int main(int argc, char* argv[]) {
double res = 0.0;
double* p_m1 = malloc(N * sizeof *p_m1);
double* p_m2 = malloc(N * sizeof *p_m2);
for (int i = 0; i < N; i++) {
if (i < M-1) p_m1[i] = 0;
else {
double prod1 = 1;
for (int j = 0; j < M-1; j++) prod1 *= (double)(i-j)/(double)(N-1-j);
p_m1[i] = prod1;
}
if (i < M-2) p_m2[i] = 0;
else {
double prod2 = 1;
for (int j = 0; j < M-2; j++) prod2 *= (double)(i-j)/(double)(N-1-j);
p_m2[i] = M*(M-1)*prod2/(N-M+1);
}
}
for (int a = 1; a <= N / M; a++) {
for (int b = a; b <= (N-a) / (M-1); b++) {
double p_b = 0;
if (a == b)
p_b = P_M1(N-1-M*(a-1)) - P_M1(N-1-M*a) - P_M2(N-1-M*a);
else
p_b = P_M2(N-1-(M-1)*(b-1)-a) - P_M2(N-1-(M-1)*b-a);
res += p_b * b;
}
}
printf("%.5f\n", res);
return 0;
}
float interp_floatvec( floatvec *fv , float x )
{
int ix , im1,ip1,ip2 , itop ;
float fx , val , abot,atop ;
if( fv == NULL || fv->ar == NULL ) return 0.0f ;
itop = fv->nar - 1 ;
if( itop <= 1 || fv->dx == 0.0 ) return(fv->ar[0]) ;
/* if input x is out of range, return the edge value */
fx = (x - fv->x0) / fv->dx ;
if( fx <= 0.0f ) return(fv->ar[0]) ;
else if( fx >= itop ) return(fv->ar[itop]) ;
/* input x is between point #ix and #ix+1 */
/* fractional offset between them is fx */
ix = (int)fx ; fx = fx - ix ;
/* get indexes below (im1) and above (ip1 and ip2) */
im1 = ix-1 ; if( im1 < 0 ) im1 = 0 ;
ip1 = ix+1 ;
if( ip1 > itop ){
ip1 = ip2 = itop ;
} else {
ip2 = ip1+1 ; if( ip2 > itop ) ip2 = itop ;
}
/* cubic interpolation between these 4 points */
val = P_M1(fx)*fv->ar[im1] + P_00(fx)*fv->ar[ix]
+ P_P1(fx)*fv->ar[ip1] + P_P2(fx)*fv->ar[ip2] ;
/* make sure result lies in the local range of values */
abot = fv->ar[ix] ; atop = fv->ar[ip1] ;
if( abot > atop ){ fx = abot; abot = atop; atop = fx; }
if( val < abot ) val = abot; else if( val > atop ) val = atop;
return(val) ;
}
void cub_shift( int n , float af , float * f )
{
int ii , ia , ix ;
float wt_m1 , wt_00 , wt_p1 , wt_p2 , aa ;
#ifdef SEPARATE_FINS
int ibot,itop ;
#endif
ENTRY("cub_shift") ;
af = -af ; ia = (int) af ; if( af < 0 ) ia-- ; /* ia = floor */
/* 15 Mar 2001: if shift is too large, return all zeros */
if( ia <= -n || ia >= n ){
for( ii=0 ; ii < n ; ii++ ) f[ii] = 0.0 ;
EXRETURN ;
}
aa = af - ia ;
wt_m1 = P_M1(aa) ; wt_00 = P_00(aa) ;
wt_p1 = P_P1(aa) ; wt_p2 = P_P2(aa) ;
if( n > nlcbuf ){
if( lcbuf != NULL ) free(lcbuf) ;
lcbuf = (float *) malloc( sizeof(float) * n ) ;
nlcbuf = n ;
}
#ifdef SEPARATE_FINS
ibot = 1-ia ; if( ibot < 0 ) ibot = 0 ;
itop = n-3-ia ; if( itop > n-1 ) itop = n-1 ;
for( ii=ibot ; ii <= itop ; ii++ ){
ix = ii + ia ;
lcbuf[ii] = wt_m1 * f[ix-1] + wt_00 * f[ix]
+ wt_p1 * f[ix+1] + wt_p2 * f[ix+2] ;
}
if( ibot > n ) ibot = n ; /* 15 Mar 2001 */
for( ii=0 ; ii < ibot ; ii++ ){
ix = ii + ia ;
lcbuf[ii] = wt_m1 * FINS(ix-1) + wt_00 * FINS(ix)
+ wt_p1 * FINS(ix+1) + wt_p2 * FINS(ix+2) ;
}
if( itop < 0 ) itop = -1 ; /* 15 Mar 2001 */
for( ii=itop+1 ; ii < n ; ii++ ){
ix = ii + ia ;
lcbuf[ii] = wt_m1 * FINS(ix-1) + wt_00 * FINS(ix)
+ wt_p1 * FINS(ix+1) + wt_p2 * FINS(ix+2) ;
}
#else /* not SEPARATE_FINS */
for( ii=0 ; ii < n ; ii++ ){
ix = ii + ia ;
if( ix > 0 && ix < n-2 )
lcbuf[ii] = wt_m1 * f[ix-1] + wt_00 * f[ix]
+ wt_p1 * f[ix+1] + wt_p2 * f[ix+2] ;
else
lcbuf[ii] = wt_m1 * FINS(ix-1) + wt_00 * FINS(ix)
+ wt_p1 * FINS(ix+1) + wt_p2 * FINS(ix+2) ;
}
#endif /* SEPARATE_FINS */
memcpy( f , lcbuf , sizeof(float)*n ) ;
EXRETURN ;
}
MRI_IMAGE *mri_rota( MRI_IMAGE *im, float aa, float bb, float phi )
{
float rot_dx , rot_dy , rot_cph , rot_sph , top,bot,val ;
MRI_IMAGE *imfl , *newImg ;
MRI_IMARR *impair ;
float *far , *nar ;
float xx,yy , fx,fy ;
int ii,jj, nx,ny , ix,jy , ifx,jfy ;
float f_jm1,f_j00,f_jp1,f_jp2 , wt_m1,wt_00,wt_p1,wt_p2 ;
#ifdef USE_CGRID
if( p_first ){
p_first = 0 ;
xx = 1.0 / CGRID ;
for( ii=0 ; ii <= CGRID ; ii++ ){
yy = ii * xx ;
p_m1[ii] = P_M1(yy) ;
p_00[ii] = P_00(yy) ;
p_p1[ii] = P_P1(yy) ;
p_p2[ii] = P_P2(yy) ;
}
}
#endif
if( im == NULL || ! MRI_IS_2D(im) ){
fprintf(stderr,"*** mri_rota only works on 2D images!\n") ; EXIT(1) ;
}
/** if complex image, break into pairs, do each separately, put back together **/
if( im->kind == MRI_complex ){
MRI_IMARR *impair ;
MRI_IMAGE * rim , * iim , * tim ;
impair = mri_complex_to_pair( im ) ;
if( impair == NULL ){
fprintf(stderr,"*** mri_complex_to_pair fails in mri_rota!\n") ; EXIT(1) ;
}
rim = IMAGE_IN_IMARR(impair,0) ;
iim = IMAGE_IN_IMARR(impair,1) ; FREE_IMARR(impair) ;
tim = mri_rota( rim , aa,bb,phi ) ; mri_free( rim ) ; rim = tim ;
tim = mri_rota( iim , aa,bb,phi ) ; mri_free( iim ) ; iim = tim ;
newImg = mri_pair_to_complex( rim , iim ) ;
mri_free( rim ) ; mri_free( iim ) ;
MRI_COPY_AUX(newImg,im) ;
return newImg ;
}
/** rotation params **/
rot_cph = cos(phi) ; rot_sph = sin(phi) ;
rot_dx = (0.5 * im->nx) * (1.0-rot_cph) - aa*rot_cph - bb*rot_sph
-(0.5 * im->ny) * rot_sph ;
rot_dy = (0.5 * im->nx) * rot_sph + aa*rot_sph - bb*rot_cph
+(0.5 * im->ny) * (1.0-rot_cph) ;
/** other initialization **/
nx = im->nx ; /* image dimensions */
ny = im->ny ;
if( im->kind == MRI_float ) imfl = im ;
else imfl = mri_to_float( im ) ;
far = MRI_FLOAT_PTR(imfl) ; /* access to float data */
newImg = mri_new( nx , nx , MRI_float ) ; /* output image */
nar = MRI_FLOAT_PTR(newImg) ; /* output image data */
bot = top = far[0] ;
for( ii=0 ; ii < nx*ny ; ii++ )
if( far[ii] < bot ) bot = far[ii] ;
else if( far[ii] > top ) top = far[ii] ;
/*** loop over output points and warp to them ***/
for( jj=0 ; jj < nx ; jj++ ){
xx = rot_sph * jj + rot_dx - rot_cph ;
yy = rot_cph * jj + rot_dy + rot_sph ;
for( ii=0 ; ii < nx ; ii++ ){
xx += rot_cph ; /* get x,y in original image */
yy -= rot_sph ;
ix = (xx >= 0.0) ? ((int) xx) : ((int) xx)-1 ; /* floor */
jy = (yy >= 0.0) ? ((int) yy) : ((int) yy)-1 ;
#ifdef USE_CGRID
ifx = (xx-ix)*CGRID + 0.499 ;
wt_m1 = p_m1[ifx] ; wt_00 = p_00[ifx] ;
wt_p1 = p_p1[ifx] ; wt_p2 = p_p2[ifx] ;
#else
fx = xx-ix ;
wt_m1 = P_M1(fx) ; wt_00 = P_00(fx) ;
wt_p1 = P_P1(fx) ; wt_p2 = P_P2(fx) ;
#endif
if( ix > 0 && ix < nx-2 && jy > 0 && jy < ny-2 ){
float * fym1, *fy00 , *fyp1 , *fyp2 ;
fym1 = far + (ix-1 + (jy-1)*nx) ;
fy00 = fym1 + nx ;
fyp1 = fy00 + nx ;
fyp2 = fyp1 + nx ;
f_jm1 = wt_m1 * fym1[0] + wt_00 * fym1[1]
+ wt_p1 * fym1[2] + wt_p2 * fym1[3] ;
f_j00 = wt_m1 * fy00[0] + wt_00 * fy00[1]
+ wt_p1 * fy00[2] + wt_p2 * fy00[3] ;
f_jp1 = wt_m1 * fyp1[0] + wt_00 * fyp1[1]
+ wt_p1 * fyp1[2] + wt_p2 * fyp1[3] ;
f_jp2 = wt_m1 * fyp2[0] + wt_00 * fyp2[1]
+ wt_p1 * fyp2[2] + wt_p2 * fyp2[3] ;
} else {
f_jm1 = wt_m1 * FINS(ix-1,jy-1)
+ wt_00 * FINS(ix ,jy-1)
+ wt_p1 * FINS(ix+1,jy-1)
+ wt_p2 * FINS(ix+2,jy-1) ;
f_j00 = wt_m1 * FINS(ix-1,jy)
+ wt_00 * FINS(ix ,jy)
+ wt_p1 * FINS(ix+1,jy)
+ wt_p2 * FINS(ix+2,jy) ;
f_jp1 = wt_m1 * FINS(ix-1,jy+1)
+ wt_00 * FINS(ix ,jy+1)
+ wt_p1 * FINS(ix+1,jy+1)
+ wt_p2 * FINS(ix+2,jy+1) ;
f_jp2 = wt_m1 * FINS(ix-1,jy+2)
+ wt_00 * FINS(ix ,jy+2)
+ wt_p1 * FINS(ix+1,jy+2)
+ wt_p2 * FINS(ix+2,jy+2) ;
}
#define THIRTYSIX 2.7777778e-2 /* 1./36.0, actually */
#ifdef USE_CGRID
jfy = (yy-jy)*CGRID + 0.499 ;
val = ( p_m1[jfy] * f_jm1 + p_00[jfy] * f_j00
+ p_p1[jfy] * f_jp1 + p_p2[jfy] * f_jp2 ) * THIRTYSIX ;
#else
fy = yy-jy ;
val = ( P_M1(fy) * f_jm1 + P_00(fy) * f_j00
+ P_P1(fy) * f_jp1 + P_P2(fy) * f_jp2 ) * THIRTYSIX ;
#endif
if( val < bot ) nar[ii+jj*nx] = bot ; /* too small! */
else if( val > top ) nar[ii+jj*nx] = top ; /* too big! */
else nar[ii+jj*nx] = val ; /* just right */
}
}
/*** cleanup and return ***/
if( im != imfl ) mri_free(imfl) ; /* throw away unneeded workspace */
MRI_COPY_AUX(newImg,im) ;
return newImg ;
}
