-- FreeFem++ v4.6 (Thu Apr  2 15:47:38 CEST 2020 - git v4.6)
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : //  Location:
    2 : //
    3 : //    http://people.sc.fsu.edu/~jburkardt/freefem_src/lapack_test/lapack_test.edp
    4 : //
    5 : cout << "\n";
    6 : cout << "lapack_test\n";
    7 : cout << "  FreeFem++ version.\n";
    8 : cout << "  Test the use of lapack functions.\n";
    9 : 
   10 : load "lapack" Add lapack interface ...
   11 : // load "fflapack" obsolete (F. Hecht version 3.8)
   12 : {
   13 : int n=5;
   14 : real[int,int] A(n,n),A1(n,n),B(n,n);
   15 : for(int i=0;i<n;++i)
   16 : for(int j=0;j<n;++j)
   17 :   A(i,j)= (i==j) ? n+1 : 1;
   18 :  A(0,n-1)=-100;
   19 : cout << A << endl;
   20 : A1=A^-1;
   21 : cout << A1 << endl;
   22 : 
   23 :  complex[int] vp(n);
   24 :  complex[int,int] VP(n,n),KK(n,n);
   25 : 
   26 :  int nn= dgeev(A,vp,VP);
   27 :  cout << "  vp = " <<vp << endl;
   28 :  cout << " VP = " << VP << endl;
   29 :  KK =0.;
   30 :  for(int i=0;i<n;++i)
   31 :    for(int j=0;j<n;++j)
   32 :      for(int k=0;k<n;++k)
   33 :        KK(i,j) += (A(i,k) - vp[j]* real(i==k) ) *VP(k,j);
   34 :  cout <<" KK " <<  KK << endl; 
   35 : B=0;
   36 : for(int i=0;i<n;++i)
   37 :   for(int j=0;j<n;++j)
   38 :     for(int k=0;k<n;++k)
   39 :       B(i,j) +=A(i,k)*A1(k,j);
   40 : cout << B << endl;
   41 :  B = A*A1; // version 3.13
   42 : cout << B << " ++++++  "<<  endl;
   43 : // A1+A^-1;  attention ne marche pas
   44 : 
   45 : inv(A1);
   46 : cout << A1 << endl;
   47 : }
   48 : {
   49 :   cout << " *****************  complex VP \n";
   50 : int n=5;
   51 : complex[int,int] A(n,n),A1(n,n),B(n,n);
   52 : for(int i=0;i<n;++i)
   53 : for(int j=0;j<n;++j)
   54 :   A(i,j)= (i==j) ? n+1 : 1;
   55 : A(0,n-1)=-100i;
   56 : cout << A << endl;
   57 : A1=A^-1;
   58 : cout << A1 << endl;
   59 : 
   60 :  complex[int] vp(n);
   61 :  complex[int,int] VP(n,n),KK(n,n);
   62 : 
   63 :  int nn= zgeev(A,vp,VP);
   64 :  cout << "  vp = " <<vp << endl;
   65 :  cout << " VP = " << VP << endl;
   66 :  KK =0.;
   67 :  for(int i=0;i<n;++i)
   68 :    for(int j=0;j<n;++j)
   69 :      for(int k=0;k<n;++k)
   70 :        KK(i,j) += (A(i,k) - vp[j]* real(i==k) ) *VP(k,j);
   71 :  cout <<" KK " <<  KK << endl; 
   72 :  assert( KK.linfty < 1e-10);
   73 : B=0;
   74 : for(int i=0;i<n;++i)
   75 :   for(int j=0;j<n;++j)
   76 :     for(int k=0;k<n;++k)
   77 :       B(i,j) +=A(i,k)*A1(k,j);
   78 : cout << B << endl;
   79 : // A1+A^-1;  attention ne marche pas
   80 : 
   81 : //inv(A1);
   82 : //cout << A1 << endl;
   83 :   cout << " *****************  fin --complex VP \n";
   84 : }
   85 : 
   86 : {
   87 :   int n=5;
   88 :   complex[int,int] A(n,n),A1(n,n),B(n,n);
   89 :   for(int i=0;i<n;++i)
   90 :     for(int j=0;j<n;++j)
   91 :       A(i,j)= (i==j) ? (n+1)*1i : 1+0i;
   92 :   cout << A << endl;
   93 :   A1=A^-1;
   94 :   cout << A1 << endl;
   95 : 
   96 :   B=0;
   97 :   for(int i=0;i<n;++i)
   98 :     for(int j=0;j<n;++j)
   99 :       for(int k=0;k<n;++k)
  100 : 	B(i,j) +=A(i,k)*A1(k,j);
  101 :   cout << B << endl;
  102 :   // A1+A^-1;  attention ne marche pas 
  103 : }
  104 : 
  105 : // FFCS - value for regression checks
  106 : real regtest=0;
  107 : 
  108 : {
  109 : 
  110 : int n=5;
  111 : real [int,int] A(n,n),  B(n,n),  C(n,n);
  112 : macro SETM(A,i,j,fij) { for(int i=0;i<A.n;++i) for(int j=0;j<A.m;++j) A(i,j)= (fij) ;} )  // 
  113 : SETM(C,i,j,1./(1+i+j))         { for(int i=0;i<C.n;++i) for(int j=0;j<C.m;++j) C(i,j)= (1./(1+i+j)) ;} ; 
  114 : SETM(B,i,j,i==j?2.:1./n)         { for(int i=0;i<B.n;++i) for(int j=0;j<B.m;++j) B(i,j)= (i==j?2.:1./n) ;} ;
  115 :  
  116 : A = B*C;
  117 : cout << A << " " << endl;
  118 : A = B + C;
  119 : real[int]  b(n),c(n);
  120 : real[int,int] AA=A;
  121 : AA=A;
  122 : real [int,int] At=A';
  123 : 
  124 : b = A*c;
  125 : 
  126 : At =A';
  127 : {
  128 : 
  129 : real [int,int] A=[[0,-1,2],[4,11,2],[0,-1,2],[4,11,2]];
  130 : real [int,int] B=[[3,-1],[1,2],[6,1]];
  131 : real [int,int] E=[[11,0],[35,20],[11,0],[35,20]];
  132 : real [int,int]  At=A';
  133 : real [int,int] C(A.n,B.m);
  134 : C=A*B;
  135 : cout << " C = " <<  C << endl;
  136 : cout << " E = " <<  E << endl;
  137 : 
  138 : C -= E;
  139 : assert( C.linfty < 1e-10);
  140 : C = A*B;
  141 : C -=E; 
  142 : assert( C.linfty < 1e-10);
  143 : }
  144 : {
  145 : 
  146 : complex [int,int] A=[[0,-1,2],[4,11,2],[0,-1,2],[4,11,2]];
  147 : complex [int,int] B=[[3,-1],[1,2],[6,1]];
  148 : complex [int,int] E=[[11,0],[35,20],[11,0],[35,20]];
  149 : 
  150 : complex [int,int] C(A.n,B.m);
  151 : complex [int,int]  At=A';
  152 : cout << "At = " << At << endl;
  153 : C=A*B;
  154 : cout << " C = " <<  C << endl;
  155 : cout << " E = " <<  E << endl;
  156 : 
  157 : C -= E;
  158 : assert( C.linfty < 1e-10);
  159 : C = A*B;
  160 : C -=E; 
  161 : assert( C.linfty < 1e-10);
  162 : 
  163 : // FFCS - value for regression checks
  164 : regtest=C.linfty;
  165 : }
  166 : }
  167 : //
  168 : //  Terminate.
  169 : //
  170 : cout << "\n";
  171 : cout << "lapack_test\n";
  172 : cout << "  Normal end of execution.\n";
  173 : 
  174 : 
  175 :  sizestack + 1024 =3696  ( 2672 )


lapack_test
  FreeFem++ version.
  Test the use of lapack functions.
5 5	
	   6   1   1   1 -100
	   1   6   1   1   1
	   1   1   6   1   1
	   1   1   1   6   1
	   1   1   1   1   6
	
5 5	
	 0.05960264901 -0.140397351 -0.140397351 -0.140397351 1.063576159
	 -0.006622516556 0.1933774834 -0.006622516556 -0.006622516556 -0.140397351
	 -0.006622516556 -0.006622516556 0.1933774834 -0.006622516556 -0.140397351
	 -0.006622516556 -0.006622516556 -0.006622516556 0.1933774834 -0.140397351
	 -0.006622516556 -0.006622516556 -0.006622516556 -0.006622516556 0.05960264901
	
  vp = 5	
	(7.5,9.733961167)	(7.5,-9.733961167)	(5,0)	(5,0)	(5,0)
	
 VP = 5 5	
	 (0.9799979794,0) (0.9799979794,0) (-0.7071067812,0) (-0.852212265,0) (0.5279822472,0)
	 (-0.01515460793,-0.09834291005) (-0.01515460793,0.09834291005) (0.7071067812,0) (0.3916509472,0) (0.05021466761,0)
	 (-0.01515460793,-0.09834291005) (-0.01515460793,0.09834291005) (1.817028946e-17,0) (0.3147952354,0) (0.236047902,0)
	 (-0.01515460793,-0.09834291005) (-0.01515460793,0.09834291005) (5.451086838e-17,0) (0.1457660824,0) (-0.8142448168,0)
	 (-0.01515460793,-0.09834291005) (-0.01515460793,0.09834291005) (5.451086838e-17,0) (3.236657218e-17,0) (-3.389975038e-17,0)
	
 KK 5 5	
	 (1.998401444e-15,1.776356839e-15) (1.998401444e-15,-1.776356839e-15) (-3.491026538e-15,0) (-2.431745525e-15,0) (3.50099734e-15,0)
	 (-3.885780586e-16,2.498001805e-16) (-3.885780586e-16,-2.498001805e-16) (-1.760187116e-15,0) (-2.729447596e-16,0) (7.712255209e-17,0)
	 (-4.440892099e-16,1.387778781e-16) (-4.440892099e-16,-1.387778781e-16) (1.271920262e-16,0) (-2.174336084e-16,0) (7.712255209e-17,0)
	 (-4.996003611e-16,1.387778781e-16) (-4.996003611e-16,-1.387778781e-16) (1.271920262e-16,0) (-7.865573029e-17,0) (7.712255209e-17,0)
	 (-5.551115123e-16,1.110223025e-16) (-5.551115123e-16,-1.110223025e-16) (1.271920262e-16,0) (6.012214779e-17,0) (7.712255209e-17,0)
	
5 5	
	   1   0   0 1.110223025e-16   0
	 -2.255140519e-17   1 -1.908195824e-17 -2.168404345e-17 1.665334537e-16
	 -3.295974604e-17 -6.245004514e-17   1 -2.168404345e-17 3.60822483e-16
	 -3.469446952e-17 -6.418476861e-17 -6.938893904e-18   1 1.387778781e-16
	 -1.387778781e-17 -5.551115123e-17 1.387778781e-17 6.938893904e-18   1
	
5 5	
	   1 3.469446952e-17 -2.775557562e-17 5.898059818e-17 3.330669074e-16
	 -2.255140519e-17   1 -1.908195824e-17 -2.168404345e-17 1.665334537e-16
	 -3.122502257e-17 -6.071532166e-17   1 -2.168404345e-17 3.053113318e-16
	 -3.816391647e-17 -6.765421556e-17 -1.040834086e-17   1 1.387778781e-16
	 -1.387778781e-17 -5.204170428e-17 1.387778781e-17 8.67361738e-18   1
	 ++++++  
5 5	
	   6   1   1   1 -100
	   1   6   1   1   1
	   1   1   6   1   1
	   1   1   1   6   1
	   1   1   1   1   6
	
 *****************  complex VP 
5 5	
	 (6,0) (1,0) (1,0) (1,0) (0,-100)
	 (1,0) (6,0) (1,0) (1,0) (1,0)
	 (1,0) (1,0) (6,0) (1,0) (1,0)
	 (1,0) (1,0) (1,0) (6,0) (1,0)
	 (1,0) (1,0) (1,0) (1,0) (6,0)
	
5 5	
	 (0.0364256805,-0.07142290294) (-0.1635743195,-0.07142290294) (-0.1635743195,-0.07142290294) (-0.1635743195,-0.07142290294) (1.272168875,0.6428061265)
	 (-0.004047297834,0.007935878105) (0.1959527022,0.007935878105) (-0.004047297834,0.007935878105) (-0.004047297834,0.007935878105) (-0.1635743195,-0.07142290294)
	 (-0.004047297834,0.007935878105) (-0.004047297834,0.007935878105) (0.1959527022,0.007935878105) (-0.004047297834,0.007935878105) (-0.1635743195,-0.07142290294)
	 (-0.004047297834,0.007935878105) (-0.004047297834,0.007935878105) (-0.004047297834,0.007935878105) (0.1959527022,0.007935878105) (-0.1635743195,-0.07142290294)
	 (-0.004047297834,0.007935878105) (-0.004047297834,0.007935878105) (-0.004047297834,0.007935878105) (-0.004047297834,0.007935878105) (0.0364256805,-0.07142290294)
	
  vp = 5	
	(0.2409464229,6.887950264)	(14.75905358,-6.887950264)	(5,0)	(5,0)	(5,0)
	
 VP = 5 5	
	 (0.9842714065,0) (0.9760761115,0) (-0.14023168,4.062520713e-17) (0.8290735144,0) (0.8232205804,0)
	 (-0.06943417571,-0.05460169237) (0.06973372763,0.08340301773) (0.8387536883,0) (-0.5019051387,-8.128818563e-17) (-0.2002154408,-1.850251993e-17)
	 (-0.06943417571,-0.05460169237) (0.06973372763,0.08340301773) (-0.477442181,-3.224086188e-18) (-0.2236207034,-6.492363346e-17) (-0.1015573969,-2.938635518e-17)
	 (-0.06943417571,-0.05460169237) (0.06973372763,0.08340301773) (-0.2210798273,-2.241172349e-18) (-0.1035476723,-5.301017147e-17) (-0.5214477427,-2.938635518e-17)
	 (-0.06943417571,-0.05460169237) (0.06973372763,0.08340301773) (-7.632281524e-17,-1.393534548e-18) (4.112970128e-17,-4.273633023e-17) (3.48282728e-17,-2.938635518e-17)
	
 KK 5 5	
	 (-2.664535259e-15,0) (-5.329070518e-15,8.881784197e-16) (1.937134526e-16,7.667441472e-15) (-5.161811443e-15,-4.312192118e-15) (-3.271702425e-15,-3.56010251e-15)
	 (-3.330669074e-16,-2.775557562e-16) (-4.440892099e-16,8.326672685e-17) (-2.407791167e-15,3.376641405e-17) (3.741966087e-16,-2.419583208e-16) (-2.982386346e-16,-1.066615855e-16)
	 (-3.330669074e-16,-2.775557562e-16) (0,8.326672685e-17) (1.089411361e-15,3.376641405e-17) (1.243964281e-16,-2.419583208e-16) (-2.982386346e-16,-1.066615855e-16)
	 (-3.330669074e-16,-2.775557562e-16) (0,6.938893904e-17) (3.955219702e-16,3.376641405e-17) (2.725191347e-17,-2.419583208e-16) (-2.982386346e-16,-1.066615855e-16)
	 (-3.330669074e-16,-2.775557562e-16) (0,5.551115123e-17) (-1.873451177e-16,3.376641405e-17) (-6.989260119e-17,-2.419583208e-16) (-2.982386346e-16,-1.066615855e-16)
	
5 5	
	 (1,0) (1.110223025e-16,0) (0,0) (0,5.551115123e-17) (-8.881784197e-16,-4.440892099e-16)
	 (-4.250072516e-17,-8.67361738e-18) (1,-1.040834086e-17) (-1.474514955e-17,-8.67361738e-18) (-3.729655473e-17,8.67361738e-18) (-2.498001805e-16,-6.938893904e-17)
	 (-3.556183126e-17,-2.255140519e-17) (-3.035766083e-17,-1.734723476e-17) (1,-2.255140519e-17) (-9.540979118e-18,-1.734723476e-18) (0,-9.714451465e-17)
	 (-2.949029909e-17,-5.204170428e-18) (-2.428612866e-17,-3.469446952e-18) (-1.561251128e-17,-5.204170428e-18) (1,-5.204170428e-18) (2.775557562e-17,-1.249000903e-16)
	 (-4.510281038e-17,-1.387778781e-17) (-4.857225733e-17,-2.081668171e-17) (-3.122502257e-17,-1.387778781e-17) (-2.775557562e-17,-1.387778781e-17) (1,-1.110223025e-16)
	
 *****************  fin --complex VP 
5 5	
	 (0,6) (1,0) (1,0) (1,0) (1,0)
	 (1,0) (0,6) (1,0) (1,0) (1,0)
	 (1,0) (1,0) (0,6) (1,0) (1,0)
	 (1,0) (1,0) (1,0) (0,6) (1,0)
	 (1,0) (1,0) (1,0) (1,0) (0,6)
	
5 5	
	 (-0.006237006237,-0.1528066528) (0.02079002079,0.009355509356) (0.02079002079,0.009355509356) (0.02079002079,0.009355509356) (0.02079002079,0.009355509356)
	 (0.02079002079,0.009355509356) (-0.006237006237,-0.1528066528) (0.02079002079,0.009355509356) (0.02079002079,0.009355509356) (0.02079002079,0.009355509356)
	 (0.02079002079,0.009355509356) (0.02079002079,0.009355509356) (-0.006237006237,-0.1528066528) (0.02079002079,0.009355509356) (0.02079002079,0.009355509356)
	 (0.02079002079,0.009355509356) (0.02079002079,0.009355509356) (0.02079002079,0.009355509356) (-0.006237006237,-0.1528066528) (0.02079002079,0.009355509356)
	 (0.02079002079,0.009355509356) (0.02079002079,0.009355509356) (0.02079002079,0.009355509356) (0.02079002079,0.009355509356) (-0.006237006237,-0.1528066528)
	
5 5	
	 (1,-1.734723476e-18) (3.469446952e-18,-6.938893904e-18) (-3.469446952e-18,-1.734723476e-18) (6.938893904e-18,-1.734723476e-18) (6.071532166e-18,-2.775557562e-17)
	 (6.938893904e-18,-2.949029909e-17) (1,6.938893904e-18) (1.040834086e-17,-1.734723476e-18) (1.387778781e-17,-5.724587471e-17) (6.071532166e-18,-2.775557562e-17)
	 (0,-1.561251128e-17) (3.469446952e-18,6.938893904e-18) (1,1.214306433e-17) (6.938893904e-18,-1.734723476e-18) (-8.67361738e-19,-2.775557562e-17)
	 (-1.387778781e-17,2.602085214e-17) (3.469446952e-18,5.204170428e-17) (-3.469446952e-18,-1.734723476e-18) (1,5.204170428e-18) (-4.33680869e-18,0)
	 (0,2.775557562e-17) (6.938893904e-18,2.775557562e-17) (1.387778781e-17,-2.775557562e-17) (6.938893904e-18,0) (1,6.938893904e-18)
	
5 5	
	 2.256666667 1.19 0.8185714286 0.6269047619 0.5091269841
	 1.356666667 0.89 0.6685714286 0.5369047619 0.4491269841
	 1.056666667 0.74 0.5785714286 0.4769047619 0.4062698413
	 0.9066666667 0.65 0.5185714286 0.434047619 0.3741269841
	 0.8166666667 0.59 0.4757142857 0.4019047619 0.3491269841
	 
 C = 4 2	
	  11   0
	  35  20
	  11   0
	  35  20
	
 E = 4 2	
	  11   0
	  35  20
	  11   0
	  35  20
	
At = 3 4	
	 (0,0) (4,0) (0,0) (4,0)
	 (-1,0) (11,0) (-1,0) (11,0)
	 (2,0) (2,0) (2,0) (2,0)
	
 C = 4 2	
	 (11,0) (0,0)
	 (35,0) (20,0)
	 (11,0) (0,0)
	 (35,0) (20,0)
	
 E = 4 2	
	 (11,0) (0,0)
	 (35,0) (20,0)
	 (11,0) (0,0)
	 (35,0) (20,0)
	

lapack_test
  Normal end of execution.
times: compile 0.006487s, execution 0.083947s,  mpirank:0
 CodeAlloc : nb ptr  4448,  size :499888 mpirank: 0
Ok: Normal End