FindPtFuncs.h

Go to the documentation of this file.

#ifndef FINDPTFUNCS_H
#define FINDPTFUNCS_H
 
#include "float.h"
#include "math.h"
 
/*======================================================
/ from types.h
/======================================================
*/
 
#define MOAB_POLY_EPS ( 128 * DBL_EPSILON )
#define MOAB_POLY_PI 3.1415926535897932384626433832795028841971693993751058209749445923
 
#define mbsqrt sqrt
#define mbabs fabs
#define mbcos cos
#define mbsin sin
#define mbfloor floor
#define mbceil ceil
 
#ifdef INTEGER
#undef INTEGER
#endif
 
#ifdef real
#undef real
#endif
 
/* integer type to use for everything */
#if defined( USE_LONG )
#define INTEGER long
#elif defined( USE_LONG_LONG )
#define INTEGER long long
#elif defined( USE_SHORT )
#define INTEGER short
#else
#define INTEGER int
#endif
 
/* when defined, use the given type for global indices instead of INTEGER */
#if defined( USE_GLOBAL_LONG_LONG )
#define GLOBAL_INT long long
#elif defined( USE_GLOBAL_LONG )
#define GLOBAL_INT long
#else
#define GLOBAL_INT long
#endif
 
/* floating point type to use for everything */
#if defined( USE_FLOAT )
typedef float realType;
#elif defined( USE_LONG_DOUBLE )
typedef long double realType;
#else
typedef double realType;
#endif
 
/* apparently uint and ulong can be defined already in standard headers */
#ifndef uint
typedef signed INTEGER sint;
#endif
 
#ifndef uint
typedef unsigned INTEGER uint;
#endif
#undef INTEGER
 
#ifndef slong
#ifdef GLOBAL_INT
typedef signed GLOBAL_INT slong;
#else
typedef sint slong;
#endif
#endif
 
#ifndef ulong
#ifdef GLOBAL_INT
typedef unsigned GLOBAL_INT ulong;
#else
typedef uint ulong;
#endif
#endif
 
/*======================================================
/ from poly.h
/======================================================
*/
 
/* 
 For brevity's sake, some names have been shortened
 Quadrature rules
 Gauss -> Gauss-Legendre quadrature (open)
 Lobatto -> Gauss-Lobatto-Legendre quadrature (closed at both ends)
 Polynomial bases
 Legendre -> Legendre basis
 Gauss -> Lagrangian basis using Gauss quadrature nodes
 Lobatto -> Lagrangian basis using Lobatto quadrature nodes
*/
 
/*--------------------------------------------------------------------------
 Legendre Polynomial Matrix Computation
 (compute P_i(x_j) for i = 0, ..., n and a given set of x)
 --------------------------------------------------------------------------*/
 
/* precondition: n >= 1
 inner index is x index (0 ... m-1);
 outer index is Legendre polynomial number (0 ... n)
 */
void legendre_matrix( const realType* x, int m, realType* P, int n );
 
/* precondition: n >= 1
 inner index is Legendre polynomial number (0 ... n)
 outer index is x index (0 ... m-1);
 */
void legendre_matrix_t( const realType* x, int m, realType* P, int n );
 
/* precondition: n >= 1
 compute P_i(x) with i = 0 ... n
 */
void legendre_row( realType x, realType* P, int n );
 
/*--------------------------------------------------------------------------
 Quadrature Nodes and Weights Calculation
 
 call the _nodes function before calling the _weights function
 --------------------------------------------------------------------------*/
 
void gauss_nodes( realType* z, int n ); /* n nodes (order = 2n-1) */
void lobatto_nodes( realType* z, int n ); /* n nodes (order = 2n-3) */
 
void gauss_weights( const realType* z, realType* w, int n );
void lobatto_weights( const realType* z, realType* w, int n );
 
/*--------------------------------------------------------------------------
 Lagrangian to Legendre Change-of-basis Matrix
 --------------------------------------------------------------------------*/
 
/* precondition: n >= 2
 given the Gauss quadrature rule (z,w,n), compute the square matrix J
 for transforming from the Gauss basis to the Legendre basis:
 
 u_legendre(i) = sum_j J(i,j) u_gauss(j)
 
 computes J = .5 (2i+1) w P (z )
 ij j i j
 
 in column major format (inner index is i, the Legendre index)
 */
void gauss_to_legendre( const realType* z, const realType* w, int n, realType* J );
 
/* precondition: n >= 2
 same as above, but
 in row major format (inner index is j, the Gauss index)
 */
void gauss_to_legendre_t( const realType* z, const realType* w, int n, realType* J );
 
/* precondition: n >= 3
 given the Lobatto quadrature rule (z,w,n), compute the square matrix J
 for transforming from the Lobatto basis to the Legendre basis:
 
 u_legendre(i) = sum_j J(i,j) u_lobatto(j)
 
 in column major format (inner index is i, the Legendre index)
 */
void lobatto_to_legendre( const realType* z, const realType* w, int n, realType* J );
 
/*--------------------------------------------------------------------------
 Lagrangian basis function evaluation
 --------------------------------------------------------------------------*/
 
/* given the Lagrangian nodes (z,n) and evaluation points (x,m)
 evaluate all Lagrangian basis functions at all points x
 
 inner index of output J is the basis function index (row-major format)
 provide work array with space for 4*n doubles
 */
void lagrange_weights( const realType* z, unsigned n, const realType* x, unsigned m, realType* J, realType* work );
 
/* given the Lagrangian nodes (z,n) and evaluation points (x,m)
 evaluate all Lagrangian basis functions and their derivatives
 
 inner index of outputs J,D is the basis function index (row-major format)
 provide work array with space for 6*n doubles
 */
void lagrange_weights_deriv( const realType* z,
 unsigned n,
 const realType* x,
 unsigned m,
 realType* J,
 realType* D,
 realType* work );
 
/*--------------------------------------------------------------------------
 Speedy Lagrangian Interpolation
 
 Usage:
 
 lagrange_data p;
 lagrange_setup(&p,z,n); * setup for nodes z[0 ... n-1] *
 
 the weights
 p->J [0 ... n-1] interpolation weights
 p->D [0 ... n-1] 1st derivative weights
 p->D2[0 ... n-1] 2nd derivative weights
 are computed for a given x with:
 lagrange_0(p,x); * compute p->J *
 lagrange_1(p,x); * compute p->J, p->D *
 lagrange_2(p,x); * compute p->J, p->D, p->D2 *
 lagrange_2u(p); * compute p->D2 after call of lagrange_1(p,x); *
 These functions use the z array supplied to setup
 (that pointer should not be freed between calls)
 Weights for x=z[0] and x=z[n-1] are computed during setup; access as:
 p->J_z0, etc. and p->J_zn, etc.
 
 lagrange_free(&p); * deallocate memory allocated by setup *
 --------------------------------------------------------------------------*/
 
typedef struct
{
 unsigned n; /* number of Lagrange nodes */
 const realType* z; /* Lagrange nodes (user-supplied) */
 realType *J, *D, *D2; /* weights for 0th,1st,2nd derivatives */
 realType *J_z0, *D_z0, *D2_z0; /* ditto at z[0] (computed at setup) */
 realType *J_zn, *D_zn, *D2_zn; /* ditto at z[n-1] (computed at setup) */
 realType *w, *d, *u0, *v0, *u1, *v1, *u2, *v2; /* work data */
} lagrange_data;
 
void lagrange_setup( lagrange_data* p, const realType* z, unsigned n );
void lagrange_free( lagrange_data* p );
 
void lagrange_0( lagrange_data* p, realType x );
void lagrange_1( lagrange_data* p, realType x );
void lagrange_2( lagrange_data* p, realType x );
void lagrange_2u( lagrange_data* p );
 
/*======================================================
/ from tensor.h
/======================================================
*/
 
/*--------------------------------------------------------------------------
 1-,2-,3-d Tensor Application
 
 the 3d case:
 tensor_f3(R,mr,nr, S,ms,ns, T,mt,nt, u,v, work1,work2)
 gives v = [ R (x) S (x) T ] u
 where R is mr x nr, S is ms x ns, T is mt x nt,
 each in row- or column-major format according to f := r | c
 u is nr x ns x nt in column-major format (inner index is r)
 v is mr x ms x mt in column-major format (inner index is r)
 --------------------------------------------------------------------------*/
 
void tensor_c1( const realType* R, unsigned mr, unsigned nr, const realType* u, realType* v );
void tensor_r1( const realType* R, unsigned mr, unsigned nr, const realType* u, realType* v );
 
/* work holds mr*ns realTypes */
void tensor_c2( const realType* R,
 unsigned mr,
 unsigned nr,
 const realType* S,
 unsigned ms,
 unsigned ns,
 const realType* u,
 realType* v,
 realType* work );
void tensor_r2( const realType* R,
 unsigned mr,
 unsigned nr,
 const realType* S,
 unsigned ms,
 unsigned ns,
 const realType* u,
 realType* v,
 realType* work );
 
/* work1 holds mr*ns*nt realTypes,
 work2 holds mr*ms*nt realTypes */
void tensor_c3( const realType* R,
 unsigned mr,
 unsigned nr,
 const realType* S,
 unsigned ms,
 unsigned ns,
 const realType* T,
 unsigned mt,
 unsigned nt,
 const realType* u,
 realType* v,
 realType* work1,
 realType* work2 );
void tensor_r3( const realType* R,
 unsigned mr,
 unsigned nr,
 const realType* S,
 unsigned ms,
 unsigned ns,
 const realType* T,
 unsigned mt,
 unsigned nt,
 const realType* u,
 realType* v,
 realType* work1,
 realType* work2 );
 
/*--------------------------------------------------------------------------
 1-,2-,3-d Tensor Application of Row Vectors (for Interpolation)
 
 the 3d case:
 v = tensor_i3(Jr,nr, Js,ns, Jt,nt, u, work)
 same effect as tensor_r3(Jr,1,nr, Js,1,ns, Jt,1,nt, u,&v, work1,work2):
 gives v = [ Jr (x) Js (x) Jt ] u
 where Jr, Js, Jt are row vectors (interpolation weights)
 u is nr x ns x nt in column-major format (inner index is r)
 v is a scalar
 --------------------------------------------------------------------------*/
 
realType tensor_i1( const realType* Jr, unsigned nr, const realType* u );
 
/* work holds ns realTypes */
realType tensor_i2( const realType* Jr,
 unsigned nr,
 const realType* Js,
 unsigned ns,
 const realType* u,
 realType* work );
 
/* work holds ns*nt + nt realTypes */
realType tensor_i3( const realType* Jr,
 unsigned nr,
 const realType* Js,
 unsigned ns,
 const realType* Jt,
 unsigned nt,
 const realType* u,
 realType* work );
 
/*--------------------------------------------------------------------------
 1-,2-,3-d Tensor Application of Row Vectors
 for simultaneous Interpolation and Gradient computation
 
 the 3d case:
 v = tensor_ig3(Jr,Dr,nr, Js,Ds,ns, Jt,Dt,nt, u,g, work)
 gives v = [ Jr (x) Js (x) Jt ] u
 g_0 = [ Dr (x) Js (x) Jt ] u
 g_1 = [ Jr (x) Ds (x) Jt ] u
 g_2 = [ Jr (x) Js (x) Dt ] u
 where Jr,Dr,Js,Ds,Jt,Dt are row vectors
 (interpolation & derivative weights)
 u is nr x ns x nt in column-major format (inner index is r)
 v is a scalar, g is an array of 3 realTypes
 --------------------------------------------------------------------------*/
 
realType tensor_ig1( const realType* Jr, const realType* Dr, unsigned nr, const realType* u, realType* g );
 
/* work holds 2*ns realTypes */
realType tensor_ig2( const realType* Jr,
 const realType* Dr,
 unsigned nr,
 const realType* Js,
 const realType* Ds,
 unsigned ns,
 const realType* u,
 realType* g,
 realType* work );
 
/* work holds 2*ns*nt + 3*ns realTypes */
realType tensor_ig3( const realType* Jr,
 const realType* Dr,
 unsigned nr,
 const realType* Js,
 const realType* Ds,
 unsigned ns,
 const realType* Jt,
 const realType* Dt,
 unsigned nt,
 const realType* u,
 realType* g,
 realType* work );
 
/*======================================================
/ from findpt.h
/======================================================
*/
 
typedef struct
{
 realType x[2], A[4], axis_bnd[4];
} obbox_2;
 
typedef struct
{
 realType x[3], A[9], axis_bnd[6];
} obbox_3;
 
typedef struct
{
 unsigned hash_n;
 realType bnd[4]; /* bounds for all elements */
 realType fac[2]; /* fac[i] = hash_n / (bnd[2*i+1]-bnd[2*i]) */
 obbox_2* obb; /* obb[nel] -- bounding box info for each element */
 uint* offset; /* hash table -- for cell i,j:
 uint index = j*hash_n+i,
 b = offset[index ],
 e = offset[index+1];
 elements in cell are
 offset[b], offset[b+1], ..., offset[e-1] */
 unsigned max; /* maximum # of elements in any cell */
} hash_data_2;
 
typedef struct
{
 unsigned hash_n;
 realType bnd[6]; /* bounds for all elements */
 realType fac[3]; /* fac[i] = hash_n / (bnd[2*i+1]-bnd[2*i]) */
 obbox_3* obb; /* obb[nel] -- bounding box info for each element */
 uint* offset; /* hash table -- for cell i,j,k:
 uint index = (k*hash_n+j)*hash_n+i,
 b = offset[index ],
 e = offset[index+1];
 elements in cell are
 offset[b], offset[b+1], ..., offset[e-1] */
 unsigned max; /* maximum # of elements in any cell */
} hash_data_3;
 
typedef struct
{
 uint el;
 realType r[3];
 realType dist;
} findpt_listel;
 
typedef struct
{
 unsigned constraints;
 unsigned de, d1;
 realType *x[2], *fd1[2];
} opt_edge_data_2;
 
typedef struct
{
 unsigned constraints;
 realType x[2], jac[4];
} opt_point_data_2;
 
typedef struct
{
 lagrange_data* ld;
 unsigned size[3];
 const realType* elx[2];
 opt_edge_data_2 ed;
 opt_point_data_2 pd;
 realType* work;
 realType x[2], jac[4];
} opt_data_2;
 
typedef struct
{
 const realType* xw[2]; /* geometry data */
 realType* z[2]; /* lobatto nodes */
 lagrange_data ld[2]; /* interpolation, derivative weights & data */
 unsigned nptel; /* nodes per element */
 hash_data_2* hash; /* geometric hashing data */
 findpt_listel *list, **sorted, **end;
 /* pre-allocated list of elements to
 check (found by hashing), and
 pre-allocated list of pointers into
 the first list for sorting */
 opt_data_2* od; /* data for the optimization algorithm */
 realType* od_work;
} findpt_data_2;
 
typedef struct
{
 unsigned constraints;
 unsigned dn, d1, d2;
 realType *x[3], *fdn[3];
} opt_face_data_3;
 
typedef struct
{
 unsigned constraints;
 unsigned de, d1, d2;
 realType *x[3], *fd1[3], *fd2[3];
} opt_edge_data_3;
 
typedef struct
{
 unsigned constraints;
 realType x[3], jac[9];
} opt_point_data_3;
 
typedef struct
{
 lagrange_data* ld;
 unsigned size[4];
 const realType* elx[3];
 opt_face_data_3 fd;
 opt_edge_data_3 ed;
 opt_point_data_3 pd;
 realType* work;
 realType x[3], jac[9];
} opt_data_3;
 
typedef struct
{
 const realType* xw[3]; /* geometry data */
 realType* z[3]; /* lobatto nodes */
 lagrange_data ld[3]; /* interpolation, derivative weights & data */
 unsigned nptel; /* nodes per element */
 hash_data_3* hash; /* geometric hashing data */
 findpt_listel *list, **sorted, **end;
 /* pre-allocated list of elements to
 check (found by hashing), and
 pre-allocated list of pointers into
 the first list for sorting */
 opt_data_3* od; /* data for the optimization algorithm */
 realType* od_work;
} findpt_data_3;
 
findpt_data_2* findpt_setup_2( const realType* const xw[2],
 const unsigned n[2],
 uint nel,
 uint max_hash_size,
 realType bbox_tol );
findpt_data_3* findpt_setup_3( const realType* const xw[3],
 const unsigned n[3],
 uint nel,
 uint max_hash_size,
 realType bbox_tol );
 
void findpt_free_2( findpt_data_2* p );
void findpt_free_3( findpt_data_3* p );
 
const realType* findpt_allbnd_2( const findpt_data_2* p );
const realType* findpt_allbnd_3( const findpt_data_3* p );
 
typedef int ( *findpt_func )( void*, const realType*, int, uint*, realType*, realType* );
int findpt_2( findpt_data_2* p, const realType x[2], int guess, uint* el, realType r[2], realType* dist );
int findpt_3( findpt_data_3* p, const realType x[3], int guess, uint* el, realType r[3], realType* dist );
 
void findpt_weights_2( findpt_data_2* p, const realType r[2] );
 
void findpt_weights_3( findpt_data_3* p, const realType r[3] );
 
double findpt_eval_2( findpt_data_2* p, const realType* u );
 
double findpt_eval_3( findpt_data_3* p, const realType* u );
 
/*======================================================
/ from extrafindpt.h
/======================================================
*/
 
void opt_alloc_3( opt_data_3* p, lagrange_data* ld );
void opt_free_3( opt_data_3* p );
double opt_findpt_3( opt_data_3* p,
 const realType* const elx[3],
 const realType xstar[3],
 realType r[3],
 unsigned* constr );
void opt_vol_set_intp_3( opt_data_3* p, const realType r[3] );
 
/* for 2d spectralQuad */
/*--------------------------------------------------------------------------
 
 2 - D
 
 --------------------------------------------------------------------------*/
 
void opt_alloc_2( opt_data_2* p, lagrange_data* ld );
void opt_free_2( opt_data_2* p );
double opt_findpt_2( opt_data_2* p,
 const realType* const elx[2],
 const realType xstar[2],
 realType r[2],
 unsigned* constr );
 
extern const unsigned opt_no_constraints_2;
extern const unsigned opt_no_constraints_3;
 
/*======================================================
/ from errmem.h
/======================================================
*/
 
/* requires:
 <stdlib.h> for malloc, calloc, realloc, free
*/
 
/*--------------------------------------------------------------------------
 Error Reporting
 Memory Allocation Wrappers to Catch Out-of-memory
 --------------------------------------------------------------------------*/
 
/* #include "malloc.h" */
#include <stdlib.h>
 
#ifdef __GNUC__
void fail( const char* fmt, ... ) __attribute__( ( noreturn ) );
#define MAYBE_UNUSED __attribute__( ( unused ) )
#else
void fail( const char* fmt, ... );
#define MAYBE_UNUSED
#endif
 
#if 0
{}
#endif
 
static void* smalloc( size_t size, const char* file ) MAYBE_UNUSED;
static void* smalloc( size_t size, const char* file )
{
 void* res = malloc( size );
 if( !res && size ) fail( "%s: allocation of %d bytes failed\n", file, (int)size );
 return res;
}
 
static void* scalloc( size_t nmemb, size_t size, const char* file ) MAYBE_UNUSED;
static void* scalloc( size_t nmemb, size_t size, const char* file )
{
 void* res = calloc( nmemb, size );
 if( !res && nmemb ) fail( "%s: allocation of %d bytes failed\n", file, (int)size * nmemb );
 return res;
}
 
static void* srealloc( void* ptr, size_t size, const char* file ) MAYBE_UNUSED;
static void* srealloc( void* ptr, size_t size, const char* file )
{
 void* res = realloc( ptr, size );
 if( !res && size ) fail( "%s: allocation of %d bytes failed\n", file, (int)size );
 return res;
}
 
#define tmalloc( type, count ) ( (type*)smalloc( ( count ) * sizeof( type ), __FILE__ ) )
#define tcalloc( type, count ) ( (type*)scalloc( ( count ), sizeof( type ), __FILE__ ) )
#define trealloc( type, ptr, count ) ( (type*)srealloc( ( ptr ), ( count ) * sizeof( type ), __FILE__ ) )
/*
typedef struct { size_t size; void *ptr; } buffer;
 
static void buffer_init_(buffer *b, size_t size, const char *file) MAYBE_UNUSED;
static void buffer_init_(buffer *b, size_t size, const char *file)
{
 b->size=size, b->ptr=smalloc(size,file);
}
static void buffer_reserve_(buffer *b, size_t min, const char *file)
 MAYBE_UNUSED;
static void buffer_reserve_(buffer *b, size_t min, const char *file)
{
 size_t size = b->size;
 if(size<min) {
 size+=size/2+1;
 if(size<min) size=min;
 b->ptr=srealloc(b->ptr,size,file);
 }
}
static void buffer_free(buffer *b) MAYBE_UNUSED;
static void buffer_free(buffer *b) { free(b->ptr); }
 
#define buffer_init(b,size) buffer_init_(b,size,__FILE__)
#define buffer_reserve(b,min) buffer_reserve_(b,min,__FILE__)
*/
 
/*======================================================
/ from minmax.h
/======================================================
*/
 
/*--------------------------------------------------------------------------
 Min, Max, Norm
 --------------------------------------------------------------------------*/
 
#ifdef __GNUC__
#define MAYBE_UNUSED __attribute__( ( unused ) )
#else
#define MAYBE_UNUSED
#endif
 
#define DECLMINMAX( type, prefix ) \
 static type prefix##min_2( type a, type b ) MAYBE_UNUSED; \
 static type prefix##min_2( type a, type b ) \
 { \
 return b < a ? b : a; \
 } \
 static type prefix##max_2( type a, type b ) MAYBE_UNUSED; \
 static type prefix##max_2( type a, type b ) \
 { \
 return a > b ? a : b; \
 } \
 static void prefix##minmax_2( type* min, type* max, type a, type b ) MAYBE_UNUSED; \
 static void prefix##minmax_2( type* min, type* max, type a, type b ) \
 { \
 if( b < a ) \
 *min = b, *max = a; \
 else \
 *min = a, *max = b; \
 } \
 static type prefix##min_3( type a, type b, type c ) MAYBE_UNUSED; \
 static type prefix##min_3( type a, type b, type c ) \
 { \
 return b < a ? ( c < b ? c : b ) : ( c < a ? c : a ); \
 } \
 static type prefix##max_3( type a, type b, type c ) MAYBE_UNUSED; \
 static type prefix##max_3( type a, type b, type c ) \
 { \
 return a > b ? ( a > c ? a : c ) : ( b > c ? b : c ); \
 } \
 static void prefix##minmax_3( type* min, type* max, type a, type b, type c ) MAYBE_UNUSED; \
 static void prefix##minmax_3( type* min, type* max, type a, type b, type c ) \
 { \
 if( b < a ) \
 *min = prefix##min_2( b, c ), *max = prefix##max_2( a, c ); \
 else \
 *min = prefix##min_2( a, c ), *max = prefix##max_2( b, c ); \
 }
 
DECLMINMAX( int, i )
DECLMINMAX( unsigned, u )
DECLMINMAX( realType, r )
#undef DECLMINMAX
 
static realType r1norm_1( realType a ) MAYBE_UNUSED;
static realType r1norm_1( realType a )
{
 return mbabs( a );
}
static realType r1norm_2( realType a, realType b ) MAYBE_UNUSED;
static realType r1norm_2( realType a, realType b )
{
 return mbabs( a ) + mbabs( b );
}
static realType r1norm_3( realType a, realType b, realType c ) MAYBE_UNUSED;
static realType r1norm_3( realType a, realType b, realType c )
{
 return mbabs( a ) + mbabs( b ) + mbabs( c );
}
static realType r2norm_1( realType a ) MAYBE_UNUSED;
static realType r2norm_1( realType a )
{
 return mbsqrt( a * a );
}
static realType r2norm_2( realType a, realType b ) MAYBE_UNUSED;
static realType r2norm_2( realType a, realType b )
{
 return mbsqrt( a * a + b * b );
}
static realType r2norm_3( realType a, realType b, realType c ) MAYBE_UNUSED;
static realType r2norm_3( realType a, realType b, realType c )
{
 return mbsqrt( a * a + b * b + c * c );
}
 
#endif