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Removed tabs from c_functions.c refaactored quadgr

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Per A Brodtkorb 10 years ago
parent 4366d3eeb0
commit c2a9247d00
2 changed files with 467 additions and 460 deletions
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307
wafo/integrate.py
Unescape Escape View File

@ -1003,163 +1003,170 @@ def richardson(Q, k):
return R
def quadgr(fun, a, b, abseps=1e-5, max_iter=17):
'''
Gauss-Legendre quadrature with Richardson extrapolation.
[Q,ERR] = QUADGR(FUN,A,B,TOL) approximates the integral of a function
FUN from A to B with an absolute error tolerance TOL. FUN is a function
handle and must accept vector arguments. TOL is 1e-6 by default. Q is
the integral approximation and ERR is an estimate of the absolute error.
QUADGR uses a 12-point Gauss-Legendre quadrature. The error estimate is
based on successive interval bisection. Richardson extrapolation
accelerates the convergence for some integrals, especially integrals
with endpoint singularities.
Examples
--------
>>> import numpy as np
>>> Q, err = quadgr(np.log,0,1)
>>> quadgr(np.exp,0,9999*1j*np.pi)
(-2.0000000000122662, 2.1933237448479304e-09)
>>> quadgr(lambda x: np.sqrt(4-x**2),0,2,1e-12)
(3.1415926535897811, 1.5809575870662229e-13)
>>> quadgr(lambda x: x**-0.75,0,1)
(4.0000000000000266, 5.6843418860808015e-14)
>>> quadgr(lambda x: 1./np.sqrt(1-x**2),-1,1)
(3.141596056985029, 6.2146261559092864e-06)
>>> quadgr(lambda x: np.exp(-x**2),-np.inf,np.inf,1e-9) #% sqrt(pi)
(1.7724538509055152, 1.9722334876348668e-11)
>>> quadgr(lambda x: np.cos(x)*np.exp(-x),0,np.inf,1e-9)
(0.50000000000000044, 7.3296813063450372e-11)
class _Quadgr(object):
def __call__(self, fun, a, b, abseps=1e-5, max_iter=17):
'''
Gauss-Legendre quadrature with Richardson extrapolation.
[Q,ERR] = QUADGR(FUN,A,B,TOL) approximates the integral of a function
FUN from A to B with an absolute error tolerance TOL. FUN is a function
handle and must accept vector arguments. TOL is 1e-6 by default. Q is
the integral approximation and ERR is an estimate of the absolute
error.
QUADGR uses a 12-point Gauss-Legendre quadrature. The error estimate is
based on successive interval bisection. Richardson extrapolation
accelerates the convergence for some integrals, especially integrals
with endpoint singularities.
Examples
--------
>>> import numpy as np
>>> Q, err = quadgr(np.log,0,1)
>>> quadgr(np.exp,0,9999*1j*np.pi)
(-2.0000000000122662, 2.1933237448479304e-09)
>>> quadgr(lambda x: np.sqrt(4-x**2),0,2,1e-12)
(3.1415926535897811, 1.5809575870662229e-13)
>>> quadgr(lambda x: x**-0.75,0,1)
(4.0000000000000266, 5.6843418860808015e-14)
>>> quadgr(lambda x: 1./np.sqrt(1-x**2),-1,1)
(3.141596056985029, 6.2146261559092864e-06)
>>> quadgr(lambda x: np.exp(-x**2),-np.inf,np.inf,1e-9) #% sqrt(pi)
(1.7724538509055152, 1.9722334876348668e-11)
>>> quadgr(lambda x: np.cos(x)*np.exp(-x),0,np.inf,1e-9)
(0.50000000000000044, 7.3296813063450372e-11)
See also
--------
QUAD,
QUADGK
'''
# Author: jonas.lundgren@saabgroup.com, 2009. license BSD
# Order limits (required if infinite limits)
a = np.asarray(a)
b = np.asarray(b)
if a == b:
Q = b - a
err = b - a
return Q, err
elif np.real(a) > np.real(b):
reverse = True
a, b = b, a
else:
reverse = False
# Infinite limits
if np.isinf(a) | np.isinf(b):
# Check real limits
if ~ np.isreal(a) | ~np.isreal(b) | np.isnan(a) | np.isnan(b):
raise ValueError('Infinite intervals must be real.')
# Change of variable
if np.isfinite(a) & np.isinf(b):
# a to inf
[Q, err] = quadgr(lambda t: fun(a + t / (1 - t)) / (1 - t) ** 2,
0, 1, abseps)
elif np.isinf(a) & np.isfinite(b):
# -inf to b
[Q, err] = quadgr(lambda t: fun(b + t / (1 + t)) / (1 + t) ** 2,
-1, 0, abseps)
else: # -inf to inf
[Q1, err1] = quadgr(lambda t: fun(t / (1 - t)) / (1 - t) ** 2,
0, 1, abseps / 2)
[Q2, err2] = quadgr(lambda t: fun(t / (1 + t)) / (1 + t) ** 2,
-1, 0, abseps / 2)
Q = Q1 + Q2
err = err1 + err2
# Reverse direction
if reverse:
Q = -Q
return Q, err
# Gauss-Legendre quadrature (12-point)
xq = np.asarray(
[0.12523340851146894, 0.36783149899818018, 0.58731795428661748,
0.76990267419430469, 0.9041172563704748, 0.98156063424671924])
wq = np.asarray(
[0.24914704581340288, 0.23349253653835478, 0.20316742672306584,
0.16007832854334636, 0.10693932599531818, 0.047175336386511842])
xq = np.hstack((xq, -xq))
wq = np.hstack((wq, wq))
nq = len(xq)
dtype = np.result_type(fun(a), fun(b))
# Initiate vectors
Q0 = zeros(max_iter, dtype=dtype) # Quadrature
Q1 = zeros(max_iter, dtype=dtype) # First Richardson extrapolation
Q2 = zeros(max_iter, dtype=dtype) # Second Richardson extrapolation
# One interval
hh = (b - a) / 2 # Half interval length
x = (a + b) / 2 + hh * xq # Nodes
# Quadrature
Q0[0] = hh * np.sum(wq * fun(x), axis=0)
# Successive bisection of intervals
for k in range(1, max_iter):
# Interval bisection
hh = hh / 2
x = np.hstack([x + a, x + b]) / 2
# Quadrature
Q0[k] = hh * np.sum(wq * np.sum(np.reshape(fun(x), (-1, nq)),
axis=0),
axis=0)
# Richardson extrapolation
if k >= 5:
Q1[k] = richardson(Q0, k)
Q2[k] = richardson(Q1, k)
elif k >= 3:
Q1[k] = richardson(Q0, k)
# Estimate absolute error
if k >= 6:
Qv = np.hstack((Q0[k], Q1[k], Q2[k]))
Qw = np.hstack((Q0[k - 1], Q1[k - 1], Q2[k - 1]))
elif k >= 4:
Qv = np.hstack((Q0[k], Q1[k]))
Qw = np.hstack((Q0[k - 1], Q1[k - 1]))
else:
Qv = np.atleast_1d(Q0[k])
Qw = Q0[k - 1]
errors = np.atleast_1d(abs(Qv - Qw))
j = errors.argmin()
err = errors[j]
Q = Qv[j]
if k >= 2: # and not iscomplex:
_val, err1 = dea3(Q0[k - 2], Q0[k - 1], Q0[k])
# Convergence
if (err < abseps) | ~np.isfinite(Q):
break
else:
warnings.warn('Max number of iterations reached without ' +
'convergence.')
See also
--------
QUAD,
QUADGK
'''
# Author: jonas.lundgren@saabgroup.com, 2009. license BSD
# Order limits (required if infinite limits)
a = np.asarray(a)
b = np.asarray(b)
if a == b:
Q = b - a
err = b - a
return Q, err
elif np.real(a) > np.real(b):
reverse = True
a, b = b, a
else:
reverse = False
# Infinite limits
if np.isinf(a) | np.isinf(b):
# Check real limits
if ~ np.isreal(a) | ~np.isreal(b) | np.isnan(a) | np.isnan(b):
raise ValueError('Infinite intervals must be real.')
# Change of variable
if np.isfinite(a) & np.isinf(b):
# a to inf
[Q, err] = quadgr(lambda t: fun(a + t / (1 - t)) / (1 - t) ** 2,
0, 1, abseps)
elif np.isinf(a) & np.isfinite(b):
# -inf to b
[Q, err] = quadgr(lambda t: fun(b + t / (1 + t)) / (1 + t) ** 2,
-1, 0, abseps)
else: # -inf to inf
[Q1, err1] = quadgr(lambda t: fun(t / (1 - t)) / (1 - t) ** 2,
0, 1, abseps / 2)
[Q2, err2] = quadgr(lambda t: fun(t / (1 + t)) / (1 + t) ** 2,
-1, 0, abseps / 2)
Q = Q1 + Q2
err = err1 + err2
if ~ np.isfinite(Q):
warnings.warn('Integral approximation is Infinite or NaN.')
# The error estimate should not be zero
err = err + 2 * np.finfo(Q).eps
# Reverse direction
if reverse:
Q = -Q
return Q, err
# Gauss-Legendre quadrature (12-point)
xq = np.asarray(
[0.12523340851146894, 0.36783149899818018, 0.58731795428661748,
0.76990267419430469, 0.9041172563704748, 0.98156063424671924])
wq = np.asarray(
[0.24914704581340288, 0.23349253653835478, 0.20316742672306584,
0.16007832854334636, 0.10693932599531818, 0.047175336386511842])
xq = np.hstack((xq, -xq))
wq = np.hstack((wq, wq))
nq = len(xq)
dtype = np.result_type(fun(a), fun(b))
# Initiate vectors
Q0 = zeros(max_iter, dtype=dtype) # Quadrature
Q1 = zeros(max_iter, dtype=dtype) # First Richardson extrapolation
Q2 = zeros(max_iter, dtype=dtype) # Second Richardson extrapolation
# One interval
hh = (b - a) / 2 # Half interval length
x = (a + b) / 2 + hh * xq # Nodes
# Quadrature
Q0[0] = hh * np.sum(wq * fun(x), axis=0)
# Successive bisection of intervals
for k in range(1, max_iter):
# Interval bisection
hh = hh / 2
x = np.hstack([x + a, x + b]) / 2
# Quadrature
Q0[k] = hh * np.sum(wq * np.sum(np.reshape(fun(x), (-1, nq)), axis=0),
axis=0)
# Richardson extrapolation
if k >= 5:
Q1[k] = richardson(Q0, k)
Q2[k] = richardson(Q1, k)
elif k >= 3:
Q1[k] = richardson(Q0, k)
# Estimate absolute error
if k >= 6:
Qv = np.hstack((Q0[k], Q1[k], Q2[k]))
Qw = np.hstack((Q0[k - 1], Q1[k - 1], Q2[k - 1]))
elif k >= 4:
Qv = np.hstack((Q0[k], Q1[k]))
Qw = np.hstack((Q0[k - 1], Q1[k - 1]))
else:
Qv = np.atleast_1d(Q0[k])
Qw = Q0[k - 1]
errors = np.atleast_1d(abs(Qv - Qw))
j = errors.argmin()
err = errors[j]
Q = Qv[j]
if k >= 2: # and not iscomplex:
_val, err1 = dea3(Q0[k - 2], Q0[k - 1], Q0[k])
# Convergence
if (err < abseps) | ~np.isfinite(Q):
break
else:
warnings.warn('Max number of iterations reached without convergence.')
if ~ np.isfinite(Q):
warnings.warn('Integral approximation is Infinite or NaN.')
# The error estimate should not be zero
err = err + 2 * np.finfo(Q).eps
# Reverse direction
if reverse:
Q = -Q
return Q, err
return Q, err
quadgr = _Quadgr()
def boole(y, x):

620
wafo/source/c_library/c_functions.c
Unescape Escape View File

@ -1,11 +1,11 @@
#include "math.h"
#include "math.h"
/*
* Install gfortran and run the following to build the module on windows:
* f2py c_library.pyf c_functions.c -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71
*/
/*
* findrfc.c -
* findrfc.c -
*
* Returns indices to RFC turningpoints of a vector
* of turningpoints
@ -17,9 +17,9 @@ void findrfc(double *y1,double hmin, int *ind, int n,int *info) {
double xminus,xplus,Tpl,Tmi,*y,Tstart;
int i,j,ix=0,NC,iy;
info[0] = 0;
if (*(y1+0)> *(y1+1)){
if (*(y1+0)> *(y1+1)){
/* if first is a max , ignore the first max*/
y=&(*(y1+1));
y=&(*(y1+1));
NC=floor((n-1)/2);
Tstart=1;
}
@ -28,85 +28,85 @@ void findrfc(double *y1,double hmin, int *ind, int n,int *info) {
NC=floor(n/2);
Tstart=0;
}
if (NC<1){
return; /* No RFC cycles*/
}
if (( *(y+0) > *(y+1)) && ( *(y+1) > *(y+2)) ){
info[0] = -1;
info[0] = -1;
return; /*This is not a sequence of turningpoints, exit */
}
if ((*(y+0) < *(y+1)) && (*(y+1)< *(y+2))){
info[0]=-1;
return; /*This is not a sequence of turningpoints, exit */
}
for (i=0; i<NC; i++) {
Tmi=Tstart+2*i;
Tpl=Tstart+2*i+2;
xminus=*(y+2*i);
xplus=*(y+2*i+2);
if(i!=0){
j=i-1;
while((j>=0) && (*(y+2*j+1)<=*(y+2*i+1))){
if( (*(y+2*j)<xminus) ){
xminus=*(y+2*j);
Tmi=Tstart+2*j;
} /*if */
j--;
} /*while j*/
j=i-1;
while((j>=0) && (*(y+2*j+1)<=*(y+2*i+1))){
if( (*(y+2*j)<xminus) ){
xminus=*(y+2*j);
Tmi=Tstart+2*j;
} /*if */
j--;
} /*while j*/
} /*if i */
if ( xminus >= xplus){
if ( (*(y+2*i+1)-xminus) >= hmin){
*(ind+ix)=Tmi;
ix++;
*(ind+ix)=(Tstart+2*i+1);
ix++;
} /*if*/
goto L180;
}
if ( (*(y+2*i+1)-xminus) >= hmin){
*(ind+ix)=Tmi;
ix++;
*(ind+ix)=(Tstart+2*i+1);
ix++;
} /*if*/
goto L180;
}
j=i+1;
while((j<NC) ) {
if (*(y+2*j+1) >= *(y+2*i+1)) goto L170;
if( (*(y+2*j+2) <= xplus) ){
xplus=*(y+2*j+2);
Tpl=(Tstart+2*j+2);
}/*if*/
j++;
if (*(y+2*j+1) >= *(y+2*i+1)) goto L170;
if( (*(y+2*j+2) <= xplus) ){
xplus=*(y+2*j+2);
Tpl=(Tstart+2*j+2);
}/*if*/
j++;
} /*while*/
if ( (*(y+2*i+1)-xminus) >= hmin) {
*(ind+ix)=Tmi;
ix++;
*(ind+ix)=(Tstart+2*i+1);
ix++;
*(ind+ix)=Tmi;
ix++;
*(ind+ix)=(Tstart+2*i+1);
ix++;
} /*if*/
goto L180;
L170:
L170:
if (xplus <= xminus ) {
if ( (*(y+2*i+1)-xminus) >= hmin){
*(ind+ix)=Tmi;
ix++;
*(ind+ix)=(Tstart+2*i+1);
ix++;
} /*if*/
/*goto L180;*/
if ( (*(y+2*i+1)-xminus) >= hmin){
*(ind+ix)=Tmi;
ix++;
*(ind+ix)=(Tstart+2*i+1);
ix++;
} /*if*/
/*goto L180;*/
}
else{
if ( (*(y+2*i+1)-xplus) >= hmin) {
*(ind+ix)=(Tstart+2*i+1);
ix++;
*(ind+ix)=Tpl;
ix++;
} /*if*/
else{
if ( (*(y+2*i+1)-xplus) >= hmin) {
*(ind+ix)=(Tstart+2*i+1);
ix++;
*(ind+ix)=Tpl;
ix++;
} /*if*/
} /*elseif*/
L180:
iy=i;
@ -118,52 +118,52 @@ void findrfc(double *y1,double hmin, int *ind, int n,int *info) {
/*
* findcross.c -
* findcross.c -
*
* Returns indices to level v crossings of argument vector
*
* 1998 by Per Andreas Brodtkorb. last modified 23.06-98
*/
*/
void findcross(double *y, double v, int *ind, int n, int *info)
{ int i,start, ix=0,dcross=0;
start=0;
if ( y[0]< v){
dcross=-1; /* first is a up-crossing*/
}
else if ( y[0]> v){
dcross=1; /* first is a down-crossing*/
}
else if ( y[0]== v){
/* Find out what type of crossing we have next time.. */
for (i=1; i<n; i++) {
start=i;
if ( y[i]< v){
ind[ix] = i-1; /* first crossing is a down crossing*/
ix++;
dcross=-1; /* The next crossing is a up-crossing*/
goto L120;
}
else if ( y[i]> v){
ind[ix] = i-1; /* first crossing is a up-crossing*/
ix++;
dcross=1; /*The next crossing is a down-crossing*/
goto L120;
}
}
}
L120:
for (i=start; i<n-1; i++) {
if (( (dcross==-1) && (y[i]<=v) && (y[i+1] > v) ) || ((dcross==1 ) && (y[i]>=v) && (y[i+1] < v) ) ) {
ind[ix] = i;
ix++;
dcross=-dcross;
}
}
info[0] = ix;
return;
start=0;
if ( y[0]< v){
dcross=-1; /* first is a up-crossing*/
}
else if ( y[0]> v){
dcross=1; /* first is a down-crossing*/
}
else if ( y[0]== v){
/* Find out what type of crossing we have next time.. */
for (i=1; i<n; i++) {
start=i;
if ( y[i]< v){
ind[ix] = i-1; /* first crossing is a down crossing*/
ix++;
dcross=-1; /* The next crossing is a up-crossing*/
goto L120;
}
else if ( y[i]> v){
ind[ix] = i-1; /* first crossing is a up-crossing*/
ix++;
dcross=1; /*The next crossing is a down-crossing*/
goto L120;
}
}
}
L120:
for (i=start; i<n-1; i++) {
if (( (dcross==-1) && (y[i]<=v) && (y[i+1] > v) ) || ((dcross==1 ) && (y[i]>=v) && (y[i+1] < v) ) ) {
ind[ix] = i;
ix++;
dcross=-dcross;
}
}
info[0] = ix;
return;
}
@ -173,19 +173,19 @@ void findcross(double *y, double v, int *ind, int n, int *info)
* CALL: disufq(rvec,ivec,rA,iA, w,kw,h,g,nmin,nmax,m,n)
*
* rvec, ivec = real and imaginary parts of the resultant (size m X n).
* rA, iA = real and imaginary parts of the amplitudes (size m X n).
* rA, iA = real and imaginary parts of the amplitudes (size m X n).
* w = vector with angular frequencies (w>=0)
* kw = vector with wavenumbers (kw>=0)
* h = water depth (h >=0)
* g = constant acceleration of gravity
* nmin = minimum index where rA(:,nmin) and iA(:,nmin) is
* nmin = minimum index where rA(:,nmin) and iA(:,nmin) is
* greater than zero.
* nmax = maximum index where rA(:,nmax) and iA(:,nmax) is
* nmax = maximum index where rA(:,nmax) and iA(:,nmax) is
* greater than zero.
* m = size(rA,1),size(iA,1)
* n = size(rA,2),size(iA,2), or size(rvec,2),size(ivec,2)
*
* DISUFQ returns the summation of difference frequency and sum
* DISUFQ returns the summation of difference frequency and sum
* frequency effects in the vector vec = rvec +sqrt(-1)*ivec.
* The 2'nd order contribution to the Stokes wave is then calculated by
* a simple 1D Fourier transform, real(FFT(vec)).
@ -195,15 +195,15 @@ void findcross(double *y, double v, int *ind, int n, int *info)
*
* by Per Andreas Brodtkorb 15.08.2001
* revised pab 14.03.2002, 01.05.2002 22.07.2002, oct 2008
*/
*/
void disufq(double *rvec, double *ivec,
double *rA, double *iA,
double *w, double *kw,
double h, double g,
int nmin, int nmax,
int m, int n)
{
double *rA, double *iA,
double *w, double *kw,
double h, double g,
int nmin, int nmax,
int m, int n)
{
double Epij, Edij;
double tmp1, tmp2, tmp3, tmp4, kfact;
double w1, w2, kw1, kw2, Cg;
@ -217,7 +217,7 @@ void disufq(double *rvec, double *ivec,
}
// kfact is set to 2 in order to exploit the symmetry.
// If you set kfact to 1, you must uncomment all statements
// If you set kfact to 1, you must uncomment all statements
// including the expressions: rvec[iz2], rvec[iv2], ivec[iz2] and ivec[iv2].
kfact = 2.0;
@ -227,70 +227,70 @@ void disufq(double *rvec, double *ivec,
iz1 = 2*ixi;
//iz2 = n*m-ixi;
kw1 = kw[ix];
Epij = kw1;
for (i=0;i<m;i++,ixi++,iz1++) {
rrA = rA[ixi]*rA[ixi]; ///
iiA = iA[ixi]*iA[ixi]; ///
riA = rA[ixi]*iA[ixi]; ///
/// Sum frequency effects along the diagonal
tmp1 = kfact*(rrA-iiA)*Epij;
tmp2 = kfact*2.0*riA*Epij;
rvec[iz1] += tmp1;
ivec[iz1] += tmp2;
//rvec[iz2] += tmp1;
//ivec[iz2] -= tmp2;
//iz2++;
/// Difference frequency effects are zero along the diagonal
/// and are thus not contributing to the mean.
Epij = kw1;
for (i=0;i<m;i++,ixi++,iz1++) {
rrA = rA[ixi]*rA[ixi]; ///
iiA = iA[ixi]*iA[ixi]; ///
riA = rA[ixi]*iA[ixi]; ///
/// Sum frequency effects along the diagonal
tmp1 = kfact*(rrA-iiA)*Epij;
tmp2 = kfact*2.0*riA*Epij;
rvec[iz1] += tmp1;
ivec[iz1] += tmp2;
//rvec[iz2] += tmp1;
//ivec[iz2] -= tmp2;
//iz2++;
/// Difference frequency effects are zero along the diagonal
/// and are thus not contributing to the mean.
}
for (jy = ix+1;jy<nmax;jy++){
kw2 = kw[jy];
Epij = 0.5*(kw2 + kw1);
Edij = -0.5*(kw2 - kw1);
//printf("Edij = %f Epij = %f \n", Edij,Epij);
ixi = ix*m;
jyi = jy*m;
iz1 = ixi+jyi;
iv1 = jyi-ixi;
//iz2 = (n*m-iz1);
//iv2 = (n*m-iv1);
for (i = 0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
/* Sum frequency effects */
tmp1 = kfact*2.0*(rrA-iiA)*Epij;
tmp2 = kfact*2.0*(riA+irA)*Epij;
rvec[iz1] += tmp1;///rvec[i][ix+jy] += tmp1;
ivec[iz1] += tmp2;///ivec[i][ix+jy] += tmp2;
//rvec[iz2] += tmp1;///rvec[i][n*m-(ix+jy)] += tmp1;
//ivec[iz2] -= tmp2;///ivec[i][n*m-(ix+jy)] -= tmp2;
// iz2++;
/* Difference frequency effects */
tmp1 = kfact*2.0*(rrA+iiA)*Edij;
tmp2 = kfact*2.0*(riA-irA)*Edij;
rvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
ivec[iv1] += tmp2;///ivec[i][jy-ix] += tmp2;
//rvec[iv2] += tmp1;///rvec[i][n*m-(jy-ix)] += tmp1;
//ivec[iv2] -= tmp2;///ivec[i][n*m-(jy-ix)] -= tmp2;
//iv2++;
}
kw2 = kw[jy];
Epij = 0.5*(kw2 + kw1);
Edij = -0.5*(kw2 - kw1);
//printf("Edij = %f Epij = %f \n", Edij,Epij);
ixi = ix*m;
jyi = jy*m;
iz1 = ixi+jyi;
iv1 = jyi-ixi;
//iz2 = (n*m-iz1);
//iv2 = (n*m-iv1);
for (i = 0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
/* Sum frequency effects */
tmp1 = kfact*2.0*(rrA-iiA)*Epij;
tmp2 = kfact*2.0*(riA+irA)*Epij;
rvec[iz1] += tmp1;///rvec[i][ix+jy] += tmp1;
ivec[iz1] += tmp2;///ivec[i][ix+jy] += tmp2;
//rvec[iz2] += tmp1;///rvec[i][n*m-(ix+jy)] += tmp1;
//ivec[iz2] -= tmp2;///ivec[i][n*m-(ix+jy)] -= tmp2;
// iz2++;
/* Difference frequency effects */
tmp1 = kfact*2.0*(rrA+iiA)*Edij;
tmp2 = kfact*2.0*(riA-irA)*Edij;
rvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
ivec[iv1] += tmp2;///ivec[i][jy-ix] += tmp2;
//rvec[iv2] += tmp1;///rvec[i][n*m-(jy-ix)] += tmp1;
//ivec[iv2] -= tmp2;///ivec[i][n*m-(jy-ix)] -= tmp2;
//iv2++;
}
}
}
}
else{ /* Finite water depth */
for (ix = nmin-1;ix<nmax;ix++) {
kw1 = kw[ix];
kw1 = kw[ix];
w1 = w[ix];
tmp1 = tanh(kw1*h);
/// Cg, wave group velocity
@ -298,7 +298,7 @@ void disufq(double *rvec, double *ivec,
tmp1 = 0.5*g*(kw1/w1)*(kw1/w1);
tmp2 = 0.5*w1*w1/g;
tmp3 = g*kw1/(w1*Cg);
if (kw1*h<300.0){
tmp4 = kw1/sinh(2.0*kw1*h);
}
@ -307,35 +307,35 @@ void disufq(double *rvec, double *ivec,
}
// Difference frequency effects finite water depth
Edij = (tmp1-tmp2+tmp3)/(1.0-g*h/(Cg*Cg))-tmp4; /// OK
// Sum frequency effects finite water depth
Epij = (3.0*(tmp1-tmp2)/(1.0-tmp1/kw1*tanh(2.0*kw1*h))+3.0*tmp2-tmp1); /// OK
//printf("Edij = %f Epij = %f \n", Edij,Epij);
ixi = ix*m;
iz1 = 2*ixi;
//iz2 = n*m-ixi;
for (i=0;i<m;i++,ixi++,iz1++) {
for (i=0;i<m;i++,ixi++,iz1++) {
rrA = rA[ixi]*rA[ixi]; ///
iiA = iA[ixi]*iA[ixi]; ///
riA = rA[ixi]*iA[ixi]; ///
/// Sum frequency effects along the diagonal
rvec[iz1] += kfact*(rrA-iiA)*Epij;
ivec[iz1] += kfact*2.0*riA*Epij;
//rvec[iz2] += kfact*(rrA-iiA)*Epij;
//ivec[iz2] -= kfact*2.0*riA*Epij;
//iz2++;
/// Difference frequency effects along the diagonal
/// are only contributing to the mean
rvec[i] += 2.0*(rrA+iiA)*Edij;
}
for (jy = ix+1;jy<nmax;jy++) {
// w1 = w[ix];
// kw1 = kw[ix];
// kw1 = kw[ix];
w2 = w[jy];
kw2 = kw[jy];
tmp1 = g*(kw1/w1)*(kw2/w2);
@ -343,7 +343,7 @@ void disufq(double *rvec, double *ivec,
tmp3 = 0.5*g*(w1*kw2*kw2+w2*kw1*kw1)/(w1*w2*(w1+w2));
tmp4 = (1-g*(kw1+kw2)/(w1+w2)/(w1+w2)*tanh((kw1+kw2)*h));
Epij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
tmp2 = 0.5/g*(w1*w1+w2*w2-w1*w2); /*OK*/
tmp3 = -0.5*g*(w1*kw2*kw2-w2*kw1*kw1)/(w1*w2*(w1-w2));
tmp4 = (1.0-g*(kw1-kw2)/(w1-w2)/(w1-w2)*tanh((kw1-kw2)*h));
@ -356,30 +356,30 @@ void disufq(double *rvec, double *ivec,
iv1 = jyi-ixi;
// iz2 = (n*m-iz1);
// iv2 = n*m-iv1;
for (i=0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
/* Sum frequency effects */
tmp1 = kfact*2.0*(rrA-iiA)*Epij;
tmp2 = kfact*2.0*(riA+irA)*Epij;
rvec[iz1] += tmp1;///rvec[i][jy+ix] += tmp1;
ivec[iz1] += tmp2;///ivec[i][jy+ix] += tmp2;
//rvec[iz2] += tmp1;///rvec[i][n*m-(jy+ix)] += tmp1;
//ivec[iz2] -= tmp2;///ivec[i][n*m-(jy+ix)] -= tmp2;
//iz2++;
/* Difference frequency effects */
tmp1 = kfact*2.0*(rrA+iiA)*Edij;
tmp2 = kfact*2.0*(riA-irA)*Edij;
rvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
ivec[iv1] += tmp2;///ivec[i][jy-ix] -= tmp2;
//rvec[iv2] += tmp1;
//ivec[iv2] -= tmp2;
//iv2++;
for (i=0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
/* Sum frequency effects */
tmp1 = kfact*2.0*(rrA-iiA)*Epij;
tmp2 = kfact*2.0*(riA+irA)*Epij;
rvec[iz1] += tmp1;///rvec[i][jy+ix] += tmp1;
ivec[iz1] += tmp2;///ivec[i][jy+ix] += tmp2;
//rvec[iz2] += tmp1;///rvec[i][n*m-(jy+ix)] += tmp1;
//ivec[iz2] -= tmp2;///ivec[i][n*m-(jy+ix)] -= tmp2;
//iz2++;
/* Difference frequency effects */
tmp1 = kfact*2.0*(rrA+iiA)*Edij;
tmp2 = kfact*2.0*(riA-irA)*Edij;
rvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
ivec[iv1] += tmp2;///ivec[i][jy-ix] -= tmp2;
//rvec[iv2] += tmp1;
//ivec[iv2] -= tmp2;
//iv2++;
}
}
}
@ -395,19 +395,19 @@ void disufq(double *rvec, double *ivec,
* effects (size m X n).
* rdvec, idvec = real and imaginary parts of the difference frequency
* effects (size m X n).
* rA, iA = real and imaginary parts of the amplitudes (size m X n).
* rA, iA = real and imaginary parts of the amplitudes (size m X n).
* w = vector with angular frequencies (w>=0)
* kw = vector with wavenumbers (kw>=0)
* h = water depth (h >=0)
* g = constant acceleration of gravity
* nmin = minimum index where rA(:,nmin) and iA(:,nmin) is
* nmin = minimum index where rA(:,nmin) and iA(:,nmin) is
* greater than zero.
* nmax = maximum index where rA(:,nmax) and iA(:,nmax) is
* nmax = maximum index where rA(:,nmax) and iA(:,nmax) is
* greater than zero.
* m = size(rA,1),size(iA,1)
* n = size(rA,2),size(iA,2), or size(rvec,2),size(ivec,2)
*
* DISUFQ2 returns the summation of sum and difference frequency
* DISUFQ2 returns the summation of sum and difference frequency
* frequency effects in the vectors svec = rsvec +sqrt(-1)*isvec and
* dvec = rdvec +sqrt(-1)*idvec.
* The 2'nd order contribution to the Stokes wave is then calculated by
@ -416,17 +416,17 @@ void disufq(double *rvec, double *ivec,
*
* This is a MEX-file for MATLAB.
* by Per Andreas Brodtkorb 15.08.2001
* revised pab 14.03.2002, 01.05.2002
*/
* revised pab 14.03.2002, 01.05.2002
*/
void disufq2(double *rsvec, double *isvec,
double *rdvec, double *idvec,
double *rA, double *iA,
double *w, double *kw,
double h, double g,
int nmin, int nmax,
int m, int n)
{
double *rdvec, double *idvec,
double *rA, double *iA,
double *w, double *kw,
double h, double g,
int nmin, int nmax,
int m, int n)
{
double Epij, Edij;
double tmp1, tmp2, tmp3, tmp4, kfact;
double w1, w2, kw1, kw2, Cg;
@ -443,7 +443,7 @@ void disufq2(double *rsvec, double *isvec,
}
// kfact is set to 2 in order to exploit the symmetry.
// If you set kfact to 1, you must uncomment all statements
// If you set kfact to 1, you must uncomment all statements
// including the expressions: rvec[iz2], rvec[iv2], ivec[iz2] and ivec[iv2].
kfact = 2.0;
@ -453,70 +453,70 @@ void disufq2(double *rsvec, double *isvec,
iz1 = 2*ixi;
//iz2 = n*m-ixi;
kw1 = kw[ix];
Epij = kw1;
for (i=0;i<m;i++,ixi++,iz1++) {
rrA = rA[ixi]*rA[ixi]; ///
iiA = iA[ixi]*iA[ixi]; ///
riA = rA[ixi]*iA[ixi]; ///
/// Sum frequency effects along the diagonal
tmp1 = kfact*(rrA-iiA)*Epij;
tmp2 = kfact*2.0*riA*Epij;
rsvec[iz1] += tmp1;
isvec[iz1] += tmp2;
//rsvec[iz2] += tmp1;
//isvec[iz2] -= tmp2;
//iz2++;
/// Difference frequency effects are zero along the diagonal
/// and are thus not contributing to the mean.
Epij = kw1;
for (i=0;i<m;i++,ixi++,iz1++) {
rrA = rA[ixi]*rA[ixi]; ///
iiA = iA[ixi]*iA[ixi]; ///
riA = rA[ixi]*iA[ixi]; ///
/// Sum frequency effects along the diagonal
tmp1 = kfact*(rrA-iiA)*Epij;
tmp2 = kfact*2.0*riA*Epij;
rsvec[iz1] += tmp1;
isvec[iz1] += tmp2;
//rsvec[iz2] += tmp1;
//isvec[iz2] -= tmp2;
//iz2++;
/// Difference frequency effects are zero along the diagonal
/// and are thus not contributing to the mean.
}
for (jy = ix+1;jy<nmax;jy++){
kw2 = kw[jy];
Epij = 0.5*(kw2 + kw1);
Edij = -0.5*(kw2 - kw1);
//printf("Edij = %f Epij = %f \n", Edij,Epij);
ixi = ix*m;
jyi = jy*m;
iz1 = ixi+jyi;
iv1 = jyi-ixi;
//iz2 = (n*m-iz1);
//iv2 = (n*m-iv1);
for (i = 0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
/* Sum frequency effects */
tmp1 = kfact*2.0*(rrA-iiA)*Epij;
tmp2 = kfact*2.0*(riA+irA)*Epij;
rsvec[iz1] += tmp1; ///rvec[i][ix+jy] += tmp1;
isvec[iz1] += tmp2; ///ivec[i][ix+jy] += tmp2;
//rsvec[iz2] += tmp1;///rvec[i][n*m-(ix+jy)] += tmp1;
//isvec[iz2] -= tmp2;///ivec[i][n*m-(ix+jy)] += tmp2;
//iz2++;
/* Difference frequency effects */
tmp1 = kfact*2.0*(rrA+iiA)*Edij;
tmp2 = kfact*2.0*(riA-irA)*Edij;
rdvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
idvec[iv1] += tmp2;///ivec[i][jy-ix] += tmp2;
//rdvec[iv2] += tmp1;///rvec[i][n*m-(jy-ix)] += tmp1;
//idvec[iv2] -= tmp2;///ivec[i][n*m-(jy-ix)] -= tmp2;
// iv2++;
}
kw2 = kw[jy];
Epij = 0.5*(kw2 + kw1);
Edij = -0.5*(kw2 - kw1);
//printf("Edij = %f Epij = %f \n", Edij,Epij);
ixi = ix*m;
jyi = jy*m;
iz1 = ixi+jyi;
iv1 = jyi-ixi;
//iz2 = (n*m-iz1);
//iv2 = (n*m-iv1);
for (i = 0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
/* Sum frequency effects */
tmp1 = kfact*2.0*(rrA-iiA)*Epij;
tmp2 = kfact*2.0*(riA+irA)*Epij;
rsvec[iz1] += tmp1; ///rvec[i][ix+jy] += tmp1;
isvec[iz1] += tmp2; ///ivec[i][ix+jy] += tmp2;
//rsvec[iz2] += tmp1;///rvec[i][n*m-(ix+jy)] += tmp1;
//isvec[iz2] -= tmp2;///ivec[i][n*m-(ix+jy)] += tmp2;
//iz2++;
/* Difference frequency effects */
tmp1 = kfact*2.0*(rrA+iiA)*Edij;
tmp2 = kfact*2.0*(riA-irA)*Edij;
rdvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
idvec[iv1] += tmp2;///ivec[i][jy-ix] += tmp2;
//rdvec[iv2] += tmp1;///rvec[i][n*m-(jy-ix)] += tmp1;
//idvec[iv2] -= tmp2;///ivec[i][n*m-(jy-ix)] -= tmp2;
// iv2++;
}
}
}
}
else{ /* Finite water depth */
for (ix = nmin-1;ix<nmax;ix++) {
kw1 = kw[ix];
kw1 = kw[ix];
w1 = w[ix];
tmp1 = tanh(kw1*h);
/// Cg, wave group velocity
@ -524,7 +524,7 @@ void disufq2(double *rsvec, double *isvec,
tmp1 = 0.5*g*(kw1/w1)*(kw1/w1);
tmp2 = 0.5*w1*w1/g;
tmp3 = g*kw1/(w1*Cg);
if (kw1*h<300.0){
tmp4 = kw1/sinh(2.0*kw1*h);
}
@ -533,27 +533,27 @@ void disufq2(double *rsvec, double *isvec,
}
// Difference frequency effects finite water depth
Edij = (tmp1-tmp2+tmp3)/(1.0-g*h/(Cg*Cg))-tmp4; /// OK
// Sum frequency effects finite water depth
Epij = (3.0*(tmp1-tmp2)/(1.0-tmp1/kw1*tanh(2.0*kw1*h))+3.0*tmp2-tmp1); /// OK
//printf("Edij = %f Epij = %f \n", Edij,Epij);
ixi = ix*m;
iz1 = 2*ixi;
//iz2 = n*m-ixi;
for (i=0;i<m;i++,ixi++,iz1++) {
for (i=0;i<m;i++,ixi++,iz1++) {
rrA = rA[ixi]*rA[ixi]; ///
iiA = iA[ixi]*iA[ixi]; ///
riA = rA[ixi]*iA[ixi]; ///
/// Sum frequency effects along the diagonal
rsvec[iz1] += kfact*(rrA-iiA)*Epij;
isvec[iz1] += kfact*2.0*riA*Epij;
//rsvec[iz2] += kfact*(rrA-iiA)*Epij;
//isvec[iz2] -= kfact*2.0*riA*Epij;
/// Difference frequency effects along the diagonal
/// are only contributing to the mean
//printf(" %f \n",2.0*(rrA+iiA)*Edij);
@ -561,7 +561,7 @@ void disufq2(double *rsvec, double *isvec,
}
for (jy = ix+1;jy<nmax;jy++) {
// w1 = w[ix];
// kw1 = kw[ix];
// kw1 = kw[ix];
w2 = w[jy];
kw2 = kw[jy];
tmp1 = g*(kw1/w1)*(kw2/w2);
@ -569,7 +569,7 @@ void disufq2(double *rsvec, double *isvec,
tmp3 = 0.5*g*(w1*kw2*kw2+w2*kw1*kw1)/(w1*w2*(w1+w2));
tmp4 = (1-g*(kw1+kw2)/(w1+w2)/(w1+w2)*tanh((kw1+kw2)*h));
Epij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
tmp2 = 0.5/g*(w1*w1+w2*w2-w1*w2); /*OK*/
tmp3 = -0.5*g*(w1*kw2*kw2-w2*kw1*kw1)/(w1*w2*(w1-w2));
tmp4 = (1.0-g*(kw1-kw2)/(w1-w2)/(w1-w2)*tanh((kw1-kw2)*h));
@ -582,30 +582,30 @@ void disufq2(double *rsvec, double *isvec,
iv1 = jyi-ixi;
// iz2 = (n*m-iz1);
// iv2 = (n*m-iv1);
for (i=0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
/* Sum frequency effects */
tmp1 = kfact*2.0*(rrA-iiA)*Epij;
tmp2 = kfact*2.0*(riA+irA)*Epij;
rsvec[iz1] += tmp1;///rsvec[i][jy+ix] += tmp1;
isvec[iz1] += tmp2;///isvec[i][jy+ix] += tmp2;
//rsvec[iz2] += tmp1;///rsvec[i][n*m-(jy+ix)] += tmp1;
//isvec[iz2] -= tmp2;///isvec[i][n*m-(jy-ix)] += tmp2;
//iz2++;
/* Difference frequency effects */
tmp1 = kfact*2.0*(rrA+iiA)*Edij;
tmp2 = kfact*2.0*(riA-irA)*Edij;
rdvec[iv1] += tmp1;
idvec[iv1] += tmp2;
//rdvec[iv2] += tmp1;
//idvec[iv2] -= tmp2;
// iv2++;
for (i=0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
/* Sum frequency effects */
tmp1 = kfact*2.0*(rrA-iiA)*Epij;
tmp2 = kfact*2.0*(riA+irA)*Epij;
rsvec[iz1] += tmp1;///rsvec[i][jy+ix] += tmp1;
isvec[iz1] += tmp2;///isvec[i][jy+ix] += tmp2;
//rsvec[iz2] += tmp1;///rsvec[i][n*m-(jy+ix)] += tmp1;
//isvec[iz2] -= tmp2;///isvec[i][n*m-(jy-ix)] += tmp2;
//iz2++;
/* Difference frequency effects */
tmp1 = kfact*2.0*(rrA+iiA)*Edij;
tmp2 = kfact*2.0*(riA-irA)*Edij;
rdvec[iv1] += tmp1;
idvec[iv1] += tmp2;
//rdvec[iv2] += tmp1;
//idvec[iv2] -= tmp2;
// iv2++;
}
}
}
@ -620,16 +620,16 @@ void disufq2(double *rsvec, double *isvec,
//Visit the MATLAB Central File Exchange for latest version
//http://www.mathworks.com/matlabcentral/fileexchange/3026
void findrfc3_astm(double *array_ext, double *array_out, int n, int *nout) {
double *pr, *po, a[16384], ampl, mean;
int tot_num, index, j, cNr1, cNr2;
int tot_num, index, j, cNr1, cNr2;
tot_num = n;
// pointers to the first element of the arrays
pr = &array_ext[0];
po = &array_out[0];
// The original rainflow counting by Nieslony, unchanged
j = -1;
cNr1 = 1;
@ -694,8 +694,8 @@ void
findrfc5_astm(double *array_ext, double *array_t, double *array_out, int n, int *nout) {
double *pr, *pt, *po, a[16384], t[16384], ampl, mean, period, atime;
int tot_num, index, j, cNr1, cNr2;
// tot_num = mxGetM(array_ext) * mxGetN(array_ext);
tot_num = n;
@ -703,9 +703,9 @@ findrfc5_astm(double *array_ext, double *array_t, double *array_out, int n, int
pr = &array_ext[0];
pt = &array_t[0];
po = &array_out[0];
// array_out = mxCreateDoubleMatrix(5, tot_num-1, mxREAL);
// The original rainflow counting by Nieslony, unchanged
j = -1;
cNr1 = 1;

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