6 March 2018   2:21:49.306 PM

SQUARE_EXACTNESS_TEST
  FORTRAN90 version
  Test the SQUARE_EXACTNESS library.
 
TEST01
  Product Gauss-Legendre rules for the 2D Legendre integral.
  Density function rho(x) = 1.
  Region: -1 <= x <= +1.
  Region: -1 <= y <= +1.
  Level: L
  Exactness: 2*L+1
  Order: N = (L+1)*(L+1)

  Quadrature rule for the 2D Legendre integral.
  Number of points in rule is   1
 
   D   I       J          Relative Error
   0
       0       0        0.0000000000000000
   1
       1       0        0.0000000000000000
       0       1        0.0000000000000000
   2
       2       0        1.0000000000000000
       1       1        0.0000000000000000
       0       2        1.0000000000000000

  Quadrature rule for the 2D Legendre integral.
  Number of points in rule is   4
 
   D   I       J          Relative Error
   0
       0       0        0.0000000000000000
   1
       1       0        0.0000000000000000
       0       1        0.0000000000000000
   2
       2       0        0.0000000000000000
       1       1        0.0000000000000000
       0       2        0.0000000000000000
   3
       3       0        0.0000000000000000
       2       1        0.0000000000000000
       1       2        0.0000000000000000
       0       3        0.0000000000000000
   4
       4       0        0.4444444444444445
       3       1        0.0000000000000000
       2       2        0.0000000000000000
       1       3        0.0000000000000000
       0       4        0.4444444444444445

  Quadrature rule for the 2D Legendre integral.
  Number of points in rule is   9
 
   D   I       J          Relative Error
   0
       0       0        0.0000000000000000
   1
       1       0        0.0000000000000000
       0       1        0.0000000000000000
   2
       2       0        0.0000000000000002
       1       1        0.0000000000000000
       0       2        0.0000000000000002
   3
       3       0        0.0000000000000000
       2       1        0.0000000000000000
       1       2        0.0000000000000000
       0       3        0.0000000000000001
   4
       4       0        0.0000000000000003
       3       1        0.0000000000000000
       2       2        0.0000000000000005
       1       3        0.0000000000000000
       0       4        0.0000000000000003
   5
       5       0        0.0000000000000000
       4       1        0.0000000000000000
       3       2        0.0000000000000000
       2       3        0.0000000000000000
       1       4        0.0000000000000000
       0       5        0.0000000000000000
   6
       6       0        0.1599999999999996
       5       1        0.0000000000000000
       4       2        0.0000000000000004
       3       3        0.0000000000000000
       2       4        0.0000000000000004
       1       5        0.0000000000000000
       0       6        0.1599999999999996

  Quadrature rule for the 2D Legendre integral.
  Number of points in rule is  16
 
   D   I       J          Relative Error
   0
       0       0        0.0000000000000002
   1
       1       0        0.0000000000000000
       0       1        0.0000000000000000
   2
       2       0        0.0000000000000002
       1       1        0.0000000000000000
       0       2        0.0000000000000003
   3
       3       0        0.0000000000000000
       2       1        0.0000000000000000
       1       2        0.0000000000000000
       0       3        0.0000000000000000
   4
       4       0        0.0000000000000008
       3       1        0.0000000000000000
       2       2        0.0000000000000005
       1       3        0.0000000000000000
       0       4        0.0000000000000008
   5
       5       0        0.0000000000000000
       4       1        0.0000000000000000
       3       2        0.0000000000000000
       2       3        0.0000000000000000
       1       4        0.0000000000000000
       0       5        0.0000000000000000
   6
       6       0        0.0000000000000010
       5       1        0.0000000000000000
       4       2        0.0000000000000010
       3       3        0.0000000000000000
       2       4        0.0000000000000010
       1       5        0.0000000000000000
       0       6        0.0000000000000012
   7
       7       0        0.0000000000000000
       6       1        0.0000000000000000
       5       2        0.0000000000000000
       4       3        0.0000000000000000
       3       4        0.0000000000000000
       2       5        0.0000000000000000
       1       6        0.0000000000000000
       0       7        0.0000000000000000
   8
       8       0        0.0522448979591847
       7       1        0.0000000000000000
       6       2        0.0000000000000012
       5       3        0.0000000000000000
       4       4        0.0000000000000012
       3       5        0.0000000000000000
       2       6        0.0000000000000010
       1       7        0.0000000000000000
       0       8        0.0522448979591847

  Quadrature rule for the 2D Legendre integral.
  Number of points in rule is  25
 
   D   I       J          Relative Error
   0
       0       0        0.0000000000000000
   1
       1       0        0.0000000000000000
       0       1        0.0000000000000000
   2
       2       0        0.0000000000000002
       1       1        0.0000000000000000
       0       2        0.0000000000000003
   3
       3       0        0.0000000000000000
       2       1        0.0000000000000001
       1       2        0.0000000000000000
       0       3        0.0000000000000000
   4
       4       0        0.0000000000000008
       3       1        0.0000000000000000
       2       2        0.0000000000000009
       1       3        0.0000000000000000
       0       4        0.0000000000000008
   5
       5       0        0.0000000000000000
       4       1        0.0000000000000000
       3       2        0.0000000000000000
       2       3        0.0000000000000000
       1       4        0.0000000000000000
       0       5        0.0000000000000000
   6
       6       0        0.0000000000000008
       5       1        0.0000000000000000
       4       2        0.0000000000000010
       3       3        0.0000000000000000
       2       4        0.0000000000000010
       1       5        0.0000000000000000
       0       6        0.0000000000000010
   7
       7       0        0.0000000000000000
       6       1        0.0000000000000000
       5       2        0.0000000000000000
       4       3        0.0000000000000000
       3       4        0.0000000000000000
       2       5        0.0000000000000000
       1       6        0.0000000000000000
       0       7        0.0000000000000000
   8
       8       0        0.0000000000000010
       7       1        0.0000000000000000
       6       2        0.0000000000000015
       5       3        0.0000000000000000
       4       4        0.0000000000000012
       3       5        0.0000000000000000
       2       6        0.0000000000000013
       1       7        0.0000000000000000
       0       8        0.0000000000000009
   9
       9       0        0.0000000000000000
       8       1        0.0000000000000000
       7       2        0.0000000000000000
       6       3        0.0000000000000000
       5       4        0.0000000000000000
       4       5        0.0000000000000000
       3       6        0.0000000000000000
       2       7        0.0000000000000000
       1       8        0.0000000000000000
       0       9        0.0000000000000000
  10
      10       0        0.0161249685059223
       9       1        0.0000000000000000
       8       2        0.0000000000000013
       7       3        0.0000000000000000
       6       4        0.0000000000000016
       5       5        0.0000000000000000
       4       6        0.0000000000000017
       3       7        0.0000000000000000
       2       8        0.0000000000000013
       1       9        0.0000000000000000
       0      10        0.0161249685059223

  Quadrature rule for the 2D Legendre integral.
  Number of points in rule is  36
 
   D   I       J          Relative Error
   0
       0       0        0.0000000000000002
   1
       1       0        0.0000000000000000
       0       1        0.0000000000000000
   2
       2       0        0.0000000000000002
       1       1        0.0000000000000000
       0       2        0.0000000000000000
   3
       3       0        0.0000000000000000
       2       1        0.0000000000000000
       1       2        0.0000000000000000
       0       3        0.0000000000000000
   4
       4       0        0.0000000000000000
       3       1        0.0000000000000000
       2       2        0.0000000000000000
       1       3        0.0000000000000000
       0       4        0.0000000000000001
   5
       5       0        0.0000000000000000
       4       1        0.0000000000000000
       3       2        0.0000000000000000
       2       3        0.0000000000000000
       1       4        0.0000000000000000
       0       5        0.0000000000000000
   6
       6       0        0.0000000000000002
       5       1        0.0000000000000000
       4       2        0.0000000000000000
       3       3        0.0000000000000000
       2       4        0.0000000000000002
       1       5        0.0000000000000000
       0       6        0.0000000000000000
   7
       7       0        0.0000000000000000
       6       1        0.0000000000000000
       5       2        0.0000000000000000
       4       3        0.0000000000000000
       3       4        0.0000000000000000
       2       5        0.0000000000000000
       1       6        0.0000000000000000
       0       7        0.0000000000000000
   8
       8       0        0.0000000000000004
       7       1        0.0000000000000000
       6       2        0.0000000000000001
       5       3        0.0000000000000000
       4       4        0.0000000000000000
       3       5        0.0000000000000000
       2       6        0.0000000000000000
       1       7        0.0000000000000000
       0       8        0.0000000000000001
   9
       9       0        0.0000000000000000
       8       1        0.0000000000000000
       7       2        0.0000000000000000
       6       3        0.0000000000000000
       5       4        0.0000000000000000
       4       5        0.0000000000000000
       3       6        0.0000000000000000
       2       7        0.0000000000000000
       1       8        0.0000000000000000
       0       9        0.0000000000000000
  10
      10       0        0.0000000000000000
       9       1        0.0000000000000000
       8       2        0.0000000000000004
       7       3        0.0000000000000000
       6       4        0.0000000000000001
       5       5        0.0000000000000000
       4       6        0.0000000000000001
       3       7        0.0000000000000000
       2       8        0.0000000000000004
       1       9        0.0000000000000000
       0      10        0.0000000000000000
  11
      11       0        0.0000000000000000
      10       1        0.0000000000000000
       9       2        0.0000000000000000
       8       3        0.0000000000000000
       7       4        0.0000000000000000
       6       5        0.0000000000000000
       5       6        0.0000000000000000
       4       7        0.0000000000000000
       3       8        0.0000000000000000
       2       9        0.0000000000000000
       1      10        0.0000000000000000
       0      11        0.0000000000000000
  12
      12       0        0.0047975112910184
      11       1        0.0000000000000000
      10       2        0.0000000000000001
       9       3        0.0000000000000000
       8       4        0.0000000000000003
       7       5        0.0000000000000000
       6       6        0.0000000000000002
       5       7        0.0000000000000000
       4       8        0.0000000000000002
       3       9        0.0000000000000000
       2      10        0.0000000000000002
       1      11        0.0000000000000000
       0      12        0.0047975112910181
 
TEST02
  Padua rule for the 2D Legendre integral.
  Density function rho(x) = 1.
  Region: -1 <= x <= +1.
  Region: -1 <= y <= +1.
  Level: L
  Exactness: L+1 when L is 0,
             L   otherwise.
  Order: N = (L+1)*(L+2)/2

  Quadrature rule for the 2D Legendre integral.
  Number of points in rule is   1
 
   D   I       J          Relative Error
   0
       0       0        0.0000000000000000
   1
       1       0        0.0000000000000000
       0       1        0.0000000000000000
   2
       2       0        1.0000000000000000
       1       1        0.0000000000000000
       0       2        1.0000000000000000

  Quadrature rule for the 2D Legendre integral.
  Number of points in rule is   3
 
   D   I       J          Relative Error
   0
       0       0        0.0000000000000000
   1
       1       0        0.0000000000000000
       0       1        0.0000000000000000
   2
       2       0        2.0000000000000004
       1       1        0.0000000000000000
       0       2        0.5000000000000001

  Quadrature rule for the 2D Legendre integral.
  Number of points in rule is   6
 
   D   I       J          Relative Error
   0
       0       0        0.0000000000000001
   1
       1       0        0.0000000000000001
       0       1        0.0000000000000004
   2
       2       0        0.0000000000000005
       1       1        0.0000000000000001
       0       2        0.0000000000000003
   3
       3       0        0.0000000000000001
       2       1        0.6666666666666665
       1       2        0.0000000000000000
       0       3        0.3333333333333338

  Quadrature rule for the 2D Legendre integral.
  Number of points in rule is  10
 
   D   I       J          Relative Error
   0
       0       0        0.0000000000000001
   1
       1       0        0.0000000000000001
       0       1        0.0000000000000006
   2
       2       0        0.0000000000000000
       1       1        0.0000000000000007
       0       2        0.0000000000000003
   3
       3       0        0.0000000000000000
       2       1        0.0000000000000007
       1       2        0.0000000000000004
       0       3        0.0000000000000009
   4
       4       0        0.1666666666666668
       3       1        0.0000000000000011
       2       2        0.2499999999999993
       1       3        0.0000000000000007
       0       4        0.0416666666666671

  Quadrature rule for the 2D Legendre integral.
  Number of points in rule is  15
 
   D   I       J          Relative Error
   0
       0       0        0.0000000000000000
   1
       1       0        0.0000000000000009
       0       1        0.0000000000000003
   2
       2       0        0.0000000000000002
       1       1        0.0000000000000002
       0       2        0.0000000000000002
   3
       3       0        0.0000000000000002
       2       1        0.0000000000000001
       1       2        0.0000000000000004
       0       3        0.0000000000000000
   4
       4       0        0.0000000000000012
       3       1        0.0000000000000004
       2       2        0.0000000000000011
       1       3        0.0000000000000002
       0       4        0.0000000000000001
   5
       5       0        0.0000000000000001
       4       1        0.0333333333333332
       3       2        0.0000000000000003
       2       3        0.0555555555555558
       1       4        0.0000000000000002
       0       5        0.0166666666666670

  Quadrature rule for the 2D Legendre integral.
  Number of points in rule is  21
 
   D   I       J          Relative Error
   0
       0       0        0.0000000000000000
   1
       1       0        0.0000000000000004
       0       1        0.0000000000000001
   2
       2       0        0.0000000000000008
       1       1        0.0000000000000002
       0       2        0.0000000000000002
   3
       3       0        0.0000000000000008
       2       1        0.0000000000000006
       1       2        0.0000000000000002
       0       3        0.0000000000000002
   4
       4       0        0.0000000000000008
       3       1        0.0000000000000005
       2       2        0.0000000000000001
       1       3        0.0000000000000002
       0       4        0.0000000000000000
   5
       5       0        0.0000000000000007
       4       1        0.0000000000000010
       3       2        0.0000000000000002
       2       3        0.0000000000000003
       1       4        0.0000000000000001
       0       5        0.0000000000000003
   6
       6       0        0.0083333333333343
       5       1        0.0000000000000013
       4       2        0.0208333333333326
       3       3        0.0000000000000004
       2       4        0.0208333333333324
       1       5        0.0000000000000004
       0       6        0.0062500000000002

SQUARE_EXACTNESS_TEST
  Normal end of execution.

 6 March 2018   2:21:49.306 PM