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686	<a href="spl_fstdrv.html?format=raw"><<prev file</a> \| <a href="spl_keep_mean.html?format=raw">next file >></a>    <a href="spl_incr.html?format=raw" target="_TOP">view single page</a> \| <a href="./../index.html?format=raw" target="_TOP">view frames</a>    summary: fields \| <a href="#routine_summary">routine</a>    details: <a href="#routine_details">routine</a>
687
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692
693	<h1 class="directory"><a href="directory-overview.html?format=raw">Interpolation/</a></h1>
694	<h2 class="pro_file">spl_incr.pro</h2>
695
696	<div id="file_attr">
697	<dl>
698	</dl>
699	</div>
700
701	<div id="file_comments">
702
703	Given the arrays X and Y, which tabulate a function (with the X[i]
704	AND Y[i] in ascending order), and given an input value X2, the
705	SPL_INCR function returns an interpolated value for the given values
706	of X2. The interpolation method is based on cubic spline, corrected
707	in a way that interpolated values are also monotonically increasing.
708	</div>
709
710
711
712
713
714
715
716
717	<div id="routine_summary">
718	<h2>Routine summary</h2>
719
720	<dl>
721
722	<dt><p><a href="#_pure_concave"><span class="result">result = </span>pure_concave(<span class="result">x1, x2, y1, y2, der2, x</span>)</a></p><dt>
723	<dd> </dd>
724
725	<dt><p><a href="#_pure_convex"><span class="result">result = </span>pure_convex(<span class="result">x1, x2, y1, y2, der2, x</span>)</a></p><dt>
726	<dd></dd>
727
728	<dt><p><a href="#_spl_incr"><span class="result">result = </span>spl_incr(<span class="result">x, y, x2</span>, YP0=<span class="result">YP0</span>, YPN_1=<span class="result">YPN_1</span>)</a></p><dt>
729	<dd></dd>
730
731	</dl>
732	</div>
733
734
735	<div id="routine_details">
736
737
738	<div class="routine_details" id="_pure_concave">
739
740	<h2><a class="top" href="#container">top</a>pure_concave </h2>
741
742	<p class="header">
743	<span class="result">result = </span>pure_concave(<span class="result"><a href="#_pure_concave_param_x1">x1</a>, <a href="#_pure_concave_param_x2">x2</a>, <a href="#_pure_concave_param_y1">y1</a>, <a href="#_pure_concave_param_y2">y2</a>, <a href="#_pure_concave_param_der2">der2</a>, <a href="#_pure_concave_param_x">x</a></span>)</p>
744
745	<div class="comments">
746	</div>
747
748	<h3>Return value</h3><div class="preformat">
749
750	y2: f(x2) = y2. Double precision array
751	</div>
752
753
754	<h3>Parameters</h3>
755
756
757	<h4 id="_pure_concave_param_x1">x1
758	<span class="attr">in</span>
759
760
761	<span class="attr">required</span>
762
763
764
765
766	</h4>
767
768	<div class="comments">
769	An n-element (at least 2) input vector that specifies the tabulate points in
770	a strict ascending order.
771	</div>
772
773	<h4 id="_pure_concave_param_x2">x2
774	<span class="attr">in</span>
775
776
777	<span class="attr">required</span>
778
779
780
781
782	</h4>
783
784	<div class="comments">
785	The input values for which the interpolated values are
786	desired. Its values must be strictly monotonically increasing.
787	</div>
788
789	<h4 id="_pure_concave_param_y1">y1
790	<span class="attr">in</span>
791
792
793	<span class="attr">required</span>
794
795
796
797
798	</h4>
799
800	<div class="comments">
801	f(x) = y. An n-element input vector that specifies the values
802	of the tabulated function F(Xi) corresponding to Xi. As f is
803	supposed to be monotonically increasing, y values must be
804	monotonically increasing. y can have equal consecutive values.
805	</div>
806
807	<h4 id="_pure_concave_param_y2">y2
808
809
810
811
812
813
814
815
816	</h4>
817
818	<div class="comments"></div>
819
820	<h4 id="_pure_concave_param_der2">der2
821
822
823
824
825
826
827
828
829	</h4>
830
831	<div class="comments">
832	</div>
833
834	<h4 id="_pure_concave_param_x">x
835
836
837
838
839
840
841
842
843	</h4>
844
845	<div class="comments">
846	</div>
847
848
849
850
851
852
853	<h3>Examples</h3><div class="preformat">
854
855	IDL> n = 100L
856	IDL> x = (dindgen(n))^2
857	IDL> y = abs(randomn(0, n))
858	IDL> y[n/2:n/2+1] = 0.
859	IDL> y[n-n/3] = 0.
860	IDL> y[n-n/6:n-n/6+5] = 0.
861	IDL> y = total(y, /cumulative, /double)
862	IDL> x2 = dindgen((n-1)^2)
863	IDL> n2 = n_elements(x2)
864	IDL> print, min(y[1:n-1]-y[0:n-2]) LT 0
865	IDL> y2 = spl_incr( x, y, x2)
866	IDL> splot, x, y, xstyle = 1, ystyle = 1, ysurx=.25, petit = [1, 2, 1], /land
867	IDL> oplot, x2, y2, color = 100
868	IDL> c = y2[1:n2-1] - y2[0:n2-2]
869	IDL> print, min(c) LT 0
870	IDL> print, min(c, max = ma), ma
871	IDL> splot,c,xstyle=1,ystyle=1, yrange=[-.01,.05], ysurx=.25, petit = [1, 2, 2], /noerase
872	IDL> oplot,[0, n_elements(c)], [0, 0], linestyle = 1
873	</div>
874	<h3>Version history</h3>
875
876	<h4>Version</h4><div class="preformat"> $Id: spl_incr.pro 136 2006-07-10 15:20:19Z pinsard $
877	</div>
878	<h4>History</h4><div class="preformat">
879	Sebastien Masson (smasson@lodyc.jussieu.fr): May-Dec 2005
880	</div>
881
882
883	<h3>Known issues</h3>
884
885
886
887	<h4>Restrictions</h4><div class="preformat">
888	It might be possible that y2[i+1]-y2[i] has very small negative
889	values (amplitude smaller than 1.e-6)...
890	</div>
891
892
893
894
895
896
897
898
899
900
901
902	</div>
903
904
905	<div class="routine_details" id="_pure_convex">
906
907	<h2><a class="top" href="#container">top</a>pure_convex </h2>
908
909	<p class="header">
910	<span class="result">result = </span>pure_convex(<span class="result"><a href="#_pure_convex_param_x1">x1</a>, <a href="#_pure_convex_param_x2">x2</a>, <a href="#_pure_convex_param_y1">y1</a>, <a href="#_pure_convex_param_y2">y2</a>, <a href="#_pure_convex_param_der2">der2</a>, <a href="#_pure_convex_param_x">x</a></span>)</p>
911
912	<div class="comments"></div>
913
914
915
916
917	<h3>Parameters</h3>
918
919
920	<h4 id="_pure_convex_param_x1">x1
921	<span class="attr">in</span>
922
923
924	<span class="attr">required</span>
925
926
927
928
929	</h4>
930
931	<div class="comments">
932	An n-element (at least 2) input vector that specifies the tabulate points in
933	a strict ascending order.
934	</div>
935
936	<h4 id="_pure_convex_param_x2">x2
937	<span class="attr">in</span>
938
939
940	<span class="attr">required</span>
941
942
943
944
945	</h4>
946
947	<div class="comments">
948	The input values for which the interpolated values are
949	desired. Its values must be strictly monotonically increasing.
950	</div>
951
952	<h4 id="_pure_convex_param_y1">y1
953	<span class="attr">in</span>
954
955
956	<span class="attr">required</span>
957
958
959
960
961	</h4>
962
963	<div class="comments">
964	f(x) = y. An n-element input vector that specifies the values
965	of the tabulated function F(Xi) corresponding to Xi. As f is
966	supposed to be monotonically increasing, y values must be
967	monotonically increasing. y can have equal consecutive values.
968	</div>
969
970	<h4 id="_pure_convex_param_y2">y2
971
972
973
974
975
976
977
978
979	</h4>
980
981	<div class="comments"></div>
982
983	<h4 id="_pure_convex_param_der2">der2
984
985
986
987
988
989
990
991
992	</h4>
993
994	<div class="comments"></div>
995
996	<h4 id="_pure_convex_param_x">x
997
998
999
1000
1001
1002
1003
1004
1005	</h4>
1006
1007	<div class="comments">
1008	</div>
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038	</div>
1039
1040
1041	<div class="routine_details" id="_spl_incr">
1042
1043	<h2><a class="top" href="#container">top</a>spl_incr </h2>
1044
1045	<p class="header">
1046	<span class="result">result = </span>spl_incr(<span class="result"><a href="#_spl_incr_param_x">x</a>, <a href="#_spl_incr_param_y">y</a>, <a href="#_spl_incr_param_x2">x2</a></span>, <a href="#_spl_incr_keyword_YP0">YP0</a>=<span class="result">YP0</span>, <a href="#_spl_incr_keyword_YPN_1">YPN_1</a>=<span class="result">YPN_1</span>)</p>
1047
1048	<div class="comments"></div>
1049
1050
1051
1052
1053	<h3>Parameters</h3>
1054
1055
1056	<h4 id="_spl_incr_param_x">x
1057
1058
1059
1060
1061
1062
1063
1064
1065	</h4>
1066
1067	<div class="comments"></div>
1068
1069	<h4 id="_spl_incr_param_y">y
1070
1071
1072
1073
1074
1075
1076
1077
1078	</h4>
1079
1080	<div class="comments"></div>
1081
1082	<h4 id="_spl_incr_param_x2">x2
1083
1084
1085
1086
1087
1088
1089
1090
1091	</h4>
1092
1093	<div class="comments"></div>
1094
1095
1096
1097
1098
1099
1100	<h3>Keywords</h3>
1101
1102	<h4 id="_spl_incr_keyword_YP0">YP0
1103
1104
1105
1106
1107
1108
1109
1110
1111	</h4>
1112
1113	<div class="comments"> The first derivative of the interpolating function at the
1114	point X0. If YP0 is omitted, the second derivative at the
1115	boundary is set to zero, resulting in a "natural spline."</div>
1116
1117	<h4 id="_spl_incr_keyword_YPN_1">YPN_1
1118
1119
1120
1121
1122
1123
1124
1125
1126	</h4>
1127
1128	<div class="comments"> The first derivative of the interpolating function at the
1129	point Xn-1. If YPN_1 is omitted, the second derivative at the
1130	boundary is set to zero, resulting in a "natural spline."</div>
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157	</div>
1158
1159	</div>
1160
1161
1162
1163	<div id="tagline">Produced by IDLdoc 2.0.</div>
1164
1165	</div>
1166
1167	</body>
1168	</html>

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