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Diffstat (limited to 'Build/source/utils/asymptote/runarray.in')
-rw-r--r-- | Build/source/utils/asymptote/runarray.in | 1834 |
1 files changed, 1834 insertions, 0 deletions
diff --git a/Build/source/utils/asymptote/runarray.in b/Build/source/utils/asymptote/runarray.in new file mode 100644 index 00000000000..61b0f9a485f --- /dev/null +++ b/Build/source/utils/asymptote/runarray.in @@ -0,0 +1,1834 @@ +/***** + * runarray.in + * + * Runtime functions for array operations. + * + *****/ + +pair => primPair() +triple => primTriple() +boolarray* => booleanArray() +Intarray* => IntArray() +Intarray2* => IntArray2() +realarray* => realArray() +realarray2* => realArray2() +pairarray* => pairArray() +triplearray2* => tripleArray2() +callableReal* => realRealFunction() + + +#include "array.h" +#include "arrayop.h" +#include "triple.h" +#include "path3.h" +#include "Delaunay.h" + +#ifdef HAVE_LIBFFTW3 +#include "fftw++.h" +#endif + +using namespace camp; +using namespace vm; + +typedef array boolarray; +typedef array Intarray; +typedef array Intarray2; +typedef array realarray; +typedef array realarray2; +typedef array pairarray; +typedef array triplearray2; + +using types::booleanArray; +using types::IntArray; +using types::IntArray2; +using types::realArray; +using types::realArray2; +using types::pairArray; +using types::tripleArray2; + +typedef callable callableReal; + +void outOfBounds(const char *op, size_t len, Int n) +{ + ostringstream buf; + buf << op << " array of length " << len << " with out-of-bounds index " << n; + error(buf); +} + +inline item& arrayRead(array *a, Int n) +{ + size_t len=checkArray(a); + bool cyclic=a->cyclic(); + if(cyclic && len > 0) n=imod(n,len); + else if(n < 0 || n >= (Int) len) outOfBounds("reading",len,n); + return (*a)[(unsigned) n]; +} + +// Helper function to create deep arrays. +static array* deepArray(Int depth, Int *dims) +{ + assert(depth > 0); + + if (depth == 1) { + return new array(dims[0]); + } else { + Int length = dims[0]; + depth--; dims++; + + array *a = new array(length); + + for (Int index = 0; index < length; index++) { + (*a)[index] = deepArray(depth, dims); + } + return a; + } +} + +namespace run { +array *Identity(Int n) +{ + size_t N=(size_t) n; + array *c=new array(N); + for(size_t i=0; i < N; ++i) { + array *ci=new array(N); + (*c)[i]=ci; + for(size_t j=0; j < N; ++j) + (*ci)[j]=0.0; + (*ci)[i]=1.0; + } + return c; +} +} + +static const char *incommensurate="Incommensurate matrices"; +static const char *singular="Singular matrix"; +static size_t *pivot,*Row,*Col; + +namespace run { + +array *copyArray(array *a) +{ + size_t size=checkArray(a); + array *c=new array(size); + for(size_t i=0; i < size; i++) + (*c)[i]=(*a)[i]; + return c; +} + +inline size_t checkdimension(const array *a, size_t dim) +{ + size_t size=checkArray(a); + if(dim && size != dim) { + ostringstream buf; + buf << "array of length " << dim << " expected"; + error(buf); + } + return size; +} + +double *copyArrayC(const array *a, size_t dim) +{ + size_t size=checkdimension(a,dim); + double *c=new double[size]; + for(size_t i=0; i < size; i++) + c[i]=read<double>(a,i); + return c; +} + +triple *copyTripleArrayC(const array *a, size_t dim) +{ + size_t size=checkdimension(a,dim); + triple *c=new triple[size]; + for(size_t i=0; i < size; i++) + c[i]=read<triple>(a,i); + return c; +} + +array *copyArray2(array *a) +{ + size_t size=checkArray(a); + array *c=new array(size); + for(size_t i=0; i < size; i++) { + array *ai=read<array*>(a,i); + size_t aisize=checkArray(ai); + array *ci=new array(aisize); + (*c)[i]=ci; + for(size_t j=0; j < aisize; j++) + (*ci)[j]=(*ai)[j]; + } + return c; +} + +array *copyArray3(array *a) +{ + size_t size=checkArray(a); + array *c=new array(size); + for(size_t i=0; i < size; i++) { + array *ai=read<array*>(a,i); + size_t aisize=checkArray(ai); + array *ci=new array(aisize); + (*c)[i]=ci; + for(size_t j=0; j < aisize; j++) { + array *aij=read<array*>(ai,j); + size_t aijsize=checkArray(aij); + array *cij=new array(aijsize); + (*ci)[j]=cij; + for(size_t k=0; k < aijsize; k++) + (*cij)[k]=(*aij)[k]; + } + } + return c; +} + +double *copyArray2C(const array *a, bool square, size_t dim2) +{ + size_t n=checkArray(a); + size_t m=(square || n == 0) ? n : checkArray(read<array*>(a,0)); + if(n > 0 && dim2 && m != dim2) { + ostringstream buf; + buf << "second matrix dimension must be " << dim2; + error(buf); + } + + double *c=new double[n*m]; + for(size_t i=0; i < n; i++) { + array *ai=read<array*>(a,i); + size_t aisize=checkArray(ai); + if(aisize == m) { + double *ci=c+i*m; + for(size_t j=0; j < m; j++) + ci[j]=read<double>(ai,j); + } else + error(square ? "matrix must be square" : "matrix must be rectangular"); + } + return c; +} + +triple *copyTripleArray2C(const array *a, bool square, size_t dim2) +{ + size_t n=checkArray(a); + size_t m=(square || n == 0) ? n : checkArray(read<array*>(a,0)); + if(n > 0 && dim2 && m != dim2) { + ostringstream buf; + buf << "second matrix dimension must be " << dim2; + error(buf); + } + + triple *c=new triple[n*m]; + for(size_t i=0; i < n; i++) { + array *ai=read<array*>(a,i); + size_t aisize=checkArray(ai); + if(aisize == m) { + triple *ci=c+i*m; + for(size_t j=0; j < m; j++) + ci[j]=read<triple>(ai,j); + } else + error(square ? "matrix must be square" : "matrix must be rectangular"); + } + return c; +} + +double *copyTripleArray2Components(array *a, bool square, size_t dim2) +{ + size_t n=checkArray(a); + size_t m=(square || n == 0) ? n : checkArray(read<array*>(a,0)); + if(n > 0 && dim2 && m != dim2) { + ostringstream buf; + buf << "second matrix dimension must be " << dim2; + error(buf); + } + + size_t nm=n*m; + double *cx=new double[3*nm]; + double *cy=cx+nm; + double *cz=cx+2*nm; + for(size_t i=0; i < n; i++) { + array *ai=read<array*>(a,i); + size_t aisize=checkArray(ai); + if(aisize == m) { + double *xi=cx+i*m; + double *yi=cy+i*m; + double *zi=cz+i*m; + for(size_t j=0; j < m; j++) { + triple v=read<triple>(ai,j); + xi[j]=v.getx(); + yi[j]=v.gety(); + zi[j]=v.getz(); + } + } else + error(square ? "matrix must be square" : "matrix must be rectangular"); + } + return cx; +} + +triple operator *(const array& t, const triple& v) +{ + size_t n=checkArray(&t); + if(n != 4) error(incommensurate); + array *t0=read<array*>(t,0); + array *t1=read<array*>(t,1); + array *t2=read<array*>(t,2); + array *t3=read<array*>(t,3); + + if(checkArray(t0) != 4 || checkArray(t1) != 4 || + checkArray(t2) != 4 || checkArray(t3) != 4) + error(incommensurate); + + double x=v.getx(); + double y=v.gety(); + double z=v.getz(); + + double f=read<real>(t3,0)*x+read<real>(t3,1)*y+read<real>(t3,2)*z+ + read<real>(t3,3); + if(f == 0.0) run::dividebyzero(); + f=1.0/f; + + return triple((read<real>(t0,0)*x+read<real>(t0,1)*y+read<real>(t0,2)*z+ + read<real>(t0,3))*f, + (read<real>(t1,0)*x+read<real>(t1,1)*y+read<real>(t1,2)*z+ + read<real>(t1,3))*f, + (read<real>(t2,0)*x+read<real>(t2,1)*y+read<real>(t2,2)*z+ + read<real>(t2,3))*f); +} + +triple multshiftless(const array& t, const triple& v) +{ + size_t n=checkArray(&t); + if(n != 4) error(incommensurate); + array *t0=read<array*>(t,0); + array *t1=read<array*>(t,1); + array *t2=read<array*>(t,2); + array *t3=read<array*>(t,3); + + if(checkArray(t0) != 4 || checkArray(t1) != 4 || + checkArray(t2) != 4 || checkArray(t3) != 4) + error(incommensurate); + + double x=v.getx(); + double y=v.gety(); + double z=v.getz(); + + double f=read<real>(t3,0)*x+read<real>(t3,1)*y+read<real>(t3,2)*z+ + read<real>(t3,3); + if(f == 0.0) run::dividebyzero(); + f=1.0/f; + + return triple((read<real>(t0,0)*x+read<real>(t0,1)*y+read<real>(t0,2)*z)*f, + (read<real>(t1,0)*x+read<real>(t1,1)*y+read<real>(t1,2)*z)*f, + (read<real>(t2,0)*x+read<real>(t2,1)*y+read<real>(t2,2)*z)*f); +} + +double norm(double *a, size_t n) +{ + if(n == 0) return 0.0; + double M=fabs(a[0]); + for(size_t i=1; i < n; ++i) + M=::max(M,fabs(a[i])); + return M; +} + +double norm(triple *a, size_t n) +{ + if(n == 0) return 0.0; + double M=a[0].abs2(); + for(size_t i=1; i < n; ++i) + M=::max(M,a[i].abs2()); + return sqrt(M); +} + +} + +static inline void inverseAllocate(size_t n) +{ + pivot=new size_t[n]; + Row=new size_t[n]; + Col=new size_t[n]; +} + +static inline void inverseDeallocate() +{ + delete[] pivot; + delete[] Row; + delete[] Col; +} + +callable *Func; +stack *FuncStack; +double wrapFunction(double x) +{ + FuncStack->push(x); + Func->call(FuncStack); + return pop<double>(FuncStack); +} + +callable *compareFunc; +bool compareFunction(const vm::item& i, const vm::item& j) +{ + FuncStack->push(i); + FuncStack->push(j); + compareFunc->call(FuncStack); + return pop<bool>(FuncStack); +} + +void checkSquare(array *a) +{ + size_t n=checkArray(a); + for(size_t i=0; i < n; i++) + if(checkArray(read<array*>(a,i)) != n) + error("matrix a must be square"); +} + +// Crout's algorithm for computing the LU decomposition of a square matrix. +// cf. routine ludcmp (Press et al., Numerical Recipes, 1991). +Int LUdecompose(double *a, size_t n, size_t* index, bool warn=true) +{ + double *vv=new double[n]; + Int swap=1; + for(size_t i=0; i < n; ++i) { + double big=0.0; + double *ai=a+i*n; + for(size_t j=0; j < n; ++j) { + double temp=fabs(ai[j]); + if(temp > big) big=temp; + } + if(big == 0.0) { + delete[] vv; + if(warn) error(singular); + else return 0; + } + vv[i]=1.0/big; + } + for(size_t j=0; j < n; ++j) { + for(size_t i=0; i < j; ++i) { + double *ai=a+i*n; + double sum=ai[j]; + for(size_t k=0; k < i; ++k) { + sum -= ai[k]*a[k*n+j]; + } + ai[j]=sum; + } + double big=0.0; + size_t imax=j; + for(size_t i=j; i < n; ++i) { + double *ai=a+i*n; + double sum=ai[j]; + for(size_t k=0; k < j; ++k) + sum -= ai[k]*a[k*n+j]; + ai[j]=sum; + double temp=vv[i]*fabs(sum); + if(temp >= big) { + big=temp; + imax=i; + } + } + double *aj=a+j*n; + double *aimax=a+imax*n; + if(j != imax) { + for(size_t k=0; k < n; ++k) { + double temp=aimax[k]; + aimax[k]=aj[k]; + aj[k]=temp; + } + swap *= -1; + vv[imax]=vv[j]; + } + if(index) + index[j]=imax; + if(j != n) { + double denom=aj[j]; + if(denom == 0.0) { + delete[] vv; + if(warn) error(singular); + else return 0; + } + for(size_t i=j+1; i < n; ++i) + a[i*n+j] /= denom; + } + } + delete[] vv; + return swap; +} + +namespace run { +void dividebyzero(size_t i) +{ + ostringstream buf; + if(i > 0) buf << "array element " << i << ": "; + buf << "Divide by zero"; + error(buf); +} + +void integeroverflow(size_t i) +{ + ostringstream buf; + if(i > 0) buf << "array element " << i << ": "; + buf << "Integer overflow"; + error(buf); +} +} + +// Autogenerated routines: + + +// Create an empty array. +array* :emptyArray() +{ + return new array(0); +} + +// Create a new array (technically a vector). +// This array will be multidimensional. First the number of dimensions +// is popped off the stack, followed by each dimension in reverse order. +// The array itself is technically a one dimensional array of one +// dimension arrays and so on. +array* :newDeepArray(Int depth) +{ + assert(depth > 0); + + Int *dims = new Int[depth]; + + for (Int index = depth-1; index >= 0; index--) { + Int i=pop<Int>(Stack); + if(i < 0) error("cannot create a negative length array"); + dims[index]=i; + } + + array *a=deepArray(depth, dims); + delete[] dims; + return a; +} + +// Creates an array with elements already specified. First, the number +// of elements is popped off the stack, followed by each element in +// reverse order. +array* :newInitializedArray(Int n) +{ + assert(n >= 0); + + array *a = new array(n); + + for (Int index = n-1; index >= 0; index--) + (*a)[index] = pop(Stack); + + return a; +} + +// Similar to newInitializedArray, but after the n elements, append another +// array to it. +array* :newAppendedArray(array* tail, Int n) +{ + assert(n >= 0); + + array *a = new array(n); + + for (Int index = n-1; index >= 0; index--) + (*a)[index] = pop(Stack); + + copy(tail->begin(), tail->end(), back_inserter(*a)); + + return a; +} + +// The function T[] array(int n, T value, int depth=0) produces a array of n +// copies of x, where each copy is copied up to depth. +array* :newDuplicateArray(Int n, item value, Int depth=Int_MAX) +{ + if(n < 0) error("cannot create a negative length array"); + if(depth < 0) error("cannot copy to a negative depth"); + + return new array(n, value, depth); +} + +// Read an element from an array. Checks for initialization & bounds. +item :arrayRead(array *a, Int n) +{ + item& i=arrayRead(a,n); + if (i.empty()) { + ostringstream buf; + buf << "read uninitialized value from array at index " << n; + error(buf); + } + return i; +} + +// Slice a substring from an array. +item :arraySliceRead(array *a, Int left, Int right) +{ + checkArray(a); + return a->slice(left, right); +} + +// Slice a substring from an array. This implements the cases a[i:] and a[:] +// where the endpoint is not given, and assumed to be the length of the array. +item :arraySliceReadToEnd(array *a, Int left) +{ + size_t len=checkArray(a); + return a->slice(left, (Int)len); +} + +// Read an element from an array of arrays. Check bounds and initialize +// as necessary. +item :arrayArrayRead(array *a, Int n) +{ + item& i=arrayRead(a,n); + if (i.empty()) i=new array(0); + return i; +} + +// Write an element to an array. Increase size if necessary. +item :arrayWrite(item value, array *a, Int n) +{ + size_t len=checkArray(a); + bool cyclic=a->cyclic(); + if(cyclic && len > 0) n=imod(n,len); + else { + if(cyclic) outOfBounds("writing cyclic",len,n); + if(n < 0) outOfBounds("writing",len,n); + if(len <= (size_t) n) + a->resize(n+1); + } + (*a)[n] = value; + return value; +} + +array * :arraySliceWrite(array *src, array *dest, Int left, Int right) +{ + checkArray(src); + checkArray(dest); + dest->setSlice(left, right, src); + return src; +} + +array * :arraySliceWriteToEnd(array *src, array *dest, Int left) +{ + checkArray(src); + size_t len=checkArray(dest); + dest->setSlice(left, (Int) len, src); + return src; +} + +// Returns the length of an array. +Int :arrayLength(array *a) +{ + return (Int) checkArray(a); +} + +// Returns an array of integers representing the keys of the array. +array * :arrayKeys(array *a) +{ + size_t size=checkArray(a); + + array *keys=new array(); + for (size_t i=0; i<size; ++i) { + item& cell = (*a)[i]; + if (!cell.empty()) + keys->push((Int)i); + } + + return keys; +} + +// Return the cyclic flag for an array. +bool :arrayCyclicFlag(array *a) +{ + checkArray(a); + return a->cyclic(); +} + +bool :arraySetCyclicFlag(bool b, array *a) +{ + checkArray(a); + a->cyclic(b); + return b; +} + +// Check to see if an array element is initialized. +bool :arrayInitializedHelper(Int n, array *a) +{ + size_t len=checkArray(a); + bool cyclic=a->cyclic(); + if(cyclic && len > 0) n=imod(n,len); + else if(n < 0 || n >= (Int) len) return false; + item&i=(*a)[(unsigned) n]; + return !i.empty(); +} + +// Returns the initialize method for an array. +callable* :arrayInitialized(array *a) +{ + return new thunk(new bfunc(arrayInitializedHelper),a); +} + +// The helper function for the cyclic method that sets the cyclic flag. +void :arrayCyclicHelper(bool b, array *a) +{ + checkArray(a); + a->cyclic(b); +} + +// Set the cyclic flag for an array. +callable* :arrayCyclic(array *a) +{ + return new thunk(new bfunc(arrayCyclicHelper),a); +} + +// The helper function for the push method that does the actual operation. +item :arrayPushHelper(item x, array *a) +{ + checkArray(a); + a->push(x); + return x; +} + +// Returns the push method for an array. +callable* :arrayPush(array *a) +{ + return new thunk(new bfunc(arrayPushHelper),a); +} + +// The helper function for the append method that appends b to a. +void :arrayAppendHelper(array *b, array *a) +{ + checkArray(a); + size_t size=checkArray(b); + for(size_t i=0; i < size; i++) + a->push((*b)[i]); +} + +// Returns the append method for an array. +callable* :arrayAppend(array *a) +{ + return new thunk(new bfunc(arrayAppendHelper),a); +} + +// The helper function for the pop method. +item :arrayPopHelper(array *a) +{ + size_t asize=checkArray(a); + if(asize == 0) + error("cannot pop element from empty array"); + return a->pop(); +} + +// Returns the pop method for an array. +callable* :arrayPop(array *a) +{ + return new thunk(new bfunc(arrayPopHelper),a); +} + +// The helper function for the insert method. +item :arrayInsertHelper(Int i, array *x, array *a) +{ + size_t asize=checkArray(a); + checkArray(x); + if(a->cyclic() && asize > 0) i=imod(i,asize); + if(i < 0 || i > (Int) asize) + outOfBounds("inserting",asize,i); + (*a).insert((*a).begin()+i,(*x).begin(),(*x).end()); +} + +// Returns the insert method for an array. +callable* :arrayInsert(array *a) +{ + return new thunk(new bfunc(arrayInsertHelper),a); +} + +// Returns the delete method for an array. +callable* :arrayDelete(array *a) +{ + return new thunk(new bfunc(arrayDeleteHelper),a); +} + +bool :arrayAlias(array *a, array *b) +{ + return a==b; +} + +// Return array formed by indexing array a with elements of integer array b +array* :arrayIntArray(array *a, array *b) +{ + size_t asize=checkArray(a); + size_t bsize=checkArray(b); + array *r=new array(bsize); + bool cyclic=a->cyclic(); + for(size_t i=0; i < bsize; i++) { + Int index=read<Int>(b,i); + if(cyclic && asize > 0) index=imod(index,asize); + else + if(index < 0 || index >= (Int) asize) + outOfBounds("reading",asize,index); + (*r)[i]=(*a)[index]; + } + return r; +} + +// returns the complement of the integer array a in {0,2,...,n-1}, +// so that b[complement(a,b.length)] yields the complement of b[a]. +Intarray* complement(Intarray *a, Int n) +{ + size_t asize=checkArray(a); + array *r=new array(0); + bool *keep=new bool[n]; + for(Int i=0; i < n; ++i) keep[i]=true; + for(size_t i=0; i < asize; ++i) { + Int j=read<Int>(a,i); + if(j >= 0 && j < n) keep[j]=false; + } + for(Int i=0; i < n; i++) + if(keep[i]) r->push(i); + + delete[] keep; + return r; +} + +// Generate the sequence {f(i) : i=0,1,...n-1} given a function f and integer n +Intarray* :arraySequence(callable *f, Int n) +{ + if(n < 0) n=0; + array *a=new array(n); + for(Int i=0; i < n; ++i) { + Stack->push(i); + f->call(Stack); + (*a)[i]=pop(Stack); + } + return a; +} + +// Return the array {0,1,...n-1} +Intarray *sequence(Int n) +{ + if(n < 0) n=0; + array *a=new array(n); + for(Int i=0; i < n; ++i) { + (*a)[i]=i; + } + return a; +} + +// Apply a function to each element of an array +array* :arrayFunction(callable *f, array *a) +{ + size_t size=checkArray(a); + array *b=new array(size); + for(size_t i=0; i < size; ++i) { + Stack->push((*a)[i]); + f->call(Stack); + (*b)[i]=pop(Stack); + } + return b; +} + +array* :arraySort(array *a, callable *f) +{ + array *c=copyArray(a); + compareFunc=f; + FuncStack=Stack; + stable_sort(c->begin(),c->end(),compareFunction); + return c; +} + +bool all(boolarray *a) +{ + size_t size=checkArray(a); + bool c=true; + for(size_t i=0; i < size; i++) + if(!get<bool>((*a)[i])) {c=false; break;} + return c; +} + +boolarray* !(boolarray* a) +{ + size_t size=checkArray(a); + array *c=new array(size); + for(size_t i=0; i < size; i++) + (*c)[i]=!read<bool>(a,i); + return c; +} + +Int sum(boolarray *a) +{ + size_t size=checkArray(a); + Int sum=0; + for(size_t i=0; i < size; i++) + sum += read<bool>(a,i) ? 1 : 0; + return sum; +} + +array* :arrayCopy(array *a) +{ + return copyArray(a); +} + +array* :arrayConcat(array *a) +{ + // a is an array of arrays to be concatenated together. + // The signature is + // T[] concat(... T[][] a); + + size_t numArgs=checkArray(a); + size_t resultSize=0; + for (size_t i=0; i < numArgs; ++i) { + resultSize += checkArray(a->read<array *>(i)); + } + + array *result=new array(resultSize); + + size_t ri=0; + for (size_t i=0; i < numArgs; ++i) { + array *arg=a->read<array *>(i); + size_t size=checkArray(arg); + + for (size_t j=0; j < size; ++j) { + (*result)[ri]=(*arg)[j]; + ++ri; + } + } + + return result; +} + +array* :array2Copy(array *a) +{ + return copyArray2(a); +} + +array* :array3Copy(array *a) +{ + return copyArray3(a); +} + +array* :array2Transpose(array *a) +{ + size_t asize=checkArray(a); + array *c=new array(0); + for(size_t i=0; i < asize; i++) { + size_t ip=i+1; + array *ai=read<array*>(a,i); + size_t aisize=checkArray(ai); + size_t csize=checkArray(c); + if(csize < aisize) { + c->resize(aisize); + for(size_t j=csize; j < aisize; j++) { + (*c)[j]=new array(ip); + } + } + for(size_t j=0; j < aisize; j++) { + array *cj=read<array*>(c,j); + if(checkArray(cj) < ip) cj->resize(ip); + (*cj)[i]=(*ai)[j]; + } + } + return c; +} + +// a is a rectangular 3D array; perm is an Int array indicating the type of +// permutation (021 or 120, etc; original is 012). +// Transpose by sending respective members to the permutated locations: +// return the array obtained by putting a[i][j][k] into position perm{ijk}. +array* :array3Transpose(array *a, array *perm) +{ + const size_t DIM=3; + + if(checkArray(perm) != DIM) { + ostringstream buf; + buf << "permutation array must have length " << DIM; + error(buf); + } + + size_t* size=new size_t[DIM]; + for(size_t i=0; i < DIM; ++i) size[i]=DIM; + + for(size_t i=0; i < DIM; ++i) { + Int p=read<Int>(perm,i); + size_t P=(size_t) p; + if(p < 0 || P >= DIM) { + ostringstream buf; + buf << "permutation index out of range: " << p; + error(buf); + } + size[P]=P; + } + + for(size_t i=0; i < DIM; ++i) + if(size[i] == DIM) error("permutation indices must be distinct"); + + static const char *rectangular= + "3D transpose implemented for rectangular matrices only"; + + size_t isize=size[0]=checkArray(a); + array *a0=read<array*>(a,0); + size[1]=checkArray(a0); + array *a00=read<array*>(a0,0); + size[2]=checkArray(a00); + for(size_t i=0; i < isize; i++) { + array *ai=read<array*>(a,i); + size_t jsize=checkArray(ai); + if(jsize != size[1]) error(rectangular); + for(size_t j=0; j < jsize; j++) { + array *aij=read<array*>(ai,j); + if(checkArray(aij) != size[2]) error(rectangular); + } + } + + size_t perm0=(size_t) read<Int>(perm,0); + size_t perm1=(size_t) read<Int>(perm,1); + size_t perm2=(size_t) read<Int>(perm,2); + + size_t sizep0=size[perm0]; + size_t sizep1=size[perm1]; + size_t sizep2=size[perm2]; + + array *c=new array(sizep0); + for(size_t i=0; i < sizep0; ++i) { + array *ci=new array(sizep1); + (*c)[i]=ci; + for(size_t j=0; j < sizep1; ++j) { + array *cij=new array(sizep2); + (*ci)[j]=cij; + } + } + + size_t* i=new size_t[DIM]; + + for(i[0]=0; i[0] < size[0]; ++i[0]) { + array *a0=read<array*>(a,i[0]); + for(i[1]=0; i[1] < size[1]; ++i[1]) { + array *a1=read<array*>(a0,i[1]); + for(i[2]=0; i[2] < size[2]; ++i[2]) { + array *c0=read<array*>(c,i[perm0]); + array *c1=read<array*>(c0,i[perm1]); + (*c1)[i[perm2]]=read<real>(a1,i[2]); + } + } + } + + delete [] i; + delete [] size; + + return c; +} + +// In a boolean array, find the index of the nth true value or -1 if not found +// If n is negative, search backwards. +Int find(boolarray *a, Int n=1) +{ + size_t size=checkArray(a); + Int j=-1; + if(n > 0) + for(size_t i=0; i < size; i++) + if(read<bool>(a,i)) { + n--; if(n == 0) {j=(Int) i; break;} + } + if(n < 0) + for(size_t i=size; i > 0;) + if(read<bool>(a,--i)) { + n++; if(n == 0) {j=(Int) i; break;} + } + return j; +} + +// construct vector obtained by replacing those elements of b for which the +// corresponding elements of a are false by the corresponding element of c. +array* :arrayConditional(array *a, array *b, array *c) +{ + size_t size=checkArray(a); + array *r=new array(size); + if(b && c) { + checkArrays(a,b); + checkArrays(b,c); + for(size_t i=0; i < size; i++) + (*r)[i]=read<bool>(a,i) ? (*b)[i] : (*c)[i]; + } else { + r->clear(); + if(b) { + checkArrays(a,b); + for(size_t i=0; i < size; i++) + if(read<bool>(a,i)) r->push((*b)[i]); + } else if(c) { + checkArrays(a,c); + for(size_t i=0; i < size; i++) + if(!read<bool>(a,i)) r->push((*c)[i]); + } + } + return r; +} + +// Return an n x n identity matrix. +realarray2 *identity(Int n) +{ + return Identity(n); +} + +// Return the diagonal matrix with diagonal entries given by a. +realarray2* :diagonal(realarray *a) +{ + size_t n=checkArray(a); + array *c=new array(n); + for(size_t i=0; i < n; ++i) { + array *ci=new array(n); + (*c)[i]=ci; + for(size_t j=0; j < i; ++j) + (*ci)[j]=0.0; + (*ci)[i]=read<real>(a,i); + for(size_t j=i+1; j < n; ++j) + (*ci)[j]=0.0; + } + return c; +} + +// Return the inverse of an n x n matrix a using Gauss-Jordan elimination. +realarray2 *inverse(realarray2 *a) +{ + a=copyArray2(a); + size_t n=checkArray(a); + checkSquare(a); + + inverseAllocate(n); + + for(size_t i=0; i < n; i++) + pivot[i]=0; + + size_t col=0, row=0; + // This is the main loop over the columns to be reduced. + for(size_t i=0; i < n; i++) { + real big=0.0; + // This is the outer loop of the search for a pivot element. + for(size_t j=0; j < n; j++) { + array *aj=read<array*>(a,j); + if(pivot[j] != 1) { + for(size_t k=0; k < n; k++) { + if(pivot[k] == 0) { + real temp=fabs(read<real>(aj,k)); + if(temp >= big) { + big=temp; + row=j; + col=k; + } + } else if(pivot[k] > 1) { + inverseDeallocate(); + error(singular); + } + } + } + } + ++(pivot[col]); + + // Interchange rows, if needed, to put the pivot element on the diagonal. + array *acol=read<array*>(a,col); + if(row != col) { + array *arow=read<array*>(a,row); + for(size_t l=0; l < n; l++) { + real temp=read<real>(arow,l); + (*arow)[l]=read<real>(acol,l); + (*acol)[l]=temp; + } + } + + Row[i]=row; + Col[i]=col; + + // Divide the pivot row by the pivot element. + real denom=read<real>(acol,col); + if(denom == 0.0) { + inverseDeallocate(); + error(singular); + } + real pivinv=1.0/denom; + (*acol)[col]=1.0; + for(size_t l=0; l < n; l++) + (*acol)[l]=read<real>(acol,l)*pivinv; + + // Reduce all rows except for the pivoted one. + for(size_t k=0; k < n; k++) { + if(k != col) { + array *ak=read<array*>(a,k); + real akcol=read<real>(ak,col); + (*ak)[col]=0.0; + for(size_t l=0; l < n; l++) + (*ak)[l]=read<real>(ak,l)-read<real>(acol,l)*akcol; + } + } + } + + // Unscramble the inverse matrix in view of the column interchanges. + for(size_t l=n; l > 0;) { + l--; + size_t r=Row[l]; + size_t c=Col[l]; + if(r != c) { + for(size_t k=0; k < n; k++) { + array *ak=read<array*>(a,k); + real temp=read<real>(ak,r); + (*ak)[r]=read<real>(ak,c); + (*ak)[c]=temp; + } + } + } + inverseDeallocate(); + return a; +} + +// Solve the linear equation ax=b by LU decomposition, returning the +// solution x, where a is an n x n matrix and b is an array of length n. +// If no solution exists, return an empty array. +realarray *solve(realarray2 *a, realarray *b, bool warn=true) +{ + size_t n=checkArray(a); + + if(n == 0) return new array(0); + + size_t m=checkArray(b); + if(m != n) error(incommensurate); + + real *A=copyArray2C(a); + size_t *index=new size_t[n]; + + if(LUdecompose(A,n,index,warn) == 0) + return new array(0); + + array *x=new array(n); + + real *B=copyArrayC(b); + + for(size_t i=0; i < n; ++i) { + size_t ip=index[i]; + real sum=B[ip]; + B[ip]=B[i]; + real *Ai=A+i*n; + for(size_t j=0; j < i; ++j) + sum -= Ai[j]*B[j]; + B[i]=sum; + } + + for(size_t i=n; i > 0;) { + --i; + real sum=B[i]; + real *Ai=A+i*n; + for(size_t j=i+1; j < n; ++j) + sum -= Ai[j]*B[j]; + B[i]=sum/Ai[i]; + } + + for(size_t i=0; i < n; ++i) + (*x)[i]=B[i]; + + delete[] index; + delete[] B; + delete[] A; + + return x; +} + +// Solve the linear equation ax=b by LU decomposition, returning the +// solution x, where a is an n x n matrix and b is an n x m matrix. +// If no solution exists, return an empty array. +realarray2 *solve(realarray2 *a, realarray2 *b, bool warn=true) +{ + size_t n=checkArray(a); + + if(n == 0) return new array(0); + + if(checkArray(b) != n) error(incommensurate); + size_t m=checkArray(read<array*>(b,0)); + + real *A=copyArray2C(a); + real *B=copyArray2C(b,false); + + size_t *index=new size_t[n]; + + if(LUdecompose(A,n,index,warn) == 0) + return new array(0); + + array *x=new array(n); + + for(size_t i=0; i < n; ++i) { + real *Ai=A+i*n; + real *Bi=B+i*m; + real *Bip=B+index[i]*m; + for(size_t k=0; k < m; ++k) { + real sum=Bip[k]; + Bip[k]=Bi[k]; + size_t jk=k; + for(size_t j=0; j < i; ++j, jk += m) + sum -= Ai[j]*B[jk]; + Bi[k]=sum; + } + } + + for(size_t i=n; i > 0;) { + --i; + real *Ai=A+i*n; + real *Bi=B+i*m; + for(size_t k=0; k < m; ++k) { + real sum=Bi[k]; + size_t jk=(i+1)*m+k; + for(size_t j=i+1; j < n; ++j, jk += m) + sum -= Ai[j]*B[jk]; + Bi[k]=sum/Ai[i]; + } + } + + for(size_t i=0; i < n; ++i) { + real *Bi=B+i*m; + array *xi=new array(m); + (*x)[i]=xi; + for(size_t j=0; j < m; ++j) + (*xi)[j]=Bi[j]; + } + + delete[] index; + delete[] B; + delete[] A; + + return x; +} + +// Compute the determinant of an n x n matrix. +real determinant(realarray2 *a) +{ + real *A=copyArray2C(a); + size_t n=checkArray(a); + + real det=LUdecompose(A,n,NULL,false); + size_t n1=n+1; + for(size_t i=0; i < n; ++i) + det *= A[i*n1]; + + delete[] A; + + return det; +} + +realarray *Operator *(realarray2 *a, realarray *b) +{ + size_t n=checkArray(a); + size_t m=checkArray(b); + array *c=new array(n); + real *B=copyArrayC(b); + for(size_t i=0; i < n; ++i) { + array *ai=read<array*>(a,i); + if(checkArray(ai) != m) error(incommensurate); + real sum=0.0; + for(size_t j=0; j < m; ++j) + sum += read<real>(ai,j)*B[j]; + (*c)[i]=sum; + } + delete[] B; + return c; +} + +realarray *Operator *(realarray *a, realarray2 *b) +{ + size_t n=checkArray(a); + if(n != checkArray(b)) error(incommensurate); + real *A=copyArrayC(a); + + array **B=new array*[n]; + array *bk=read<array *>(b,0); + B[0]=bk; + size_t m=bk->size(); + for(size_t k=1; k < n; k++) { + array *bk=read<array *>(b,k); + if(bk->size() != m) error(incommensurate); + B[k]=bk; + } + array *c=new array(m); + + for(size_t i=0; i < m; ++i) { + real sum=0.0; + for(size_t k=0; k < n; ++k) + sum += A[k]*read<real>(B[k],i); + (*c)[i]=sum; + } + delete[] B; + delete[] A; + return c; +} + +realarray2 *Operator *(realarray2 *a, realarray2 *b) +{ + size_t n=checkArray(a); + + size_t nb=checkArray(b); + size_t na0=n == 0 ? 0 : checkArray(read<array*>(a,0)); + if(na0 != nb) + error(incommensurate); + + size_t nb0=nb == 0 ? 0 : checkArray(read<array*>(b,0)); + + array *c=new array(n); + + real *A=copyArray2C(a,false); + real *B=copyArray2C(b,false); + + for(size_t i=0; i < n; ++i) { + real *Ai=A+i*nb; + array *ci=new array(nb0); + (*c)[i]=ci; + for(size_t j=0; j < nb0; ++j) { + real sum=0.0; + size_t kj=j; + for(size_t k=0; k < nb; ++k, kj += nb0) + sum += Ai[k]*B[kj]; + (*ci)[j]=sum; + } + } + + delete[] B; + delete[] A; + + return c; +} + +triple Operator *(realarray2 *t, triple v) +{ + return *t*v; +} + +pair project(triple v, realarray2 *t) +{ + size_t n=checkArray(t); + if(n != 4) error(incommensurate); + array *t0=read<array*>(t,0); + array *t1=read<array*>(t,1); + array *t3=read<array*>(t,3); + if(checkArray(t0) != 4 || checkArray(t1) != 4 || checkArray(t3) != 4) + error(incommensurate); + + real x=v.getx(); + real y=v.gety(); + real z=v.getz(); + + real f=read<real>(t3,0)*x+read<real>(t3,1)*y+read<real>(t3,2)*z+ + read<real>(t3,3); + if(f == 0.0) dividebyzero(); + f=1.0/f; + + return pair((read<real>(t0,0)*x+read<real>(t0,1)*y+read<real>(t0,2)*z+ + read<real>(t0,3))*f, + (read<real>(t1,0)*x+read<real>(t1,1)*y+read<real>(t1,2)*z+ + read<real>(t1,3))*f); +} + +// Compute the dot product of vectors a and b. +real dot(realarray *a, realarray *b) +{ + size_t n=checkArrays(a,b); + real sum=0.0; + for(size_t i=0; i < n; ++i) + sum += read<real>(a,i)*read<real>(b,i); + return sum; +} + +// Solve the problem L\inv f, where f is an n vector and L is the n x n matrix +// +// [ b[0] c[0] a[0] ] +// [ a[1] b[1] c[1] ] +// [ a[2] b[2] c[2] ] +// [ ... ] +// [ c[n-1] a[n-1] b[n-1] ] +realarray *tridiagonal(realarray *a, realarray *b, realarray *c, realarray *f) +{ + size_t n=checkArrays(a,b); + checkEqual(n,checkArray(c)); + checkEqual(n,checkArray(f)); + + array *up=new array(n); + array& u=*up; + + if(n == 0) return up; + + // Special case: zero Dirichlet boundary conditions + if(read<real>(a,0) == 0.0 && read<real>(c,n-1) == 0.0) { + real temp=read<real>(b,0); + if(temp == 0.0) dividebyzero(); + temp=1.0/temp; + + real *work=new real[n]; + u[0]=read<real>(f,0)*temp; + work[0]=-read<real>(c,0)*temp; + + for(size_t i=1; i < n; i++) { + real temp=(read<real>(b,i)+read<real>(a,i)*work[i-1]); + if(temp == 0.0) {delete[] work; dividebyzero();} + temp=1.0/temp; + u[i]=(read<real>(f,i)-read<real>(a,i)*read<real>(u,i-1))*temp; + work[i]=-read<real>(c,i)*temp; + } + + for(size_t i=n-1; i >= 1; i--) + u[i-1]=read<real>(u,i-1)+work[i-1]*read<real>(u,i); + + delete[] work; + return up; + } + + real binv=read<real>(b,0); + if(binv == 0.0) dividebyzero(); + binv=1.0/binv; + + if(n == 1) {u[0]=read<real>(f,0)*binv; return up;} + if(n == 2) { + real factor=(read<real>(b,0)*read<real>(b,1)- + read<real>(a,0)*read<real>(c,1)); + if(factor== 0.0) dividebyzero(); + factor=1.0/factor; + real temp=(read<real>(b,0)*read<real>(f,1)- + read<real>(c,1)*read<real>(f,0))*factor; + u[0]=(read<real>(b,1)*read<real>(f,0)- + read<real>(a,0)*read<real>(f,1))*factor; + u[1]=temp; + return up; + } + + real *gamma=new real[n-2]; + real *delta=new real[n-2]; + + gamma[0]=read<real>(c,0)*binv; + delta[0]=read<real>(a,0)*binv; + u[0]=read<real>(f,0)*binv; + real beta=read<real>(c,n-1); + real fn=read<real>(f,n-1)-beta*read<real>(u,0); + real alpha=read<real>(b,n-1)-beta*delta[0]; + + for(size_t i=1; i <= n-3; i++) { + real alphainv=read<real>(b,i)-read<real>(a,i)*gamma[i-1]; + if(alphainv == 0.0) {delete[] gamma; delete[] delta; dividebyzero();} + alphainv=1.0/alphainv; + beta *= -gamma[i-1]; + gamma[i]=read<real>(c,i)*alphainv; + u[i]=(read<real>(f,i)-read<real>(a,i)*read<real>(u,i-1))*alphainv; + fn -= beta*read<real>(u,i); + delta[i]=-read<real>(a,i)*delta[i-1]*alphainv; + alpha -= beta*delta[i]; + } + + real alphainv=read<real>(b,n-2)-read<real>(a,n-2)*gamma[n-3]; + if(alphainv == 0.0) {delete[] gamma; delete[] delta; dividebyzero();} + alphainv=1.0/alphainv; + u[n-2]=(read<real>(f,n-2)-read<real>(a,n-2)*read<real>(u,n-3)) + *alphainv; + beta=read<real>(a,n-1)-beta*gamma[n-3]; + real dnm1=(read<real>(c,n-2)-read<real>(a,n-2)*delta[n-3])*alphainv; + real temp=alpha-beta*dnm1; + if(temp == 0.0) {delete[] gamma; delete[] delta; dividebyzero();} + u[n-1]=temp=(fn-beta*read<real>(u,n-2))/temp; + u[n-2]=read<real>(u,n-2)-dnm1*temp; + + for(size_t i=n-2; i >= 1; i--) + u[i-1]=read<real>(u,i-1)-gamma[i-1]*read<real>(u,i)-delta[i-1]*temp; + + delete[] delta; + delete[] gamma; + + return up; +} + +// Root solve by Newton-Raphson +real newton(Int iterations=100, callableReal *f, callableReal *fprime, real x, + bool verbose=false) +{ + static const real fuzz=1000.0*DBL_EPSILON; + Int i=0; + size_t oldPrec=0; + if(verbose) + oldPrec=cout.precision(DBL_DIG); + + real diff=DBL_MAX; + real lastdiff; + do { + real x0=x; + + Stack->push(x); + fprime->call(Stack); + real dfdx=pop<real>(Stack); + + if(dfdx == 0.0) { + x=DBL_MAX; + break; + } + + Stack->push(x); + f->call(Stack); + real fx=pop<real>(Stack); + + x -= fx/dfdx; + + lastdiff=diff; + + if(verbose) + cout << "Newton-Raphson: " << x << endl; + + diff=fabs(x-x0); + if(++i == iterations) { + x=DBL_MAX; + break; + } + } while (diff != 0.0 && (diff < lastdiff || diff > fuzz*fabs(x))); + + if(verbose) + cout.precision(oldPrec); + return x; +} + +// Root solve by Newton-Raphson bisection +// cf. routine rtsafe (Press et al., Numerical Recipes, 1991). +real newton(Int iterations=100, callableReal *f, callableReal *fprime, real x1, + real x2, bool verbose=false) +{ + static const real fuzz=1000.0*DBL_EPSILON; + size_t oldPrec=0; + if(verbose) + oldPrec=cout.precision(DBL_DIG); + + Stack->push(x1); + f->call(Stack); + real f1=pop<real>(Stack); + if(f1 == 0.0) return x1; + + Stack->push(x2); + f->call(Stack); + real f2=pop<real>(Stack); + if(f2 == 0.0) return x2; + + if((f1 > 0.0 && f2 > 0.0) || (f1 < 0.0 && f2 < 0.0)) { + ostringstream buf; + buf << "root not bracketed, f(x1)=" << f1 << ", f(x2)=" << f2 << endl; + error(buf); + } + + real x=0.5*(x1+x2); + real dxold=fabs(x2-x1); + if(f1 > 0.0) { + real temp=x1; + x1=x2; + x2=temp; + } + + if(verbose) + cout << "midpoint: " << x << endl; + + real dx=dxold; + Stack->push(x); + f->call(Stack); + real y=pop<real>(Stack); + + Stack->push(x); + fprime->call(Stack); + real dy=pop<real>(Stack); + + Int j; + for(j=0; j < iterations; j++) { + if(((x-x2)*dy-y)*((x-x1)*dy-y) >= 0.0 || fabs(2.0*y) > fabs(dxold*dy)) { + dxold=dx; + dx=0.5*(x2-x1); + x=x1+dx; + if(verbose) + cout << "bisection: " << x << endl; + if(x1 == x) return x; + } else { + dxold=dx; + dx=y/dy; + real temp=x; + x -= dx; + if(verbose) + cout << "Newton-Raphson: " << x << endl; + if(temp == x) return x; + } + if(fabs(dx) < fuzz*fabs(x)) return x; + + Stack->push(x); + f->call(Stack); + y=pop<real>(Stack); + + Stack->push(x); + fprime->call(Stack); + dy=pop<real>(Stack); + + if(y < 0.0) x1=x; + else x2=x; + } + if(verbose) + cout.precision(oldPrec); + return (j == iterations) ? DBL_MAX : x; +} + +real simpson(callableReal *f, real a, real b, real acc=DBL_EPSILON, + real dxmax=0) +{ + real integral; + if(dxmax == 0) dxmax=b-a; + Func=f; + FuncStack=Stack; + if(!simpson(integral,wrapFunction,a,b,acc,dxmax)) + error("nesting capacity exceeded in simpson"); + return integral; +} + +// Compute the fast Fourier transform of a pair array +pairarray* :pairArrayFFT(pairarray *a, Int sign=1) +{ + unsigned n=(unsigned) checkArray(a); +#ifdef HAVE_LIBFFTW3 + array *c=new array(n); + if(n) { + Complex *f=FFTWComplex(n); + fft1d Forward(n,intcast(sign),f); + + for(size_t i=0; i < n; i++) { + pair z=read<pair>(a,i); + f[i]=Complex(z.getx(),z.gety()); + } + Forward.fft(f); + + for(size_t i=0; i < n; i++) { + Complex z=f[i]; + (*c)[i]=pair(z.real(),z.imag()); + } + FFTWdelete(f); + } +#else + unused(&n); + unused(&sign); + array *c=new array(0); +#endif // HAVE_LIBFFTW3 + return c; +} + +Intarray2 *triangulate(pairarray *z) +{ + size_t nv=checkArray(z); +// Call robust version of Gilles Dumoulin's port of Paul Bourke's +// triangulation code. + + XYZ *pxyz=new XYZ[nv+3]; + ITRIANGLE *V=new ITRIANGLE[4*nv]; + + for(size_t i=0; i < nv; ++i) { + pair w=read<pair>(z,i); + pxyz[i].p[0]=w.getx(); + pxyz[i].p[1]=w.gety(); + pxyz[i].i=(Int) i; + } + + Int ntri; + Triangulate((Int) nv,pxyz,V,ntri,true,false); + + size_t nt=(size_t) ntri; + array *t=new array(nt); + for(size_t i=0; i < nt; ++i) { + array *ti=new array(3); + (*t)[i]=ti; + ITRIANGLE *Vi=V+i; + (*ti)[0]=pxyz[Vi->p1].i; + (*ti)[1]=pxyz[Vi->p2].i; + (*ti)[2]=pxyz[Vi->p3].i; + } + + delete[] V; + delete[] pxyz; + return t; +} + +real norm(realarray *a) +{ + size_t n=checkArray(a); + real M=0.0; + for(size_t i=0; i < n; ++i) { + real x=fabs(vm::read<real>(a,i)); + if(x > M) M=x; + } + return M; +} + +real norm(realarray2 *a) +{ + size_t n=checkArray(a); + real M=0.0; + for(size_t i=0; i < n; ++i) { + vm::array *ai=vm::read<vm::array*>(a,i); + size_t m=checkArray(ai); + for(size_t j=0; j < m; ++j) { + real a=fabs(vm::read<real>(ai,j)); + if(a > M) M=a; + } + } + return M; +} + +real norm(triplearray2 *a) +{ + size_t n=checkArray(a); + real M=0.0; + for(size_t i=0; i < n; ++i) { + vm::array *ai=vm::read<vm::array*>(a,i); + size_t m=checkArray(ai); + for(size_t j=0; j < m; ++j) { + real a=vm::read<triple>(ai,j).abs2(); + if(a > M) M=a; + } + } + return sqrt(M); +} + +real change2(triplearray2 *a) +{ + size_t n=checkArray(a); + if(n == 0) return 0.0; + + vm::array *a0=vm::read<vm::array*>(a,0); + size_t m=checkArray(a0); + if(m == 0) return 0.0; + triple a00=vm::read<triple>(a0,0); + real M=0.0; + + for(size_t i=0; i < n; ++i) { + vm::array *ai=vm::read<vm::array*>(a,i); + size_t m=checkArray(ai); + for(size_t j=0; j < m; ++j) { + real a=(vm::read<triple>(ai,j)-a00).abs2(); + if(a > M) M=a; + } + } + return M; +} + +triple minbezier(triplearray2 *P, triple b) +{ + real *A=copyTripleArray2Components(P,true,4); + b=triple(bound(A,::min,b.getx(),sqrtFuzz*norm(A,16)), + bound(A+16,::min,b.gety(),sqrtFuzz*norm(A+16,16)), + bound(A+32,::min,b.getz(),sqrtFuzz*norm(A+32,16))); + delete[] A; + return b; +} + +triple maxbezier(triplearray2 *P, triple b) +{ + real *A=copyTripleArray2Components(P,true,4); + b=triple(bound(A,::max,b.getx(),sqrtFuzz*norm(A,16)), + bound(A+16,::max,b.gety(),sqrtFuzz*norm(A+16,16)), + bound(A+32,::max,b.getz(),sqrtFuzz*norm(A+32,16))); + delete[] A; + return b; +} + +pair minratio(triplearray2 *P, pair b) +{ + triple *A=copyTripleArray2C(P,true,4); + real fuzz=sqrtFuzz*norm(A,16); + b=pair(bound(A,::min,xratio,b.getx(),fuzz), + bound(A,::min,yratio,b.gety(),fuzz)); + delete[] A; + return b; +} + +pair maxratio(triplearray2 *P, pair b) +{ + triple *A=copyTripleArray2C(P,true,4); + real fuzz=sqrtFuzz*norm(A,16); + b=pair(bound(A,::max,xratio,b.getx(),fuzz), + bound(A,::max,yratio,b.gety(),fuzz)); + delete[] A; + return b; +} |