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normal.f90
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normal.f90
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function c4_normal_01 ( seed )
!*****************************************************************************80
!
!! C4_NORMAL_01 returns a unit pseudonormal C4.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 31 May 2007
!
! Author:
!
! John Burkardt
!
! Parameters:
!
! Input/output, integer ( kind = 4 ) SEED, a seed for the random
! number generator.
!
! Output, complex ( kind = 4 ) C4_NORMAL_01, a unit pseudonormal value.
!
implicit none
complex ( kind = 4 ) c4_normal_01
real ( kind = 4 ), parameter :: r4_pi = 3.141592653589793E+00
real ( kind = 4 ) r4_uniform_01
integer ( kind = 4 ) seed
real ( kind = 4 ) v1
real ( kind = 4 ) v2
real ( kind = 4 ) x_c
real ( kind = 4 ) x_r
v1 = r4_uniform_01 ( seed )
v2 = r4_uniform_01 ( seed )
x_r = sqrt ( - 2.0E+00 * log ( v1 ) ) * cos ( 2.0E+00 * r4_pi * v2 )
x_c = sqrt ( - 2.0E+00 * log ( v1 ) ) * sin ( 2.0E+00 * r4_pi * v2 )
c4_normal_01 = cmplx ( x_r, x_c )
return
end
function c8_normal_01 ( seed )
!*****************************************************************************80
!
!! C8_NORMAL_01 returns a unit pseudonormal C8.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 31 May 2007
!
! Author:
!
! John Burkardt
!
! Parameters:
!
! Input, integer ( kind = 4 ) SEED, a seed for the random number
! generator.
!
! Output, complex ( kind = 8 ) C8_NORMAL_01, a sample of the PDF.
!
! Output, integer ( kind = 4 ) SEED, a seed for the random number
! generator.
!
implicit none
complex ( kind = 8 ) c8_normal_01
real ( kind = 8 ), parameter :: r8_pi = 3.141592653589793D+00
real ( kind = 8 ) r8_uniform_01
integer ( kind = 4 ) seed
real ( kind = 8 ) v1
real ( kind = 8 ) v2
real ( kind = 8 ) x_c
real ( kind = 8 ) x_r
v1 = r8_uniform_01 ( seed )
v2 = r8_uniform_01 ( seed )
x_r = sqrt ( - 2.0D+00 * log ( v1 ) ) * cos ( 2.0D+00 * r8_pi * v2 )
x_c = sqrt ( - 2.0D+00 * log ( v1 ) ) * sin ( 2.0D+00 * r8_pi * v2 )
c8_normal_01 = cmplx ( x_r, x_c, kind = 8 )
return
end
function i4_normal_ab ( a, b, seed )
!*****************************************************************************80
!
!! I4_NORMAL_AB returns a scaled pseudonormal I4.
!
! Discussion:
!
! The normal probability distribution function (PDF) is sampled,
! with mean A and standard deviation B.
!
! The result is then rounded to the nearest integer.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 06 August 2013
!
! Author:
!
! John Burkardt
!
! Parameters:
!
! Input, real ( kind = 4 ) A, the mean of the PDF.
!
! Input, real ( kind = 4 ) B, the standard deviation of the PDF.
!
! Input/output, integer ( kind = 4 ) SEED, a seed for the
! random number generator.
!
! Output, integer ( kind = 4 ) I4_NORMAL_AB, a sample of the normal PDF.
!
implicit none
real ( kind = 4 ) a
real ( kind = 4 ) b
integer ( kind = 4 ) i4_normal_ab
real ( kind = 4 ) r1
real ( kind = 4 ) r2
real ( kind = 4 ), parameter :: r4_pi = 3.141592653589793E+00
real ( kind = 4 ) r4_uniform_01
integer ( kind = 4 ) seed
real ( kind = 4 ) x
r1 = r4_uniform_01 ( seed )
r2 = r4_uniform_01 ( seed )
x = sqrt ( - 2.0E+00 * log ( r1 ) ) * cos ( 2.0E+00 * r4_pi * r2 )
i4_normal_ab = nint ( a + b * x )
return
end
function i8_normal_ab ( a, b, seed )
!*****************************************************************************80
!
!! I8_NORMAL_AB returns a scaled pseudonormal I8.
!
! Discussion:
!
! The normal probability distribution function (PDF) is sampled,
! with mean A and standard deviation B.
!
! The result is then rounded to the nearest integer.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 06 August 2013
!
! Author:
!
! John Burkardt
!
! Parameters:
!
! Input, real ( kind = 8 ) A, the mean of the PDF.
!
! Input, real ( kind = 8 ) B, the standard deviation of the PDF.
!
! Input/output, integer ( kind = 8 ) SEED, a seed for the
! random number generator.
!
! Output, integer ( kind = 8 ) I8_NORMAL_AB, a sample of the normal PDF.
!
implicit none
real ( kind = 8 ) a
real ( kind = 8 ) b
integer ( kind = 8 ) i8_normal_ab
real ( kind = 8 ) r1
real ( kind = 8 ) r2
real ( kind = 8 ), parameter :: r8_pi = 3.141592653589793D+00
real ( kind = 8 ) r8_uniform_01
integer ( kind = 8 ) seed
real ( kind = 8 ) x
r1 = r8_uniform_01 ( seed )
r2 = r8_uniform_01 ( seed )
x = sqrt ( - 2.0D+00 * log ( r1 ) ) * cos ( 2.0D+00 * r8_pi * r2 )
i8_normal_ab = nint ( a + b * x )
return
end
function r4_normal_01 ( seed )
!*****************************************************************************80
!
!! R4_NORMAL_01 returns a unit pseudonormal R4.
!
! Discussion:
!
! The standard normal probability distribution function (PDF) has
! mean 0 and standard deviation 1.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 06 August 2013
!
! Author:
!
! John Burkardt
!
! Parameters:
!
! Input/output, integer ( kind = 4 ) SEED, a seed for the random
! number generator.
!
! Output, real ( kind = 4 ) R4_NORMAL_01, a sample of the standard
! normal PDF.
!
implicit none
real ( kind = 4 ) r1
real ( kind = 4 ) r2
real ( kind = 4 ) r4_normal_01
real ( kind = 4 ), parameter :: r4_pi = 3.141592653589793E+00
real ( kind = 4 ) r4_uniform_01
integer ( kind = 4 ) seed
real ( kind = 4 ) x
r1 = r4_uniform_01 ( seed )
r2 = r4_uniform_01 ( seed )
x = sqrt ( - 2.0E+00 * log ( r1 ) ) * cos ( 2.0E+00 * r4_pi * r2 )
r4_normal_01 = x
return
end
function r4_normal_ab ( a, b, seed )
!*****************************************************************************80
!
!! R4_NORMAL_AB returns a scaled pseudonormal R4.
!
! Discussion:
!
! The normal probability distribution function (PDF) is sampled,
! with mean A and standard deviation B.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 06 August 2013
!
! Author:
!
! John Burkardt
!
! Parameters:
!
! Input, real ( kind = 4 ) A, the mean of the PDF.
!
! Input, real ( kind = 4 ) B, the standard deviation of the PDF.
!
! Input/output, integer ( kind = 4 ) SEED, a seed for the random
! number generator.
!
! Output, real ( kind = 4 ) R4_NORMAL_AB, a sample of the normal PDF.
!
implicit none
real ( kind = 4 ) a
real ( kind = 4 ) b
real ( kind = 4 ) r1
real ( kind = 4 ) r2
real ( kind = 4 ) r4_normal_ab
real ( kind = 4 ), parameter :: r4_pi = 3.141592653589793E+00
real ( kind = 4 ) r4_uniform_01
integer ( kind = 4 ) seed
real ( kind = 4 ) x
r1 = r4_uniform_01 ( seed )
r2 = r4_uniform_01 ( seed )
x = sqrt ( - 2.0E+00 * log ( r1 ) ) * cos ( 2.0E+00 * r4_pi * r2 )
r4_normal_ab = a + b * x
return
end
function r4_uniform_01 ( seed )
!*****************************************************************************80
!
!! R4_UNIFORM_01 returns a unit pseudorandom R4.
!
! Discussion:
!
! An R4 is a real ( kind = 4 ) value.
!
! This routine implements the recursion
!
! seed = 16807 * seed mod ( 2^31 - 1 )
! r4_uniform_01 = seed / ( 2^31 - 1 )
!
! The integer arithmetic never requires more than 32 bits,
! including a sign bit.
!
! If the initial seed is 12345, then the first three computations are
!
! Input Output R4_UNIFORM_01
! SEED SEED
!
! 12345 207482415 0.096616
! 207482415 1790989824 0.833995
! 1790989824 2035175616 0.947702
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 31 May 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! Paul Bratley, Bennett Fox, Linus Schrage,
! A Guide to Simulation,
! Second Edition,
! Springer, 1987,
! ISBN: 0387964673,
! LC: QA76.9.C65.B73.
!
! Bennett Fox,
! Algorithm 647:
! Implementation and Relative Efficiency of Quasirandom
! Sequence Generators,
! ACM Transactions on Mathematical Software,
! Volume 12, Number 4, December 1986, pages 362-376.
!
! Pierre L'Ecuyer,
! Random Number Generation,
! in Handbook of Simulation,
! edited by Jerry Banks,
! Wiley, 1998,
! ISBN: 0471134031,
! LC: T57.62.H37.
!
! Peter Lewis, Allen Goodman, James Miller,
! A Pseudo-Random Number Generator for the System/360,
! IBM Systems Journal,
! Volume 8, Number 2, 1969, pages 136-143.
!
! Parameters:
!
! Input/output, integer ( kind = 4 ) SEED, the "seed" value, which
! should NOT be 0. On output, SEED has been updated.
!
! Output, real ( kind = 4 ) R4_UNIFORM_01, a new pseudorandom variate,
! strictly between 0 and 1.
!
implicit none
integer ( kind = 4 ), parameter :: i4_huge = 2147483647
integer ( kind = 4 ) k
integer ( kind = 4 ) seed
real ( kind = 4 ) r4_uniform_01
if ( seed == 0 ) then
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'R4_UNIFORM_01 - Fatal error!'
write ( *, '(a)' ) ' Input value of SEED = 0.'
stop 1
end if
k = seed / 127773
seed = 16807 * ( seed - k * 127773 ) - k * 2836
if ( seed < 0 ) then
seed = seed + i4_huge
end if
r4_uniform_01 = real ( seed, kind = 4 ) * 4.656612875E-10
return
end
subroutine r4vec_uniform_01 ( n, seed, r )
!*****************************************************************************80
!
!! R4VEC_UNIFORM_01 returns a unit pseudorandom R4VEC.
!
! Discussion:
!
! An R4VEC is an array of real ( kind = 4 ) values.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 31 May 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! Paul Bratley, Bennett Fox, Linus Schrage,
! A Guide to Simulation,
! Second Edition,
! Springer, 1987,
! ISBN: 0387964673,
! LC: QA76.9.C65.B73.
!
! Bennett Fox,
! Algorithm 647:
! Implementation and Relative Efficiency of Quasirandom
! Sequence Generators,
! ACM Transactions on Mathematical Software,
! Volume 12, Number 4, December 1986, pages 362-376.
!
! Pierre L'Ecuyer,
! Random Number Generation,
! in Handbook of Simulation,
! edited by Jerry Banks,
! Wiley, 1998,
! ISBN: 0471134031,
! LC: T57.62.H37.
!
! Peter Lewis, Allen Goodman, James Miller,
! A Pseudo-Random Number Generator for the System/360,
! IBM Systems Journal,
! Volume 8, Number 2, 1969, pages 136-143.
!
! Parameters:
!
! Input, integer ( kind = 4 ) N, the number of entries in the vector.
!
! Input/output, integer ( kind = 4 ) SEED, the "seed" value,
! which should NOT be 0.
! On output, SEED has been updated.
!
! Output, real ( kind = 4 ) R(N), the vector of pseudorandom values.
!
implicit none
integer ( kind = 4 ) n
integer ( kind = 4 ) i
integer ( kind = 4 ), parameter :: i4_huge = 2147483647
integer ( kind = 4 ) k
integer ( kind = 4 ) seed
real ( kind = 4 ) r(n)
if ( seed == 0 ) then
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'R4VEC_UNIFORM_01 - Fatal error!'
write ( *, '(a)' ) ' Input value of SEED = 0.'
stop 1
end if
do i = 1, n
k = seed / 127773
seed = 16807 * ( seed - k * 127773 ) - k * 2836
if ( seed < 0 ) then
seed = seed + i4_huge
end if
r(i) = real ( seed, kind = 4 ) * 4.656612875E-10
end do
return
end
subroutine r4vec_normal_ab ( n, a, b, seed, x )
!*****************************************************************************80
!
!! R4VEC_NORMAL_AB returns a scaled pseudonormal R4VEC.
!
! Discussion:
!
! The standard normal probability distribution function (PDF) has
! mean 0 and standard deviation 1.
!
! An R4VEC is a vector of R4's.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 06 August 2013
!
! Author:
!
! John Burkardt
!
! Parameters:
!
! Input, integer ( kind = 4 ) N, the number of values desired.
!
! Input, real ( kind = 4 ) A, B, the mean and standard deviation.
!
! Input/output, integer ( kind = 4 ) SEED, a seed for the random
! number generator.
!
! Output, real ( kind = 4 ) X(N), a sample of the standard normal PDF.
!
! Local parameters:
!
! Local, real ( kind = 4 ) R(N+1), is used to store some uniform
! random values. Its dimension is N+1, but really it is only needed
! to be the smallest even number greater than or equal to N.
!
! Local, integer ( kind = 4 ) X_LO_INDEX, X_HI_INDEX, records the range
! of entries of X that we need to compute.
!
implicit none
integer ( kind = 4 ) n
real ( kind = 4 ) a
real ( kind = 4 ) b
integer ( kind = 4 ) m
real ( kind = 4 ) r(n+1)
real ( kind = 4 ), parameter :: r4_pi = 3.141592653589793E+00
real ( kind = 4 ) r4_uniform_01
integer ( kind = 4 ) seed
real ( kind = 4 ) x(n)
integer ( kind = 4 ) x_hi_index
integer ( kind = 4 ) x_lo_index
!
! Record the range of X we need to fill in.
!
x_lo_index = 1
x_hi_index = n
!
! If we need just one new value, do that here to avoid null arrays.
!
if ( x_hi_index - x_lo_index + 1 == 1 ) then
r(1) = r4_uniform_01 ( seed )
if ( r(1) == 0.0E+00 ) then
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'R4VEC_NORMAL_AB - Fatal error!'
write ( *, '(a)' ) ' R4_UNIFORM_01 returned a value of 0.'
stop 1
end if
r(2) = r4_uniform_01 ( seed )
x(x_hi_index) = &
sqrt ( - 2.0E+00 * log ( r(1) ) ) * cos ( 2.0E+00 * r4_pi * r(2) )
!
! If we require an even number of values, that's easy.
!
else if ( mod ( x_hi_index - x_lo_index, 2 ) == 1 ) then
m = ( x_hi_index - x_lo_index + 1 ) / 2
call r4vec_uniform_01 ( 2*m, seed, r )
x(x_lo_index:x_hi_index-1:2) = &
sqrt ( - 2.0E+00 * log ( r(1:2*m-1:2) ) ) &
* cos ( 2.0E+00 * r4_pi * r(2:2*m:2) )
x(x_lo_index+1:x_hi_index:2) = &
sqrt ( - 2.0E+00 * log ( r(1:2*m-1:2) ) ) &
* sin ( 2.0E+00 * r4_pi * r(2:2*m:2) )
!
! If we require an odd number of values, we generate an even number,
! and handle the last pair specially, storing one in X(N), and
! saving the other for later.
!
else
x_hi_index = x_hi_index - 1
m = ( x_hi_index - x_lo_index + 1 ) / 2 + 1
call r4vec_uniform_01 ( 2*m, seed, r )
x(x_lo_index:x_hi_index-1:2) = &
sqrt ( - 2.0E+00 * log ( r(1:2*m-3:2) ) ) &
* cos ( 2.0E+00 * r4_pi * r(2:2*m-2:2) )
x(x_lo_index+1:x_hi_index:2) = &
sqrt ( - 2.0E+00 * log ( r(1:2*m-3:2) ) ) &
* sin ( 2.0E+00 * r4_pi * r(2:2*m-2:2) )
x(n) = sqrt ( - 2.0E+00 * log ( r(2*m-1) ) ) &
* cos ( 2.0E+00 * r4_pi * r(2*m) )
end if
x(1:n) = a + b * x(1:n)
return
end
function r8_normal_01 ( seed )
!*****************************************************************************80
!
!! R8_NORMAL_01 returns a unit pseudonormal R8.
!
! Discussion:
!
! The standard normal probability distribution function (PDF) has
! mean 0 and standard deviation 1.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 06 August 2013
!
! Author:
!
! John Burkardt
!
! Parameters:
!
! Input/output, integer ( kind = 4 ) SEED, a seed for the random
! number generator.
!
! Output, real ( kind = 8 ) R8_NORMAL_01, a normally distributed
! random value.
!
implicit none
real ( kind = 8 ) r1
real ( kind = 8 ) r2
real ( kind = 8 ) r8_normal_01
real ( kind = 8 ), parameter :: r8_pi = 3.141592653589793D+00
real ( kind = 8 ) r8_uniform_01
integer ( kind = 4 ) seed
real ( kind = 8 ) x
r1 = r8_uniform_01 ( seed )
r2 = r8_uniform_01 ( seed )
x = sqrt ( - 2.0D+00 * log ( r1 ) ) * cos ( 2.0D+00 * r8_pi * r2 )
r8_normal_01 = x
return
end
function r8_normal_ab ( a, b, seed )
!*****************************************************************************80
!
!! R8_NORMAL_AB returns a scaled pseudonormal R8.
!
! Discussion:
!
! The normal probability distribution function (PDF) is sampled,
! with mean A and standard deviation B.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 06 August 2013
!
! Author:
!
! John Burkardt
!
! Parameters:
!
! Input, real ( kind = 8 ) A, the mean of the PDF.
!
! Input, real ( kind = 8 ) B, the standard deviation of the PDF.
!
! Input/output, integer ( kind = 4 ) SEED, a seed for the random
! number generator.
!
! Output, real ( kind = 8 ) R8_NORMAL_AB, a sample of the normal PDF.
!
implicit none
real ( kind = 8 ) a
real ( kind = 8 ) b
real ( kind = 8 ) r1
real ( kind = 8 ) r2
real ( kind = 8 ) r8_normal_ab
real ( kind = 8 ), parameter :: r8_pi = 3.141592653589793D+00
real ( kind = 8 ) r8_uniform_01
integer ( kind = 4 ) seed
real ( kind = 8 ) x
r1 = r8_uniform_01 ( seed )
r2 = r8_uniform_01 ( seed )
x = sqrt ( - 2.0D+00 * log ( r1 ) ) * cos ( 2.0D+00 * r8_pi * r2 )
r8_normal_ab = a + b * x
return
end
function r8_uniform_01 ( seed )
!*****************************************************************************80
!
!! R8_UNIFORM_01 returns a unit pseudorandom R8.
!
! Discussion:
!
! This routine implements the recursion
!
! seed = 16807 * seed mod ( 2^31 - 1 )
! r8_uniform_01 = seed / ( 2^31 - 1 )
!
! The integer arithmetic never requires more than 32 bits,
! including a sign bit.
!
! If the initial seed is 12345, then the first three computations are
!
! Input Output R8_UNIFORM_01
! SEED SEED
!
! 12345 207482415 0.096616
! 207482415 1790989824 0.833995
! 1790989824 2035175616 0.947702
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 31 May 2007
!
! Author:
!
! John Burkardt
!
! Reference:
!
! Paul Bratley, Bennett Fox, Linus Schrage,
! A Guide to Simulation,
! Second Edition,
! Springer, 1987,
! ISBN: 0387964673,
! LC: QA76.9.C65.B73.
!
! Bennett Fox,
! Algorithm 647:
! Implementation and Relative Efficiency of Quasirandom
! Sequence Generators,
! ACM Transactions on Mathematical Software,
! Volume 12, Number 4, December 1986, pages 362-376.
!
! Pierre L'Ecuyer,
! Random Number Generation,
! in Handbook of Simulation,
! edited by Jerry Banks,
! Wiley, 1998,
! ISBN: 0471134031,
! LC: T57.62.H37.
!
! Peter Lewis, Allen Goodman, James Miller,
! A Pseudo-Random Number Generator for the System/360,
! IBM Systems Journal,
! Volume 8, 1969, pages 136-143.
!
! Parameters:
!
! Input/output, integer ( kind = 4 ) SEED, the "seed" value, which
! should NOT be 0.
! On output, SEED has been updated.
!
! Output, real ( kind = 8 ) R8_UNIFORM_01, a new pseudorandom variate,
! strictly between 0 and 1.
!
implicit none
integer ( kind = 4 ) k
real ( kind = 8 ) r8_uniform_01
integer ( kind = 4 ) seed
k = seed / 127773
seed = 16807 * ( seed - k * 127773 ) - k * 2836
if ( seed < 0 ) then
seed = seed + 2147483647
end if
!
! Although SEED can be represented exactly as a 32 bit integer,
! it generally cannot be represented exactly as a 32 bit real number!
!
r8_uniform_01 = real ( seed, kind = 8 ) * 4.656612875D-10
return
end
subroutine r8mat_normal_01 ( m, n, seed, r )
!*****************************************************************************80
!
!! R8MAT_NORMAL_01 returns a unit pseudonormal R8MAT.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 12 November 2010
!
! Author:
!
! John Burkardt
!
! Reference:
!
! Paul Bratley, Bennett Fox, Linus Schrage,
! A Guide to Simulation,
! Second Edition,
! Springer, 1987,
! ISBN: 0387964673,
! LC: QA76.9.C65.B73.
!
! Bennett Fox,
! Algorithm 647:
! Implementation and Relative Efficiency of Quasirandom
! Sequence Generators,
! ACM Transactions on Mathematical Software,
! Volume 12, Number 4, December 1986, pages 362-376.
!
! Pierre L'Ecuyer,
! Random Number Generation,
! in Handbook of Simulation,
! edited by Jerry Banks,
! Wiley, 1998,
! ISBN: 0471134031,
! LC: T57.62.H37.
!
! Peter Lewis, Allen Goodman, James Miller,
! A Pseudo-Random Number Generator for the System/360,
! IBM Systems Journal,
! Volume 8, 1969, pages 136-143.
!
! Parameters:
!
! Input, integer ( kind = 4 ) M, N, the number of rows and columns
! in the array.
!
! Input/output, integer ( kind = 4 ) SEED, the "seed" value, which
! should NOT be 0. On output, SEED has been updated.
!
! Output, real ( kind = 8 ) R(M,N), the array of pseudonormal values.
!
implicit none
integer ( kind = 4 ) m
integer ( kind = 4 ) n
integer ( kind = 4 ) seed
real ( kind = 8 ) r(m,n)
call r8vec_normal_01 ( m * n, seed, r )
return
end
subroutine r8mat_normal_ab ( m, n, a, b, seed, r )
!*****************************************************************************80
!
!! R8MAT_NORMAL_AB returns a scaled pseudonormal R8MAT.
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 06 August 2013
!
! Author:
!
! John Burkardt
!
! Reference:
!
! Paul Bratley, Bennett Fox, Linus Schrage,
! A Guide to Simulation,
! Second Edition,
! Springer, 1987,
! ISBN: 0387964673,
! LC: QA76.9.C65.B73.
!
! Bennett Fox,
! Algorithm 647:
! Implementation and Relative Efficiency of Quasirandom
! Sequence Generators,
! ACM Transactions on Mathematical Software,
! Volume 12, Number 4, December 1986, pages 362-376.
!
! Pierre L'Ecuyer,
! Random Number Generation,
! in Handbook of Simulation,
! edited by Jerry Banks,
! Wiley, 1998,
! ISBN: 0471134031,
! LC: T57.62.H37.
!
! Peter Lewis, Allen Goodman, James Miller,
! A Pseudo-Random Number Generator for the System/360,
! IBM Systems Journal,
! Volume 8, 1969, pages 136-143.
!
! Parameters:
!
! Input, integer ( kind = 4 ) M, N, the number of rows and columns
! in the array.
!
! Input, real ( kind = 8 ) A, B, the mean and standard deviation.
!
! Input/output, integer ( kind = 4 ) SEED, the "seed" value, which
! should NOT be 0. On output, SEED has been updated.
!
! Output, real ( kind = 8 ) R(M,N), the array of pseudonormal values.
!
implicit none
integer ( kind = 4 ) m
integer ( kind = 4 ) n
real ( kind = 8 ) a
real ( kind = 8 ) b
integer ( kind = 4 ) seed
real ( kind = 8 ) r(m,n)
call r8vec_normal_ab ( m * n, a, b, seed, r )
return
end
subroutine r8mat_print ( m, n, a, title )
!*****************************************************************************80
!
!! R8MAT_PRINT prints an R8MAT.
!
! Discussion:
!
! An R8MAT is an MxN array of R8's, stored by (I,J) -> [I+J*M].
!
! Licensing:
!
! This code is distributed under the GNU LGPL license.
!
! Modified:
!
! 12 September 2004
!
! Author:
!
! John Burkardt
!
! Parameters:
!
! Input, integer ( kind = 4 ) M, the number of rows in A.