Xu's antinormalisation (broken, though)

Former-commit-id: 36ce5c8fdb1e63fe790cb40097f22b38fb2dff00

BUGS.rst

@@ -3,11 +3,19 @@ Known bugs
 
 Wrong factor on B coefficient
 -----------------------------
+(Probably fixed in the "calculator object" versions!)
 Under Kristensson normalisation (with CS = -1), my code gives
 B(1,0,n,n)/B(1,0,n,-n) == -(2n)! at (x,y,z) = (x,0,0)
 (expected plus or minus 1).
 A-coefficients seem to behave correctly.
 
+Xu's antinormalisation
+----------------------
+"Xu's antinormalisation" is broken (most likely in legendre.c and maybe
+also in qpms_types.h) – the plane wave test fails and the spherical wave
+reconstruction as well (but the translation coefficients match the 
+Xu's tables).
+
 Translation coefficients inconsistent
 -------------------------------------
 The translation coefficients currently do not work correctly except for certain

qpms/legendre.c

@@ -92,10 +92,14 @@ qpms_pitau_t qpms_pitau_get(double theta, qpms_l_t lMax, qpms_normalisation_t no
           res.tau[qpms_mn2y(-1, l)] = -((ct>0) ? +1 : lpar) * n * csphase;
         }
         break;
+#ifdef USE_XU_ANTINORMALISATION // broken
       case QPMS_NORMALISATION_XU: // Rather useless except for testing.
         for (qpms_l_t l = 1; l <= lMax; ++l) {
           res.leg[qpms_mn2y(0, l)] = ((l%2)?ct:1.)*sqrt(0.25*M_1_PI *(2*l+1)/(l*(l+1)));
-          double p = ..... HERE TODO ENDED CO
+          double p = l*(l+1)/2 /* as in _NONE */ 
+            * sqrt(0.25 * M_1_PI * (2*l + 1));
+          double n = 0.5 /* as in _NONE */
+            * sqrt(0.25 * M_1_PI * (2*l + 1)) / (l * (l+1));
           int lpar = (l%2)?-1:1;
           res.pi [qpms_mn2y(+1, l)] = -((ct>0) ? -1 : lpar) * p * csphase;
           res.pi [qpms_mn2y(-1, l)] = -((ct>0) ? -1 : lpar) * n * csphase;
@@ -103,6 +107,7 @@ qpms_pitau_t qpms_pitau_get(double theta, qpms_l_t lMax, qpms_normalisation_t no
           res.tau[qpms_mn2y(-1, l)] = -((ct>0) ? +1 : lpar) * n * csphase;
         }
         break;
+#endif
       case QPMS_NORMALISATION_TAYLOR:
         for (qpms_l_t l = 1; l <= lMax; ++l) {
           res.leg[qpms_mn2y(0, l)] = ((l%2)?ct:1.)*sqrt((2*l+1)*0.25*M_1_PI);
@@ -149,10 +154,12 @@ qpms_pitau_t qpms_pitau_get(double theta, qpms_l_t lMax, qpms_normalisation_t no
           legder[qpms_mn2y(m,l)] *= prefac;
         }
       }
+#ifdef USE_XU_ANTINORMALISATION
     else if (norm == QPMS_NORMALISATION_XU)
       /* for Xu (anti-normalized), we start from spharm-normalized Legendre functions
        * Do not use this normalisation except for testing
        */
+      // FIXME PROBABLY BROKEN HERE
       for (qpms_l_t l = 1; l <= lMax; ++l) {
         double prefac = (2*l + 1) / sqrt(4*M_PI / (l*(l+1)));
         for (qpms_m_t m = -l; m <= l; ++m) {
@@ -161,6 +168,7 @@ qpms_pitau_t qpms_pitau_get(double theta, qpms_l_t lMax, qpms_normalisation_t no
           legder[qpms_mn2y(m,l)] *= fac;
         }
       }
+#endif
     for (qpms_l_t l = 1; l <= lMax; ++l) {
       for (qpms_m_t m = -l; m <= l; ++m) {
         res.pi [qpms_mn2y(m,l)] = m / st * res.leg[qpms_mn2y(m,l)];

qpms/qpms_types.h

@@ -26,8 +26,11 @@ typedef enum {
 //const int QPMS_NORMALISATION_T_CSBIT = 128;
 #define QPMS_NORMALISATION_T_CSBIT 128
 typedef enum {
+#ifdef USE_XU_ANTINORMALISATION
 	// As in TODO
 	QPMS_NORMALISATION_XU = 4, // such that the numerical values in Xu's tables match, not recommended to use otherwise
+	QPMS_NORMALISATION_XU_CS = QPMS_NORMALISATION_XU | QPMS_NORMALISATION_T_CSBIT, 
+#endif
 	QPMS_NORMALISATION_NONE = 3, // genuine unnormalised waves (with unnormalised Legendre polynomials)
 	// As in http://www.eit.lth.se/fileadmin/eit/courses/eit080f/Literature/book.pdf, power-normalised
 	QPMS_NORMALISATION_KRISTENSSON = 2,
@@ -36,7 +39,6 @@ typedef enum {
 	QPMS_NORMALISATION_TAYLOR = 1,
 	QPMS_NORMALISATION_SPHARM = QPMS_NORMALISATION_TAYLOR,
 	// Variants with Condon-Shortley phase
-	QPMS_NORMALISATION_XU_CS = QPMS_NORMALISATION_XU | QPMS_NORMALISATION_T_CSBIT, 
 	QPMS_NORMALISATION_NONE_CS = QPMS_NORMALISATION_NONE | QPMS_NORMALISATION_T_CSBIT,
 	QPMS_NORMALISATION_KRISTENSSON_CS = QPMS_NORMALISATION_KRISTENSSON | QPMS_NORMALISATION_T_CSBIT, 
 	QPMS_NORMALISATION_POWER_CS = QPMS_NORMALISATION_KRISTENSSON_CS,
@@ -83,9 +85,11 @@ static inline double qpms_normalisation_t_factor(qpms_normalisation_t norm, qpms
 		case QPMS_NORMALISATION_NONE:
 			factor = sqrt(l*(l+1) * 4 * M_PI / (2*l+1) * exp(lgamma(l+m+1)-lgamma(l-m+1)));
 			break;
+#ifdef USE_XU_ANTINORMALISATION // broken probably in legendre.c
 		case QPMS_NORMALISATION_XU:
 			factor = sqrt(4 * M_PI) / (2*l+1) * exp(lgamma(l+m+1)-lgamma(l-m+1));
 			break;
+#endif
 		default:
 			assert(0);
 	}
@@ -107,10 +111,14 @@ static inline double qpms_normalisation_t_factor_abssquare(qpms_normalisation_t
 		case QPMS_NORMALISATION_NONE:
 			return l*(l+1) * 4 * M_PI / (2*l+1) * exp(lgamma(l+m+1)-lgamma(l-m+1));
 			break;
+#ifdef USE_XU_ANTINORMALISATION // broken probably in legendre.c
 		case QPMS_NORMALISATION_XU:
+			{
 			  double fac = sqrt(4 * M_PI) / (2*l+1) * exp(lgamma(l+m+1)-lgamma(l-m+1));
 			  return fac * fac;
+			}
 			break;
+#endif 
 		default:
 			assert(0);
 			return NAN;

qpms/tests/test_planewave_decomposition.c

@@ -8,6 +8,9 @@
 #include "string.h"
 #include "indexing.h"
 
+#define _GNU_SOURCE
+#include <fenv.h>
+
 char *normstr(qpms_normalisation_t norm) {
 	//int csphase = qpms_normalisation_t_csphase(norm);
 	norm = qpms_normalisation_t_normonly(norm);
@@ -18,6 +21,8 @@ char *normstr(qpms_normalisation_t norm) {
 			return "spharm";
 		case QPMS_NORMALISATION_POWER:
 			return "power";
+    case QPMS_NORMALISATION_XU:
+      return "xu";
 		default:
 			return "!!!undef!!!";
 	}
@@ -28,8 +33,9 @@ int test_planewave_decomposition_silent(cart3_t k, ccart3_t E, qpms_l_t lMax, qp
 int main() {
 	gsl_rng *rng =  gsl_rng_alloc(gsl_rng_ranlxs0);
 	gsl_rng_set(rng, 666);
+  feenableexcept(FE_INVALID | FE_OVERFLOW);
 
-	qpms_l_t lMax = 50;
+	qpms_l_t lMax = 30;
 	int npoints = 10;
 	double sigma = 1.3;
 	cart3_t points[npoints];
@@ -76,7 +82,7 @@ int main() {
 			for(int p = 0; p < npoints; ++p) printf("%.3g ", relerrs[p]);
 		}
 #endif 
-		for(int i = 1; i <= 3; ++i){
+		for(int i = 1; i <= 4; ++i){
 			test_planewave_decomposition(k, E, lMax, i, npoints, points);
 			test_planewave_decomposition(k, E, lMax, i | QPMS_NORMALISATION_T_CSBIT, npoints, points);
 		}

qpms/tests/test_vswf_translations.c

@@ -20,6 +20,10 @@ char *normstr(qpms_normalisation_t norm) {
 			return "spharm";
 		case QPMS_NORMALISATION_POWER:
 			return "power";
+#ifdef USE_XU_ANTINORMALISATION
+    case QPMS_NORMALISATION_XU:
+      return "xu";
+#endif
 		default:
 			return "!!!undef!!!";
 	}
@@ -37,13 +41,13 @@ int main() {
 	qpms_l_t lMax = 8;
 	//qpms_l_t viewlMax = 2;
 	int npoints = 10;
-	double sigma = 0.1;
+	double sigma = 4;
-	double shiftsigma = 2.;
+  //double shiftsigma = 2.;
 
 	cart3_t o2minuso1;
-	o2minuso1.x = gsl_ran_gaussian(rng, shiftsigma);
+	o2minuso1.x = 1; //gsl_ran_gaussian(rng, shiftsigma);
-	o2minuso1.y = gsl_ran_gaussian(rng, shiftsigma);
+	o2minuso1.y = 2; //gsl_ran_gaussian(rng, shiftsigma);
-	o2minuso1.z = gsl_ran_gaussian(rng, shiftsigma);
+	o2minuso1.z = 5; //gsl_ran_gaussian(rng, shiftsigma);
 	
 	cart3_t points[npoints];
 	double relerrs[npoints];
@@ -58,7 +62,13 @@ int main() {
 	}
 	
 	for(int use_csbit = 0; use_csbit <= 1; ++use_csbit) {
-		for(int i = 1; i <= 3; ++i){
+		for(int i = 1; 
+#ifdef USE_XU_ANTINORMALISATION
+        i <= 4; 
+#else
+        i <= 3; 
+#endif
+        ++i){
 			qpms_normalisation_t norm = i | (use_csbit ? QPMS_NORMALISATION_T_CSBIT : 0);
 			qpms_trans_calculator *c = qpms_trans_calculator_init(lMax, norm);
 			for(int J = 1; J <= 4; ++J)
@@ -109,7 +119,7 @@ int test_sphwave_translation(const qpms_trans_calculator *c, qpms_bessel_t wavet
 			for(qpms_y_t y2 = 0; y2 < nelem; ++y2){
 				qpms_m_t m2; qpms_l_t l2;
 				qpms_y2mn_p(y2, &m2, &l2);
-				if(qpms_trans_calculator_get_AB_p(c, A+y2, B+y2, m2, l2, m1, l1, ss, (w1s.r > ss.r), wavetype))
+				if(qpms_trans_calculator_get_AB_p(c, &(A[y2]), &(B[y2]), m2, l2, m1, l1, ss, (w1s.r > ss.r) , wavetype))
 					abort();
 			}
 

qpms/tests/testcases_translations_Xu

@@ -8,7 +8,7 @@
 {QPMS_NORMALISATION_XU, 22,40,-39,45, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .34997554e216 + .45574651e216 * I, -.23949371e214 + .18391132e214* I},
 {QPMS_NORMALISATION_XU, 5,50,-22,61, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .89567769e226 + -.12101307e227 * I, .50442227e224 + .37334790e224* I},
 // Yu-lin Xu, Journal of computational physics 139, 137–165 (1998), Table 12
-{QPMS_NORMALISATION_XU, 8,10,-9,12, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .3663964990e+35 + -.2762412192e+35 * I, -.8370892023e+32 + -.1110285257e+33* I /* N.B. article value is erroneous */},
+{QPMS_NORMALISATION_XU, 8,10,-9,12, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .3663964990e+35 + -.2762412192e+35 * I, -.8370892023e+32 + -.1110285257e+33 * I},/* N.B. article value is erroneous */
 {QPMS_NORMALISATION_XU, 0,10,0,10, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .2969682019e+00 + -.1928601440e+18 * I, .0000000000e+00 + .0000000000e+00* I},
 {QPMS_NORMALISATION_XU, -2,11,3,9, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .7726121583e+12 + .1034255820e+13 * I, .1222239141e+11 + -.9130398908e+10* I},
 {QPMS_NORMALISATION_XU, -12,13,10,15, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .3290937356e+01 + .1456483748e-01 * I, -.1763167849e-03 + .3983892680e-01* I},
@@ -28,12 +28,11 @@
 {QPMS_NORMALISATION_XU, -72,72,1,3, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .6946365327e-42 + -.1782022552e-41 * I, .1833377882e-43 + .7146549596e-44* I},
 {QPMS_NORMALISATION_XU, 42,52,9,81, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .3656934399e+271 + .3705813223e+271 * I, -.4499925012e+269 + -.4440572037e+269* I},
 {QPMS_NORMALISATION_XU, 18,100,-5,45, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .4118769973e+293 + .7460688240e+293 * I, .5914795871e+291 + -.3265339985e+291* I},
-// Yu-lin Xu, Journal of computational physics 139, 137–165 (1998), Table 14 // FIXME not in the .fodt file because of motherfucking ubuntu at work
+// Yu-lin Xu, Journal of computational physics 139, 137–165 (1998), Table 14
 {QPMS_NORMALISATION_XU, -2,6,-2,10, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .1377011649e-01 + .2385575934e+13 * I, -.3282035237e+12 + .1587043209e-02* I},
-{QPMS_NORMALISATION_XU, -15,16,-15,20, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .2074318970e-01 + -.2653706899e+36 * I, -.5072175010e+35 + .9852438545E-02 * I},
+{QPMS_NORMALISATION_XU, -15,16,-15,20, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .2074318970e-01 + -.2653706899e+36 * I, -.5072175010e+35 + .9852438545e-02* I},
-{QPMS_NORMALISATION_XU, -20,35,-20,45, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .1851837652E-05 + -.4993981811e+115 * I, -.2073152255+114 + .4193366215E-07 * I},
+{QPMS_NORMALISATION_XU, -20,35,-20,45, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .1851837652e-05 + -.4993981811e+115 * I, -.2073152255e+114 + .4193366215e-07* I},
-{QPMS_NORMALISATION_XU, 41,45,-42,45, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .2276246420e+247 + .2937180509e+247 * I, -.8692874643e+243 + .6736775193e+243 * I},
+{QPMS_NORMALISATION_XU, 41,45,-42,45, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .2276246420e+247 + .2937180509e+247 * I, -.8692874643e+243 + .6736775193e+243* I},
-{QPMS_NORMALISATION_XU, 45,57,-38,42, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .4293609827e+274 + .3327447520e+274 * I, -.4939385256e+271 + -.6373592055e+271 * I},
+{QPMS_NORMALISATION_XU, 45,57,-38,42, {2., 0.5, 0.5}, QPMS_HANKEL_PLUS, .4293609827e+274 + .3327447520e+274 * I, -.4939385256e+271 + -.6373592055e+271* I},
 // THE END
 {QPMS_NORMALISATION_UNDEF, 0,0,0,0, {0, 0, 0}, QPMS_BESSEL_UNDEF, 0 + 0 * I, 0 + 0* I}
-

qpms/tests/testcases_translations_Xu.fods

@@ -1,20 +1,20 @@
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- <office:meta><meta:creation-date>2018-02-07T18:03:11.644802081</meta:creation-date><dc:date>2018-02-07T19:45:24.778557362</dc:date><meta:editing-duration>PT29M30S</meta:editing-duration><meta:editing-cycles>6</meta:editing-cycles><meta:generator>LibreOffice/5.1.6.2$Linux_X86_64 LibreOffice_project/10m0$Build-2</meta:generator><meta:document-statistic meta:table-count="1" meta:cell-count="787" meta:object-count="0"/></office:meta>
+ <office:meta><meta:creation-date>2018-02-07T18:03:11.644802081</meta:creation-date><dc:date>2018-05-08T18:45:46.807538258</dc:date><meta:editing-duration>PT36M22S</meta:editing-duration><meta:editing-cycles>7</meta:editing-cycles><meta:generator>LibreOffice/4.3.3.2$Linux_X86_64 LibreOffice_project/430m0$Build-2</meta:generator><meta:document-statistic meta:table-count="1" meta:cell-count="924" meta:object-count="0"/></office:meta>
  <office:settings>
   <config:config-item-set config:name="ooo:view-settings">
    <config:config-item config:name="VisibleAreaTop" config:type="int">0</config:config-item>
    <config:config-item config:name="VisibleAreaLeft" config:type="int">0</config:config-item>
-   <config:config-item config:name="VisibleAreaWidth" config:type="int">36119</config:config-item>
+   <config:config-item config:name="VisibleAreaWidth" config:type="int">38376</config:config-item>
-   <config:config-item config:name="VisibleAreaHeight" config:type="int">14449</config:config-item>
+   <config:config-item config:name="VisibleAreaHeight" config:type="int">17159</config:config-item>
    <config:config-item-map-indexed config:name="Views">
     <config:config-item-map-entry>
      <config:config-item config:name="ViewId" config:type="string">view1</config:config-item>
      <config:config-item-map-named config:name="Tables">
       <config:config-item-map-entry config:name="Taulukko1">
-       <config:config-item config:name="CursorPositionX" config:type="int">10</config:config-item>
+       <config:config-item config:name="CursorPositionX" config:type="int">4</config:config-item>
-       <config:config-item config:name="CursorPositionY" config:type="int">9</config:config-item>
+       <config:config-item config:name="CursorPositionY" config:type="int">36</config:config-item>
        <config:config-item config:name="HorizontalSplitMode" config:type="short">0</config:config-item>
        <config:config-item config:name="VerticalSplitMode" config:type="short">0</config:config-item>
        <config:config-item config:name="HorizontalSplitPosition" config:type="int">0</config:config-item>
@@ -23,7 +23,7 @@
        <config:config-item config:name="PositionLeft" config:type="int">0</config:config-item>
        <config:config-item config:name="PositionRight" config:type="int">0</config:config-item>
        <config:config-item config:name="PositionTop" config:type="int">0</config:config-item>
-       <config:config-item config:name="PositionBottom" config:type="int">0</config:config-item>
+       <config:config-item config:name="PositionBottom" config:type="int">5</config:config-item>
        <config:config-item config:name="ZoomType" config:type="short">0</config:config-item>
        <config:config-item config:name="ZoomValue" config:type="int">100</config:config-item>
        <config:config-item config:name="PageViewZoomValue" config:type="int">60</config:config-item>
@@ -31,7 +31,7 @@
       </config:config-item-map-entry>
      </config:config-item-map-named>
      <config:config-item config:name="ActiveTable" config:type="string">Taulukko1</config:config-item>
-     <config:config-item config:name="HorizontalScrollbarWidth" config:type="int">1853</config:config-item>
+     <config:config-item config:name="HorizontalScrollbarWidth" config:type="int">1228</config:config-item>
      <config:config-item config:name="ZoomType" config:type="short">0</config:config-item>
      <config:config-item config:name="ZoomValue" config:type="int">100</config:config-item>
      <config:config-item config:name="PageViewZoomValue" config:type="int">60</config:config-item>
@@ -44,7 +44,6 @@
      <config:config-item config:name="HasColumnRowHeaders" config:type="boolean">true</config:config-item>
      <config:config-item config:name="HasSheetTabs" config:type="boolean">true</config:config-item>
      <config:config-item config:name="IsOutlineSymbolsSet" config:type="boolean">true</config:config-item>
-     <config:config-item config:name="IsValueHighlightingEnabled" config:type="boolean">false</config:config-item>
      <config:config-item config:name="IsSnapToRaster" config:type="boolean">false</config:config-item>
      <config:config-item config:name="RasterIsVisible" config:type="boolean">false</config:config-item>
      <config:config-item config:name="RasterResolutionX" config:type="int">1000</config:config-item>
@@ -56,34 +55,34 @@
    </config:config-item-map-indexed>
   </config:config-item-set>
   <config:config-item-set config:name="ooo:configuration-settings">
-   <config:config-item config:name="IsDocumentShared" config:type="boolean">false</config:config-item>
    <config:config-item config:name="LoadReadonly" config:type="boolean">false</config:config-item>
-   <config:config-item config:name="AllowPrintJobCancel" config:type="boolean">true</config:config-item>
-   <config:config-item config:name="UpdateFromTemplate" config:type="boolean">true</config:config-item>
-   <config:config-item config:name="IsKernAsianPunctuation" config:type="boolean">false</config:config-item>
-   <config:config-item config:name="EmbedFonts" config:type="boolean">false</config:config-item>
-   <config:config-item config:name="IsSnapToRaster" config:type="boolean">false</config:config-item>
-   <config:config-item config:name="RasterResolutionX" config:type="int">1000</config:config-item>
-   <config:config-item config:name="RasterResolutionY" config:type="int">1000</config:config-item>
-   <config:config-item config:name="HasSheetTabs" config:type="boolean">true</config:config-item>
-   <config:config-item config:name="IsRasterAxisSynchronized" config:type="boolean">true</config:config-item>
-   <config:config-item config:name="ShowPageBreaks" config:type="boolean">true</config:config-item>
-   <config:config-item config:name="ShowGrid" config:type="boolean">true</config:config-item>
-   <config:config-item config:name="ShowNotes" config:type="boolean">true</config:config-item>
-   <config:config-item config:name="IsOutlineSymbolsSet" config:type="boolean">true</config:config-item>
-   <config:config-item config:name="ShowZeroValues" config:type="boolean">true</config:config-item>
    <config:config-item config:name="SaveVersionOnClose" config:type="boolean">false</config:config-item>
-   <config:config-item config:name="GridColor" config:type="long">12632256</config:config-item>
+   <config:config-item config:name="IsDocumentShared" config:type="boolean">false</config:config-item>
-   <config:config-item config:name="RasterIsVisible" config:type="boolean">false</config:config-item>
+   <config:config-item config:name="IsKernAsianPunctuation" config:type="boolean">false</config:config-item>
-   <config:config-item config:name="PrinterName" config:type="string"/>
-   <config:config-item config:name="LinkUpdateMode" config:type="short">3</config:config-item>
-   <config:config-item config:name="RasterSubdivisionX" config:type="int">1</config:config-item>
-   <config:config-item config:name="HasColumnRowHeaders" config:type="boolean">true</config:config-item>
-   <config:config-item config:name="RasterSubdivisionY" config:type="int">1</config:config-item>
-   <config:config-item config:name="AutoCalculate" config:type="boolean">true</config:config-item>
-   <config:config-item config:name="PrinterSetup" config:type="base64Binary"/>
    <config:config-item config:name="ApplyUserData" config:type="boolean">true</config:config-item>
    <config:config-item config:name="CharacterCompressionType" config:type="short">0</config:config-item>
+   <config:config-item config:name="PrinterSetup" config:type="base64Binary">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</config:config-item>
+   <config:config-item config:name="PrinterName" config:type="string">HP-LaserJet-3390</config:config-item>
+   <config:config-item config:name="UpdateFromTemplate" config:type="boolean">true</config:config-item>
+   <config:config-item config:name="AutoCalculate" config:type="boolean">true</config:config-item>
+   <config:config-item config:name="EmbedFonts" config:type="boolean">false</config:config-item>
+   <config:config-item config:name="RasterIsVisible" config:type="boolean">false</config:config-item>
+   <config:config-item config:name="IsSnapToRaster" config:type="boolean">false</config:config-item>
+   <config:config-item config:name="RasterSubdivisionX" config:type="int">1</config:config-item>
+   <config:config-item config:name="IsOutlineSymbolsSet" config:type="boolean">true</config:config-item>
+   <config:config-item config:name="AllowPrintJobCancel" config:type="boolean">true</config:config-item>
+   <config:config-item config:name="RasterResolutionX" config:type="int">1000</config:config-item>
+   <config:config-item config:name="HasSheetTabs" config:type="boolean">true</config:config-item>
+   <config:config-item config:name="LinkUpdateMode" config:type="short">3</config:config-item>
+   <config:config-item config:name="IsRasterAxisSynchronized" config:type="boolean">true</config:config-item>
+   <config:config-item config:name="ShowPageBreaks" config:type="boolean">true</config:config-item>
+   <config:config-item config:name="HasColumnRowHeaders" config:type="boolean">true</config:config-item>
+   <config:config-item config:name="GridColor" config:type="long">12632256</config:config-item>
+   <config:config-item config:name="ShowGrid" config:type="boolean">true</config:config-item>
+   <config:config-item config:name="RasterSubdivisionY" config:type="int">1</config:config-item>
+   <config:config-item config:name="RasterResolutionY" config:type="int">1000</config:config-item>
+   <config:config-item config:name="ShowNotes" config:type="boolean">true</config:config-item>
+   <config:config-item config:name="ShowZeroValues" config:type="boolean">true</config:config-item>
   </config:config-item-set>
  </office:settings>
  <office:scripts>
@@ -101,21 +100,21 @@
  </office:font-face-decls>
  <office:styles>
   <style:default-style style:family="table-cell">
-   <style:paragraph-properties style:tab-stop-distance="12.5mm"/>
+   <style:paragraph-properties style:tab-stop-distance="1.25cm"/>
    <style:text-properties style:font-name="Liberation Sans" fo:language="fi" fo:country="FI" style:font-name-asian="DejaVu Sans" style:language-asian="zh" style:country-asian="CN" style:font-name-complex="DejaVu Sans" style:language-complex="hi" style:country-complex="IN"/>
   </style:default-style>
   <number:number-style style:name="N0">
    <number:number number:min-integer-digits="1"/>
   </number:number-style>
   <number:currency-style style:name="N107P0" style:volatile="true">
-   <number:number number:decimal-places="2" loext:min-decimal-places="2" number:min-integer-digits="1" number:grouping="true"/>
+   <number:number number:decimal-places="2" number:min-integer-digits="1" number:grouping="true"/>
    <number:text> </number:text>
    <number:currency-symbol number:language="fi" number:country="FI">€</number:currency-symbol>
   </number:currency-style>
   <number:currency-style style:name="N107">
    <style:text-properties fo:color="#ff0000"/>
    <number:text>-</number:text>
-   <number:number number:decimal-places="2" loext:min-decimal-places="2" number:min-integer-digits="1" number:grouping="true"/>
+   <number:number number:decimal-places="2" number:min-integer-digits="1" number:grouping="true"/>
    <number:text> </number:text>
    <number:currency-symbol number:language="fi" number:country="FI">€</number:currency-symbol>
    <style:map style:condition="value()&gt;=0" style:apply-style-name="N107P0"/>
@@ -138,78 +137,78 @@
  </office:styles>
  <office:automatic-styles>
   <style:style style:name="co1" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="22.58mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="2.258cm"/>
   </style:style>
   <style:style style:name="co2" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="4.89mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.489cm"/>
   </style:style>
   <style:style style:name="co3" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="5.17mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.517cm"/>
   </style:style>
   <style:style style:name="co4" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="6.79mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.679cm"/>
   </style:style>
   <style:style style:name="co5" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="5.43mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.543cm"/>
   </style:style>
   <style:style style:name="co6" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="5.72mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.572cm"/>
   </style:style>
   <style:style style:name="co7" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="8.17mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.817cm"/>
   </style:style>
   <style:style style:name="co8" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="4.07mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.407cm"/>
   </style:style>
   <style:style style:name="co9" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="9.79mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.979cm"/>
   </style:style>
   <style:style style:name="co10" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="4.62mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.462cm"/>
   </style:style>
   <style:style style:name="co11" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="10.34mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="1.034cm"/>
   </style:style>
   <style:style style:name="co12" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="6.53mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.653cm"/>
   </style:style>
   <style:style style:name="co13" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="7.88mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.788cm"/>
   </style:style>
   <style:style style:name="co14" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="5.98mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.598cm"/>
   </style:style>
   <style:style style:name="co15" style:family="table-column">
-   <style:table-column-properties fo:break-before="auto" style:column-width="7.62mm"/>
+   <style:table-column-properties fo:break-before="auto" style:column-width="0.762cm"/>
   </style:style>
   <style:style style:name="ro1" style:family="table-row">
-   <style:table-row-properties style:row-height="4.52mm" fo:break-before="auto" style:use-optimal-row-height="true"/>
+   <style:table-row-properties style:row-height="0.452cm" fo:break-before="auto" style:use-optimal-row-height="true"/>
   </style:style>
   <style:style style:name="ta1" style:family="table" style:master-page-name="Default">
    <style:table-properties table:display="true" style:writing-mode="lr-tb"/>
   </style:style>
   <style:style style:name="ce1" style:family="table-cell" style:parent-style-name="Default">
    <style:table-cell-properties style:text-align-source="value-type" style:repeat-content="false"/>
-   <style:paragraph-properties fo:margin-left="0mm"/>
+   <style:paragraph-properties fo:margin-left="0cm"/>
   </style:style>
   <style:page-layout style:name="pm1">
    <style:page-layout-properties style:writing-mode="lr-tb"/>
    <style:header-style>
-    <style:header-footer-properties fo:min-height="7.5mm" fo:margin-left="0mm" fo:margin-right="0mm" fo:margin-bottom="2.5mm"/>
+    <style:header-footer-properties fo:min-height="0.75cm" fo:margin-left="0cm" fo:margin-right="0cm" fo:margin-bottom="0.25cm"/>
    </style:header-style>
    <style:footer-style>
-    <style:header-footer-properties fo:min-height="7.5mm" fo:margin-left="0mm" fo:margin-right="0mm" fo:margin-top="2.5mm"/>
+    <style:header-footer-properties fo:min-height="0.75cm" fo:margin-left="0cm" fo:margin-right="0cm" fo:margin-top="0.25cm"/>
    </style:footer-style>
   </style:page-layout>
   <style:page-layout style:name="pm2">
    <style:page-layout-properties style:writing-mode="lr-tb"/>
    <style:header-style>
-    <style:header-footer-properties fo:min-height="7.5mm" fo:margin-left="0mm" fo:margin-right="0mm" fo:margin-bottom="2.5mm" fo:border="2.49pt solid #000000" fo:padding="0.18mm" fo:background-color="#c0c0c0">
+    <style:header-footer-properties fo:min-height="0.75cm" fo:margin-left="0cm" fo:margin-right="0cm" fo:margin-bottom="0.25cm" fo:border="2.49pt solid #000000" fo:padding="0.018cm" fo:background-color="#c0c0c0">
      <style:background-image/>
     </style:header-footer-properties>
    </style:header-style>
    <style:footer-style>
-    <style:header-footer-properties fo:min-height="7.5mm" fo:margin-left="0mm" fo:margin-right="0mm" fo:margin-top="2.5mm" fo:border="2.49pt solid #000000" fo:padding="0.18mm" fo:background-color="#c0c0c0">
+    <style:header-footer-properties fo:min-height="0.75cm" fo:margin-left="0cm" fo:margin-right="0cm" fo:margin-top="0.25cm" fo:border="2.49pt solid #000000" fo:padding="0.018cm" fo:background-color="#c0c0c0">
      <style:background-image/>
     </style:header-footer-properties>
    </style:footer-style>
@@ -232,7 +231,7 @@
      <text:p><text:sheet-name>???</text:sheet-name> (<text:title>???</text:title>)</text:p>
     </style:region-left>
     <style:region-right>
-     <text:p><text:date style:data-style-name="N2" text:date-value="2018-02-07">00.00.0000</text:date>, <text:time>00:00:00</text:time></text:p>
+     <text:p><text:date style:data-style-name="N2" text:date-value="2018-05-08">00.00.0000</text:date>, <text:time style:data-style-name="N2" text:time-value="18:38:54.840458010">00:00:00</text:time></text:p>
     </style:region-right>
    </style:header>
    <style:header-left style:display="false"/>
@@ -272,6 +271,7 @@
     <table:table-column table:style-name="co14" table:default-cell-style-name="Default"/>
     <table:table-column table:style-name="co1" table:default-cell-style-name="ce1"/>
     <table:table-column table:style-name="co15" table:default-cell-style-name="Default"/>
+    <table:table-column table:style-name="co1" table:default-cell-style-name="Default"/>
     <table:table-row table:style-name="ro1">
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>//</text:p>
@@ -357,6 +357,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell office:value-type="string" calcext:value-type="string">
@@ -370,7 +371,7 @@
      <table:table-cell table:style-name="Default"/>
      <table:table-cell/>
      <table:table-cell table:style-name="Default"/>
-     <table:table-cell/>
+     <table:table-cell table:number-columns-repeated="2"/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -455,6 +456,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -539,6 +541,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -623,6 +626,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -707,6 +711,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -791,6 +796,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -875,6 +881,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -959,6 +966,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell office:value-type="string" calcext:value-type="string">
@@ -972,7 +980,7 @@
      <table:table-cell table:style-name="Default"/>
      <table:table-cell/>
      <table:table-cell table:style-name="Default"/>
-     <table:table-cell/>
+     <table:table-cell table:number-columns-repeated="2"/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -1051,12 +1059,15 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p><text:s/>+ </text:p>
      </table:table-cell>
-     <table:table-cell office:value-type="string" calcext:value-type="string">
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
-      <text:p>-.1110285257e+32</text:p>
+      <text:p>-.1110285257e+33</text:p>
      </table:table-cell>
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>/* N.B. article value is erroneous */</text:p>
+     </table:table-cell>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -1141,6 +1152,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -1225,6 +1237,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -1309,6 +1322,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -1393,6 +1407,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -1477,6 +1492,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -1561,6 +1577,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -1645,6 +1662,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -1729,6 +1747,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -1813,6 +1832,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -1897,6 +1917,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -1981,6 +2002,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -2065,6 +2087,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -2149,6 +2172,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -2233,6 +2257,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -2317,6 +2342,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -2401,6 +2427,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -2485,6 +2512,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -2569,6 +2597,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -2653,6 +2682,438 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I},</text:p>
      </table:table-cell>
+     <table:table-cell/>
+    </table:table-row>
+    <table:table-row table:style-name="ro1">
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>// Yu-lin Xu, Journal of computational physics 139, 137–165 (1998), Table 14</text:p>
+     </table:table-cell>
+     <table:table-cell table:number-columns-repeated="28"/>
+    </table:table-row>
+    <table:table-row table:style-name="ro1">
+     <table:table-cell/>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>{</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>QPMS_NORMALISATION_XU</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="-2" calcext:value-type="float">
+      <text:p>-2</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="6" calcext:value-type="float">
+      <text:p>6</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="-2" calcext:value-type="float">
+      <text:p>-2</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="10" calcext:value-type="float">
+      <text:p>10</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, {</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>2.</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>0.5</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>0.5</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>}, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>QPMS_HANKEL_PLUS</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>.1377011649e-01</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>+ </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>.2385575934e+13</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>* I, </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>-.3282035237e+12</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>+ </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>.1587043209e-02</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>* I},</text:p>
+     </table:table-cell>
+     <table:table-cell/>
+    </table:table-row>
+    <table:table-row table:style-name="ro1">
+     <table:table-cell/>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>{</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>QPMS_NORMALISATION_XU</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="-15" calcext:value-type="float">
+      <text:p>-15</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>16</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="-15" calcext:value-type="float">
+      <text:p>-15</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="20" calcext:value-type="float">
+      <text:p>20</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, {</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>2.</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>0.5</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>0.5</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>}, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>QPMS_HANKEL_PLUS</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>.2074318970e-01</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>+ </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>-.2653706899e+36</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>* I, </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>-.5072175010e+35</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>+ </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>.9852438545e-02</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>* I},</text:p>
+     </table:table-cell>
+     <table:table-cell/>
+    </table:table-row>
+    <table:table-row table:style-name="ro1">
+     <table:table-cell/>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>{</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>QPMS_NORMALISATION_XU</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="-20" calcext:value-type="float">
+      <text:p>-20</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="35" calcext:value-type="float">
+      <text:p>35</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="-20" calcext:value-type="float">
+      <text:p>-20</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="45" calcext:value-type="float">
+      <text:p>45</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, {</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>2.</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>0.5</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>0.5</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>}, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>QPMS_HANKEL_PLUS</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>.1851837652e-05</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>+ </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>-.4993981811e+115</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>* I, </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>-.2073152255e+114</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>+ </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>.4193366215e-07</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>* I},</text:p>
+     </table:table-cell>
+     <table:table-cell/>
+    </table:table-row>
+    <table:table-row table:style-name="ro1">
+     <table:table-cell/>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>{</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>QPMS_NORMALISATION_XU</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="41" calcext:value-type="float">
+      <text:p>41</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="45" calcext:value-type="float">
+      <text:p>45</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="-42" calcext:value-type="float">
+      <text:p>-42</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="45" calcext:value-type="float">
+      <text:p>45</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, {</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>2.</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>0.5</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>0.5</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>}, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>QPMS_HANKEL_PLUS</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>.2276246420e+247</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>+ </text:p>
+     </table:table-cell>
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+      <text:p>.2937180509e+247</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>* I, </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>-.8692874643e+243</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>+ </text:p>
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+      <text:p>.6736775193e+243</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>* I},</text:p>
+     </table:table-cell>
+     <table:table-cell/>
+    </table:table-row>
+    <table:table-row table:style-name="ro1">
+     <table:table-cell/>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>{</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>QPMS_NORMALISATION_XU</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
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+     <table:table-cell office:value-type="float" office:value="45" calcext:value-type="float">
+      <text:p>45</text:p>
+     </table:table-cell>
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+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="57" calcext:value-type="float">
+      <text:p>57</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="-38" calcext:value-type="float">
+      <text:p>-38</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>,</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="float" office:value="42" calcext:value-type="float">
+      <text:p>42</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, {</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>2.</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>0.5</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>0.5</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>}, </text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>QPMS_HANKEL_PLUS</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>, </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>.4293609827e+274</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>+ </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>.3327447520e+274</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>* I, </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>-.4939385256e+271</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p><text:s/>+ </text:p>
+     </table:table-cell>
+     <table:table-cell table:style-name="Default" office:value-type="string" calcext:value-type="string">
+      <text:p>-.6373592055e+271</text:p>
+     </table:table-cell>
+     <table:table-cell office:value-type="string" calcext:value-type="string">
+      <text:p>* I},</text:p>
+     </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell office:value-type="string" calcext:value-type="string">
@@ -2666,7 +3127,7 @@
      <table:table-cell table:style-name="Default"/>
      <table:table-cell/>
      <table:table-cell table:style-name="Default"/>
-     <table:table-cell/>
+     <table:table-cell table:number-columns-repeated="2"/>
     </table:table-row>
     <table:table-row table:style-name="ro1">
      <table:table-cell/>
@@ -2751,6 +3212,7 @@
      <table:table-cell office:value-type="string" calcext:value-type="string">
       <text:p>* I}</text:p>
      </table:table-cell>
+     <table:table-cell/>
     </table:table-row>
    </table:table>
    <table:named-expressions/>

qpms/tests/translations_xutable_test.c

@@ -1,4 +1,4 @@
-// c99 -ggdb -I .. -DUSE_BROKEN_SINGLETC -o translations_xutable translations_xutable_test.c ../translations.c ../gaunt.c -lgsl -lblas -lm
+// c99 -ggdb -I .. -DUSE_XU_ANTINORMALISATION -DUSE_BROKEN_SINGLETC -o translations_xutable translations_xutable_test.c ../translations.c ../gaunt.c -lgsl -lblas -lm
 #include "translations.h"
 #include <stdio.h>
 //#include <math.h>

qpms/translations.c

@@ -140,9 +140,11 @@ static inline double qpms_trans_normlogfac(qpms_normalisation_t norm,
     case QPMS_NORMALISATION_NONE:
       return -(lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1));
       break;
+#ifdef USE_XU_ANTINORMALISATION
     case QPMS_NORMALISATION_XU:
       return 0;
       break;
+#endif
     default:
       abort();
   }
@@ -164,8 +166,10 @@ static inline double qpms_trans_normfac(qpms_normalisation_t norm,
     case QPMS_NORMALISATION_NONE:
       normfac *= (2.*n+1)/(2.*nu+1);
       break;
+#ifdef USE_XU_ANTINORMALISATION
     case QPMS_NORMALISATION_XU:
       break;
+#endif
     default:
       abort();
   }
@@ -787,7 +791,9 @@ int qpms_trans_calculator_multipliers_A(qpms_normalisation_t norm, complex doubl
       break;
 #endif
     case QPMS_NORMALISATION_NONE:
+#ifdef USE_XU_ANTINORMALISATION
     case QPMS_NORMALISATION_XU:
+#endif   
     case QPMS_NORMALISATION_KRISTENSSON:
       qpms_trans_calculator_multipliers_A_general(norm, dest, m, n, mu, nu, qmax);
       return 0;
@@ -807,7 +813,9 @@ int qpms_trans_calculator_multipliers_B(qpms_normalisation_t norm, complex doubl
       break;
 #endif
     case QPMS_NORMALISATION_NONE:
+#ifdef USE_XU_ANTINORMALISATION
     case QPMS_NORMALISATION_XU:
+#endif   
     case QPMS_NORMALISATION_KRISTENSSON:
       qpms_trans_calculator_multipliers_B_general(norm, dest, m, n, mu, nu, Qmax);
       return 0;
@@ -917,7 +925,9 @@ complex double qpms_trans_calculator_get_A_buf(const qpms_trans_calculator *c,
     case QPMS_NORMALISATION_TAYLOR:
     case QPMS_NORMALISATION_KRISTENSSON:
     case QPMS_NORMALISATION_NONE:
+#ifdef USE_XU_ANTINORMALISATION
     case QPMS_NORMALISATION_XU:   
+#endif
       {
         double costheta = cos(kdlj.theta);
         if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,
@@ -967,7 +977,9 @@ complex double qpms_trans_calculator_get_B_buf(const qpms_trans_calculator *c,
     case QPMS_NORMALISATION_TAYLOR:
     case QPMS_NORMALISATION_KRISTENSSON:
     case QPMS_NORMALISATION_NONE:
+#ifdef USE_XU_ANTINORMALISATION
     case QPMS_NORMALISATION_XU:   
+#endif
       {
         double costheta = cos(kdlj.theta);
         if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,
@@ -999,7 +1011,9 @@ int qpms_trans_calculator_get_AB_buf_p(const qpms_trans_calculator *c,
     case QPMS_NORMALISATION_TAYLOR:
     case QPMS_NORMALISATION_KRISTENSSON:
     case QPMS_NORMALISATION_NONE:
+#ifdef USE_XU_ANTINORMALISATION
     case QPMS_NORMALISATION_XU:   
+#endif
       {
         double costheta = cos(kdlj.theta);
         if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,