, "RHO%i ^ 2 + RHO%i ^ 2 - 2 * RHO%i * RHO%i * myTrigonometrics ( THETA%i , THETA%i : 2 )", j, i, j, i, j, i); CHECK_XPRSCALL(XPRSnlpchgformulastr(xprob, iRow, CoefBuffer)); iRow++; } } CHECK_XPRSCALL(XPRSchgobjsense(xprob, XPRS_OBJ_MAXIMIZE)); CHECK_XPRSCALL(XPRSoptimize(xprob, "s", NULL, NULL)); goto NormalReturn; BufferReturn: printf("\nWorking buffer too short\n"); goto NormalReturn; MemoryReturn: printf("\nOut of memory\n"); goto NormalReturn; returnWithError: ReturnValue = -1; NormalReturn: // Retrieve error from Xpress if (ReturnValue) { fprintf(stderr, "An error was detected during execution.\n"); if (xprob) { int errorcode = 0; char errorMessage[512]; XPRSgetintattrib(xprob, XPRS_ERRORCODE, &errorcode); XPRSgetlasterror(xprob, errorMessage); fprintf(stderr, "Optimizer returned error code '%i' with message:\n%s\n", errorcode, errorMessage); } } XPRSdestroyprob(xprob); XPRSfree(); free(RHS); free(RowType); free(RowNames); free(OBJ); free(Lower); free(Upper); free(ColStart); free(Element); free(RowIndex); free(ColNames); free(CoefBuffer); return(ReturnValue); } | |||||||||||
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