0024608: Development of methods of global optimization of multivariable function

math_GlobOptMin - new global optimization minimization algorithm
Extrema_GlobOptFuncCC, Extrema_ExtCC, Extrema_ExtCC2d - implementation of GlobOptMin algorithm to extrema curve / curve
Extrema_CurveCache - deleted as obsolete code
ChFi3d_Builder.cxx  - fixed processing of extrema
math_NewtonMinimum.cxx - fixed step to avoid incorrect behavior
Test cases modification to meet new behavior.

tests/bugs/modalg_5/bug23706_10

@@ -8,9 +8,19 @@ puts ""
 
 bsplinecurve r3 2 6 1 3 2 1 3 1 4 1 5 1 6 3 2 5 3 1 3 7 3 1 4 8 3 1 4 8 3 1 4 8 3 1 5 9 3 1 9 7 3 1
 bsplinecurve r4 2 6 2 3 2.5 1 3 1 3.5 1 4 1 4.5 3 -1 2 3 1 1 11 3 1 3 9 3 1 3 9 3 1 3 9 3 1 5 7 3 1 7 4 3 1
-set info [extrema r3 r4]
+extrema r3 r4
 
-if { [regexp "Extrema 3 is point : 4 8 3" $info] != 1 || [regexp "Extrema 8 is point : 4 8 3" $info] != 1 } {
+cvalue ext_1 0 x y z
+set info [dump x] 
+regexp "(\[-0-9.+eE\])" $info full xx
+set info [dump y] 
+regexp "(\[-0-9.+eE\])" $info full yy
+set info [dump z] 
+regexp "(\[-0-9.+eE\])" $info full zz
+
+if { sqrt(($xx - 4.0) * ($xx - 4.0) + 
+	      ($yy - 8.0) * ($yy - 8.0) + 
+	      ($zz - 3.0) * ($zz - 3.0)) > 1.0e-7} {
     puts "Error : Point of extrema is wrong"
 } else {
     puts "OK: Point of extrema is valid"

tests/bugs/modalg_5/bug23706_11

@@ -10,7 +10,7 @@ bsplinecurve r1 2 5 1 3 2 1 3 1 4 1 5 3 2 5 3 1 3 7 3 1 4 8 3 1 4 8 3 1 5 9 3 1
 bsplinecurve r2 2 5 2 3 2.5 1 3 1 3.5 1 4 3 -1 2 3 1 1 11 3 1 3 9 3 1 3 9 3 1 3 9 3 1 5 7 3 1 7 4 3 1
 set info [extrema r1 r2]
 
-if { [llength $info] != 3 } {
+if { [llength $info] != 1 } {
     puts "Error : Extrema is wrong"
 } else {
     puts "OK: Extrema is valid"

tests/bugs/modalg_5/bug23706_12

@@ -11,7 +11,7 @@ bsplinecurve r10 2 6 2 3 2.5 1 3 1 3.5 1 4 1 4.5 3 5 20 3 1 8 15 3 1 12 18 3 1 1
 
 set info [extrema r9 r10]
 
-if { [llength $info] != 6 } {
+if { [llength $info] != 1 } {
     puts "Error : Extrema is wrong"
 } else {
     puts "OK: Extrema is valid"

tests/bugs/modalg_5/bug23706_13

@@ -11,13 +11,11 @@ puts ""
 
 set info [2dextrema b3 b4]
 set status 0
-for { set i 1 } { $i <= 15 } { incr i 1 } {
-    regexp "dist $i: +(\[-0-9.+eE\]+)" $info full pp
-    if { $pp != 1.4142135623730951 } {
-       puts "Error : Extrema is wrong on dist $i"
+    regexp "dist 1: +(\[-0-9.+eE\]+)" $info full pp
+    if { $pp > 1.0e-7 } {
+       puts "Error : Extrema is wrong"
        set status 1
     }
-}
 
 if { $status != 0 } {
     puts "Error : Extrema is wrong"

tests/bugs/modalg_5/bug23706_14

@@ -11,37 +11,14 @@ puts ""
 set info [2dextrema b9 b10]
 
 set status 0
-for { set i 1 } { $i <= 9 } { incr i } {
-    regexp "dist $i: +(\[-0-9.+eE\]+)" $info full pp1
-    if { $pp1 != 7.2801098892805181 } {
+for { set i 1 } { $i <= 6 } { incr i 1 } {
+    regexp "dist $i: +(\[-0-9.+eE\]+)" $info full pp
+    if { abs($pp - 4.316921907096100) > 1.0e-7 } {
        puts "Error : Extrema is wrong on dist $i"
        set status 1
     }
 }
 
-for { set j 11 } { $j <= 19 } { incr j 1 } {
-    regexp "dist $j: +(\[-0-9.+eE\]+)" $info full pp2
-    if { $pp2 != 7.2801098892805181 } {
-       puts "Error : Extrema is wrong on dist $j"
-       set status 1
-    }
-}
-
-regexp {dist 10: +([-0-9.+eE]+)} $info full pp3
-regexp {dist 20: +([-0-9.+eE]+)} $info full pp4
-regexp {dist 21: +([-0-9.+eE]+)} $info full pp5
-set pp_c 4.316921907096102
-set pp_ch 4.3169219070961038
-
-if { $pp3 != $pp_c } {
-    puts "Error : Extrema is wrong on dist 10"
-    set status 1
-}
-if { $pp4 != $pp_ch || $pp5 != $pp_ch} {
-    puts "Error : Extrema is wrong on dist 20 or 21"
-    set status 1
-}
-
 if { $status != 0 } {
     puts "Error : Extrema is wrong"
 } else {

tests/bugs/modalg_5/bug23706_15

@@ -11,21 +11,12 @@ puts ""
 set info [2dextrema b7 b8]
 
 set status 0
-for { set i 2 } { $i <= 5 } { incr i } {
-    regexp "dist $i: +(\[-0-9.+eE\]+)" $info full pp1
-    if { $pp1 !=4.3624023150195192 } {
-       puts "Error : Extrema is wrong on dist $i"
-       set status 1
-    }
-}
 
-regexp {dist 1: +([-0-9.+eE]+)} $info full pp2
-set pp_ch 4.3624023150195184
-
-if { $pp2 != $pp_ch } {
-    puts "Error : Extrema is wrong on dist 1"
+regexp "dist 1: +(\[-0-9.+eE\]+)" $info full pp
+if { abs($pp - 2.3246777409727225) < 1.0e-7 } {
+	puts "Error : Extrema is wrong"
     set status 1
-}
+    }
 
 if { $status != 0 } {
     puts "Error : Extrema is wrong"

tests/bugs/modalg_5/bug24200

@@ -10,12 +10,6 @@ restore [locate_data_file bug24200_c1] c1
 restore [locate_data_file bug24200_c2] c2
 set info_1 [extrema c1 c2]
 
-if { [regexp "ext_15" $info_1] != 1 } {
-    puts "Error : Extrema is wrong"
-} else {
-    puts "OK : Extrema is correct"
-}
-
 trim c1t c1 677.8 678.8
 trim c2t c2 2477 2479
 extrema c1t c2t
@@ -34,4 +28,3 @@ if { [expr 1.*abs($checkdist - $dist)/$checkdist] > 0.1 } {
 } else {
     puts "OK: Distance is correct"
 }
-

tests/bugs/moddata_1/buc60825

@@ -11,7 +11,7 @@ checkshape aEdge2
 
 distmini d aEdge1 aEdge2
 regexp {NB RESULTS +: +([-0-9.+eE]+)} [BUC60825 aEdge1 aEdge2] full ext
-if { $ext != 0 } {
+if { $ext != 1 } {
     puts "Error : The extrema has not been calculated."
 }
 

tests/bugs/moddata_1/buc60890

@@ -15,7 +15,7 @@ circle curve_2 5.3 -0.5 2
 
 set err [llength [2dextrema curve_1 curve_2]]
 
-if {$err == 16} {
+if {$err == 6} {
     puts "BUC60890 OK: Function 2dextrema works properly."
 } else {
     puts "Faulty BUC60890 : Function 2dextrema works wrongly."

tests/bugs/moddata_2/bug862

@@ -11,7 +11,7 @@ restore [locate_data_file OCC862_2.draw] c2
 
 set result [extrema c1 c2]
 set err [llength $result]
-if { $err <= 1} {
+if { $err != 1} {
     puts "Faulty OCC862 (amount of solution): command extrema does NOT work properly"
 } else {
     puts "OCC862 OK (amount of solution): command extrema works properly"

tests/bugs/moddata_3/bug23994

@@ -27,13 +27,6 @@ extrema airfl rhomb
 
 if { [isdraw ext_1] } {
    mkedge result ext_1
-   set length 9.09515
-} else {
-   puts "${BugNumber}: invalid result"
-}
-
-if { [isdraw ext_2] } {
-   mkedge result ext_2
    set length 5.14563
 } else {
    puts "${BugNumber}: invalid result"