From 36b7c17ca3343d31ac73cad9baa54347cba2d5e1 Mon Sep 17 00:00:00 2001 From: jaosch Date: Mon, 8 Sep 2025 17:02:10 +0200 Subject: [PATCH 1/2] fpm-compatibility initial commit The project was restuctured to enable the use of fpm as a build system and dependency manager for DNAOD. NOTE: The current version has only been tested with gfortran. To enable parallel compatibility with ifx, the used of cpp for preprocessing could be explored in the future. CPP support may be enabled within fpm by adding the following lines to the `fpm.toml` file: ```toml [preprocess] [preprocess.cpp] ``` --- .../prec_real128/LibDualzn128/diff_mod.mod | Bin 3411 -> 0 bytes .../prec_real128/LibDualzn128/dualzn_mod.mod | Bin 7445 -> 0 bytes .../prec_real128/LibDualzn128/libdualzn.a | Bin 253736 -> 0 bytes .../LibDualzn128/precision_mod.mod | Bin 396 -> 0 bytes .../prec_real128/examples/create_exec.sh | 13 - .../prec_real128/examples/ex1.f90 | 37 - .../prec_real128/examples/ex2.f90 | 53 - .../prec_real128/examples/ex3.f90 | 90 - .../prec_real64/LibDualzn64/diff_mod.mod | Bin 3413 -> 0 bytes .../prec_real64/LibDualzn64/dualzn_mod.mod | Bin 7431 -> 0 bytes .../prec_real64/LibDualzn64/libdualzn.a | Bin 223112 -> 0 bytes .../prec_real64/LibDualzn64/precision_mod.mod | Bin 395 -> 0 bytes .../prec_real64/examples/create_exec.sh | 13 - .../prec_real64/examples/ex1.f90 | 35 - .../prec_real64/examples/ex2.f90 | 53 - .../prec_real64/examples/ex3.f90 | 90 - .../prec_real128/LibDualzn128/diff_mod.mod | Bin 9691 -> 0 bytes .../prec_real128/LibDualzn128/dualzn_mod.mod | Bin 44075 -> 0 bytes .../prec_real128/LibDualzn128/libdualzn.a | Bin 474384 -> 0 bytes .../LibDualzn128/precision_mod.mod | Bin 1560 -> 0 bytes .../prec_real128/examples/create_exec.sh | 13 - .../ifx_case/prec_real128/examples/ex1.f90 | 36 - .../ifx_case/prec_real128/examples/ex2.f90 | 52 - .../ifx_case/prec_real128/examples/ex3.f90 | 90 - .../prec_real64/LibDualzn64/diff_mod.mod | Bin 9691 -> 0 bytes .../prec_real64/LibDualzn64/dualzn_mod.mod | Bin 44075 -> 0 bytes .../prec_real64/LibDualzn64/libdualzn.a | Bin 427688 -> 0 bytes .../prec_real64/LibDualzn64/precision_mod.mod | Bin 1559 -> 0 bytes .../prec_real64/examples/create_exec.sh | 13 - .../ifx_case/prec_real64/examples/ex1.f90 | 37 - .../ifx_case/prec_real64/examples/ex2.f90 | 52 - README.md | 31 +- SourcesF/diff_mod.f90 | 178 -- SourcesF/ex1.f90 | 42 - SourcesF/ex2.f90 | 54 - SourcesF/ex3.f90 | 92 - SourcesF_gfortran/Readme.txt | 2 - SourcesF_gfortran/dualzn_mod.f90 | 1816 ----------------- SourcesF_gfortran/ex3.f90 | 92 - SourcesF_gfortran/precision_mod.f90 | 7 - .../prec_real128/LibDualzn128/diff_mod.mod | Bin 3411 -> 0 bytes .../prec_real128/LibDualzn128/dualzn_mod.mod | Bin 7439 -> 0 bytes .../prec_real128/LibDualzn128/libdualzn.a | Bin 222110 -> 0 bytes .../LibDualzn128/precision_mod.mod | Bin 396 -> 0 bytes .../prec_real128/examples/create_exec.bat | 20 - .../prec_real128/examples/ex1.f90 | 35 - .../prec_real128/examples/ex2.f90 | 52 - .../prec_real128/examples/ex3.f90 | 90 - .../prec_real64/LibDualzn64/diff_mod.mod | Bin 3413 -> 0 bytes .../prec_real64/LibDualzn64/dualzn_mod.mod | Bin 7425 -> 0 bytes .../prec_real64/LibDualzn64/libdualzn.a | Bin 186676 -> 0 bytes .../prec_real64/LibDualzn64/precision_mod.mod | Bin 395 -> 0 bytes .../prec_real64/examples/create_exec.bat | 20 - .../gfortranCase/prec_real64/examples/ex1.f90 | 35 - .../gfortranCase/prec_real64/examples/ex2.f90 | 52 - .../gfortranCase/prec_real64/examples/ex3.f90 | 90 - .../prec_real128/LibDualzn128/diff_mod.mod | Bin 9912 -> 0 bytes .../prec_real128/LibDualzn128/dualzn_mod.mod | Bin 44261 -> 0 bytes .../prec_real128/LibDualzn128/libdualzn.lib | Bin 347610 -> 0 bytes .../LibDualzn128/precision_mod.mod | Bin 1781 -> 0 bytes .../prec_real128/examples/create_exec.bat | 19 - Windows/ifxCase/prec_real128/examples/ex1.f90 | 37 - Windows/ifxCase/prec_real128/examples/ex2.f90 | 52 - Windows/ifxCase/prec_real128/examples/ex3.f90 | 90 - .../prec_real64/LibDualzn64/diff_mod.mod | Bin 9912 -> 0 bytes .../prec_real64/LibDualzn64/dualzn_mod.mod | Bin 44261 -> 0 bytes .../prec_real64/LibDualzn64/libdualzn.lib | Bin 313010 -> 0 bytes .../prec_real64/LibDualzn64/precision_mod.mod | Bin 1780 -> 0 bytes .../prec_real64/examples/create_exec.bat | 19 - Windows/ifxCase/prec_real64/examples/ex1.f90 | 35 - Windows/ifxCase/prec_real64/examples/ex2.f90 | 52 - Windows/ifxCase/prec_real64/examples/ex3.f90 | 90 - {SourcesF_gfortran => example}/ex1.f90 | 15 +- {SourcesF_gfortran => example}/ex2.f90 | 13 +- .../prec_real64/examples => example}/ex3.f90 | 16 +- fpm.toml | 21 + {SourcesF_gfortran => src}/diff_mod.f90 | 2 +- {SourcesF => src}/dualzn_mod.f90 | 0 {SourcesF => src}/precision_mod.f90 | 0 test/test_dualzn_mod.f90 | 37 + test/tester.f90 | 16 + 81 files changed, 96 insertions(+), 3803 deletions(-) delete mode 100644 GNU_Linux/gfortran_case/prec_real128/LibDualzn128/diff_mod.mod delete mode 100644 GNU_Linux/gfortran_case/prec_real128/LibDualzn128/dualzn_mod.mod delete mode 100644 GNU_Linux/gfortran_case/prec_real128/LibDualzn128/libdualzn.a delete mode 100644 GNU_Linux/gfortran_case/prec_real128/LibDualzn128/precision_mod.mod delete mode 100755 GNU_Linux/gfortran_case/prec_real128/examples/create_exec.sh delete mode 100644 GNU_Linux/gfortran_case/prec_real128/examples/ex1.f90 delete mode 100644 GNU_Linux/gfortran_case/prec_real128/examples/ex2.f90 delete mode 100644 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mode 100644 Windows/ifxCase/prec_real64/LibDualzn64/dualzn_mod.mod delete mode 100644 Windows/ifxCase/prec_real64/LibDualzn64/libdualzn.lib delete mode 100644 Windows/ifxCase/prec_real64/LibDualzn64/precision_mod.mod delete mode 100644 Windows/ifxCase/prec_real64/examples/create_exec.bat delete mode 100644 Windows/ifxCase/prec_real64/examples/ex1.f90 delete mode 100644 Windows/ifxCase/prec_real64/examples/ex2.f90 delete mode 100644 Windows/ifxCase/prec_real64/examples/ex3.f90 rename {SourcesF_gfortran => example}/ex1.f90 (85%) rename {SourcesF_gfortran => example}/ex2.f90 (84%) rename {GNU_Linux/ifx_case/prec_real64/examples => example}/ex3.f90 (92%) create mode 100644 fpm.toml rename {SourcesF_gfortran => src}/diff_mod.f90 (99%) rename {SourcesF => src}/dualzn_mod.f90 (100%) rename {SourcesF => src}/precision_mod.f90 (100%) create mode 100644 test/test_dualzn_mod.f90 create mode 100644 test/tester.f90 diff --git a/GNU_Linux/gfortran_case/prec_real128/LibDualzn128/diff_mod.mod 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-I../LibDualzn128 -o "$OUTPUT_NAME" "$SOURCE_FILE" -L../LibDualzn128 -ldualzn diff --git a/GNU_Linux/gfortran_case/prec_real128/examples/ex1.f90 b/GNU_Linux/gfortran_case/prec_real128/examples/ex1.f90 deleted file mode 100644 index 66e94b2..0000000 --- a/GNU_Linux/gfortran_case/prec_real128/examples/ex1.f90 +++ /dev/null @@ -1,37 +0,0 @@ -!gfortran -I../LibDualzn128 -o e1 ex1.f90 -L../LibDualzn128 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - - call set_order(5) !before anything we set the 'order' to work with - - z0 = (1.1_prec,2.2_prec) - r = 0 !we initialize the dual number to 0 - - !we set the 0-th and 1-th components. If dual numbers are used to - !calculate D^n f(z0) then r must be of the form r = r0 + 1*eps_1 - r%f(0) = z0 - r%f(1) = 1 - - fval = sin(r)**log(r*r) - - !writing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - print*,fval%f(k) - end do - - deallocate(r%f) - deallocate(fval%f) - -end program main - - - - diff --git a/GNU_Linux/gfortran_case/prec_real128/examples/ex2.f90 b/GNU_Linux/gfortran_case/prec_real128/examples/ex2.f90 deleted file mode 100644 index c935727..0000000 --- a/GNU_Linux/gfortran_case/prec_real128/examples/ex2.f90 +++ /dev/null @@ -1,53 +0,0 @@ -!gfortran -I../LibDualzn128 -o e2 ex2.f90 -L../LibDualzn128 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - real :: t1,t2 - - call set_order(5) !we set the order to work with - - !since a dualzn numbers is an allocatable entity, do not forget to - !initialize it - r = 0 !<--- initializing r to 0 - r%f(0) = (1.1_prec,0.0_prec) - r%f(1) = 1 !since we want to differentiate, r = r0 +1*eps_1 - !all the other components are 0 as r was initialized to 0 - - call cpu_time(t1) - fval = ftest(r) - call cpu_time(t2) - - !Computing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - write(*,"(i0,a,f0.1,a,e17.10)") k,"-th derivative at x = ", & - real(r%f(0)),":",real(fval%f(k)) - end do - - print*,"elapsed time (s):",t2-t1 - - deallocate(r%f) - deallocate(fval%f) - -contains - function ftest(x) result(fr) - type(dualzn), intent(in) :: x - type(dualzn) :: fr - integer :: k - - !nested function f(x) = sin(x) * exp(-x^2), f(f(...(f(x))...)) - !applied 1000 times - fr = sin(x)*exp(-x*x) - do k=1, 1000-1 - fr = sin(fr)*exp(-fr*fr) - end do - end function ftest -end program main - - diff --git a/GNU_Linux/gfortran_case/prec_real128/examples/ex3.f90 b/GNU_Linux/gfortran_case/prec_real128/examples/ex3.f90 deleted file mode 100644 index 041011e..0000000 --- a/GNU_Linux/gfortran_case/prec_real128/examples/ex3.f90 +++ /dev/null @@ -1,90 +0,0 @@ -!gfortran -I../LibDualzn128 -o ExDO ex3.f90 -L../LibDualzn128 -ldualzn - -!module with example of functions -module function_mod - use dualzn_mod - implicit none - private - - public :: fstest, fvectest - -contains - !Example of scalar function f = sin(x*y*z) + cos(x*y*z) - function fstest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn) :: fr - type(dualzn) :: x,y,z - - x = r(1); y = r(2); z = r(3) - fr = sin(x*y*z) + cos(x*y*z) - end function fstest - - !Example of vector function f = [f1,f2,f3] - !f = fvectest(r) is a function f:D^m ---> Dn - function fvectest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn), allocatable, dimension(:) :: fr - type(dualzn) :: f1,f2,f3 - type(dualzn) :: x,y,z,w - - x = r(1); y = r(2); z = r(3); w = r(4) - - f1 = sin(x*y*z*w) - f2 = cos(x*y*z*w)*sqrt(w/y - x/z) - f3 = sin(log(x*y*z*w)) - - allocate(fr(3)) - fr = [f1,f2,f3] - end function fvectest -end module function_mod - -!----------------------------------------------------------------------- -!main program -program main - use precision_mod - use dualzn_mod - use diff_mod - use function_mod - implicit none - - integer, parameter :: nf =3, mq = 4 - complex(prec), parameter :: ii = (0,1) - complex(prec), dimension(mq) :: q, vec - complex(prec), dimension(nf,mq) :: Jmat - complex(prec), dimension(nf) :: JV - complex(prec), dimension(3) :: GV - complex(prec), dimension(3,3) :: Hmat - integer :: i - - vec = [1.0_prec,2.0_prec,3.0_prec,4.0_prec] - q = vec/10.0_prec + ii - - print*,"Jv using matmul" - Jmat = Jacobian(fvectest, q , nf) - JV = matmul(Jmat,vec) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"Jv using vector directional derivative" - JV = d1fvector(fvectest,vec,q,nf) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"---Hessian matrix---" - Hmat = 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a/GNU_Linux/gfortran_case/prec_real64/examples/ex1.f90 b/GNU_Linux/gfortran_case/prec_real64/examples/ex1.f90 deleted file mode 100644 index dbe9810..0000000 --- a/GNU_Linux/gfortran_case/prec_real64/examples/ex1.f90 +++ /dev/null @@ -1,35 +0,0 @@ -!gfortran -I../LibDualzn64 -o e1 ex1.f90 -L../LibDualzn64 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - - call set_order(5) !before anything we set the 'order' to work with - - z0 = (1.1_prec,2.2_prec) - r = 0 !we initialize the dual number to 0 - - !we set the 0-th and 1-th components. If dual numbers are used to - !calculate D^n f(z0) then r must be of the form r = r0 + 1*eps_1 - r%f(0) = z0 - r%f(1) = 1 - - fval = sin(r)**log(r*r) - - !writing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - print*,fval%f(k) - end do - deallocate(r%f) - deallocate(fval%f) -end program main - - - - diff --git a/GNU_Linux/gfortran_case/prec_real64/examples/ex2.f90 b/GNU_Linux/gfortran_case/prec_real64/examples/ex2.f90 deleted file mode 100644 index 2d86ba2..0000000 --- a/GNU_Linux/gfortran_case/prec_real64/examples/ex2.f90 +++ /dev/null @@ -1,53 +0,0 @@ -!gfortran -I../LibDualzn64 -o e2 ex2.f90 -L../LibDualzn64 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - real :: t1,t2 - - call set_order(5) !we set the order to work with - - !since a dualzn numbers is an allocatable entity, do not forget to - !initialize it - r = 0 !<--- initializing r to 0 - r%f(0) = (1.1_prec,0.0_prec) - r%f(1) = 1 !since we want to differentiate, r = r0 +1*eps_1 - !all the other components are 0 as r was initialized to 0 - - call cpu_time(t1) - fval = ftest(r) - call cpu_time(t2) - - !Computing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - write(*,"(i0,a,f0.1,a,e17.10)") k,"-th derivative at x = ", & - real(r%f(0)),":",real(fval%f(k)) - end do - - print*,"elapsed time (s):",t2-t1 - - deallocate(r%f) - deallocate(fval%f) - -contains - function ftest(x) result(fr) - type(dualzn), intent(in) :: x - type(dualzn) :: fr - integer :: k - - !nested function f(x) = sin(x) * exp(-x^2), f(f(...(f(x))...)) - !applied 1000 times - fr = sin(x)*exp(-x*x) - do k=1, 1000-1 - fr = sin(fr)*exp(-fr*fr) - end do - end function ftest -end program main - - diff --git a/GNU_Linux/gfortran_case/prec_real64/examples/ex3.f90 b/GNU_Linux/gfortran_case/prec_real64/examples/ex3.f90 deleted file mode 100644 index 73fdc70..0000000 --- a/GNU_Linux/gfortran_case/prec_real64/examples/ex3.f90 +++ /dev/null @@ -1,90 +0,0 @@ -!gfortran -I../LibDualzn64 -o e3 ex3.f90 -L../LibDualzn64 -ldualzn - -!module with example of functions -module function_mod - use dualzn_mod - implicit none - private - - public :: fstest, fvectest - -contains - !Example of scalar function f = sin(x*y*z) + cos(x*y*z) - function fstest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn) :: fr - type(dualzn) :: x,y,z - - x = r(1); y = r(2); z = r(3) - fr = sin(x*y*z) + cos(x*y*z) - end function fstest - - !Example of vector function f = [f1,f2,f3] - !f = fvectest(r) is a function f:D^m ---> Dn - function fvectest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn), allocatable, dimension(:) :: fr - type(dualzn) :: f1,f2,f3 - type(dualzn) :: x,y,z,w - - x = r(1); y = r(2); z = r(3); w = r(4) - - f1 = sin(x*y*z*w) - f2 = cos(x*y*z*w)*sqrt(w/y - x/z) - f3 = sin(log(x*y*z*w)) - - allocate(fr(3)) - fr = [f1,f2,f3] - end function fvectest -end module function_mod - -!----------------------------------------------------------------------- -!main program -program main - use precision_mod - use dualzn_mod - use diff_mod - use function_mod - implicit none - - integer, parameter :: nf =3, mq = 4 - complex(prec), parameter :: ii = (0,1) - complex(prec), dimension(mq) :: q, vec - complex(prec), dimension(nf,mq) :: Jmat - complex(prec), dimension(nf) :: JV - complex(prec), dimension(3) :: GV - complex(prec), dimension(3,3) :: Hmat - integer :: i - - vec = [1.0_prec,2.0_prec,3.0_prec,4.0_prec] - q = vec/10.0_prec + ii - - print*,"Jv using matmul" - Jmat = Jacobian(fvectest, q , nf) - JV = matmul(Jmat,vec) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"Jv using vector directional derivative" - JV = d1fvector(fvectest,vec,q,nf) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"---Hessian matrix---" - Hmat = 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z{{X^_xl4vwOY4MhHbZu~u!{++_AI66yv(JiI~W^s;_48gc;OBRlMxrt;&Ka8Ywa3F zD>a(}AVoU}8m(D#CJIv&XX;y~slz^QSNpafhUq6Ilu{7FdFB8C>8P(j!l9BT?F zN=Te^hhzo~EKZ{Tz_OAudT!9bVKxNlwhiTjv|Qg!NBwZ=hM+2gLQKMrGCkHmR_(86PVS r)`!9p573V^6SrMD6AzS+#&vlE?G~DaX?VbVyjiRj(8`j>4=a5Euz6rs diff --git a/GNU_Linux/ifx_case/prec_real128/examples/create_exec.sh b/GNU_Linux/ifx_case/prec_real128/examples/create_exec.sh deleted file mode 100755 index a322a79..0000000 --- a/GNU_Linux/ifx_case/prec_real128/examples/create_exec.sh +++ /dev/null @@ -1,13 +0,0 @@ -#!/bin/bash - -#Check if at least one argument (the source file) is provided -if [ "$#" -lt 1 ]; then - echo "Usage: $0 [output_executable_name]" - exit 1 -fi - -#Use the provided source file and output executable name or default to "a.out" -SOURCE_FILE=$1 -OUTPUT_NAME=${2:-a.out} - -ifx -I../LibDualzn128 -o "$OUTPUT_NAME" "$SOURCE_FILE" -L../LibDualzn128 -ldualzn diff --git a/GNU_Linux/ifx_case/prec_real128/examples/ex1.f90 b/GNU_Linux/ifx_case/prec_real128/examples/ex1.f90 deleted file mode 100644 index e46e527..0000000 --- a/GNU_Linux/ifx_case/prec_real128/examples/ex1.f90 +++ /dev/null @@ -1,36 +0,0 @@ -!ifx -I../LibDualzn128 -o e1 ex1.f90 -L../LibDualzn128 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - - call set_order(5) !before anything we set the 'order' to work with - - z0 = (1.1_prec,2.2_prec) - r = 0 !we initialize the dual number to 0 - - !we set the 0-th and 1-th components. If dual numbers are used to - !calculate D^n f(z0) then r must be of the form r = r0 + 1*eps_1 - r%f(0) = z0 - r%f(1) = 1 - - fval = sin(r)**log(r*r) - - !writing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - print*,fval%f(k) - end do - - deallocate(r%f) - deallocate(fval%f) -end program main - - - - diff --git a/GNU_Linux/ifx_case/prec_real128/examples/ex2.f90 b/GNU_Linux/ifx_case/prec_real128/examples/ex2.f90 deleted file mode 100644 index d5fce47..0000000 --- a/GNU_Linux/ifx_case/prec_real128/examples/ex2.f90 +++ /dev/null @@ -1,52 +0,0 @@ -!ifx -I../LibDualzn128 -o e2 ex2.f90 -L../LibDualzn128 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - real :: t1,t2 - - call set_order(5) !we set the order to work with - - !since a dualzn numbers is an allocatable entity, do not forget to - !initialize it - r = 0 !<--- initializing r to 0 - r%f(0) = (1.1_prec,0.0_prec) - r%f(1) = 1 !since we want to differentiate, r = r0 +1*eps_1 - !all the other components are 0 as r was initialized to 0 - - call cpu_time(t1) - fval = ftest(r) - call cpu_time(t2) - - !Computing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - write(*,"(i0,a,f0.1,a,e17.10)") k,"-th derivative at x = ", & - real(r%f(0)),":",real(fval%f(k)) - end do - - print*,"elapsed time (s):",t2-t1 - deallocate(r%f) - deallocate(fval%f) - -contains - function ftest(x) result(fr) - type(dualzn), intent(in) :: x - type(dualzn) :: fr - integer :: k - - !nested function f(x) = sin(x) * exp(-x^2), f(f(...(f(x))...)) - !applied 1000 times - fr = sin(x)*exp(-x*x) - do k=1, 1000-1 - fr = sin(fr)*exp(-fr*fr) - end do - end function ftest -end program main - - diff --git a/GNU_Linux/ifx_case/prec_real128/examples/ex3.f90 b/GNU_Linux/ifx_case/prec_real128/examples/ex3.f90 deleted file mode 100644 index d1fe232..0000000 --- a/GNU_Linux/ifx_case/prec_real128/examples/ex3.f90 +++ /dev/null @@ -1,90 +0,0 @@ -!ifx -I../LibDualzn128 -o e3 ex3.f90 -L../LibDualzn128 -ldualzn - -!module with example of functions -module function_mod - use dualzn_mod - implicit none - private - - public :: fstest, fvectest - -contains - !Example of scalar function f = sin(x*y*z) + cos(x*y*z) - function fstest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn) :: fr - type(dualzn) :: x,y,z - - x = r(1); y = r(2); z = r(3) - fr = sin(x*y*z) + cos(x*y*z) - end function fstest - - !Example of vector function f = [f1,f2,f3] - !f = fvectest(r) is a function f:D^m ---> Dn - function fvectest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn), allocatable, dimension(:) :: fr - type(dualzn) :: f1,f2,f3 - type(dualzn) :: x,y,z,w - - x = r(1); y = r(2); z = r(3); w = r(4) - - f1 = sin(x*y*z*w) - f2 = cos(x*y*z*w)*sqrt(w/y - x/z) - f3 = sin(log(x*y*z*w)) - - allocate(fr(3)) - fr = [f1,f2,f3] - end function fvectest -end module function_mod - -!----------------------------------------------------------------------- -!main program -program main - use precision_mod - use dualzn_mod - use diff_mod - use function_mod - implicit none - - integer, parameter :: nf =3, mq = 4 - complex(prec), parameter :: ii = (0,1) - complex(prec), dimension(mq) :: q, vec - complex(prec), dimension(nf,mq) :: Jmat - complex(prec), dimension(nf) :: JV - complex(prec), dimension(3) :: GV - complex(prec), dimension(3,3) :: Hmat - integer :: i - - vec = [1.0_prec,2.0_prec,3.0_prec,4.0_prec] - q = vec/10.0_prec + ii - - print*,"Jv using matmul" - Jmat = Jacobian(fvectest, q , nf) - JV = matmul(Jmat,vec) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"Jv using vector directional derivative" - JV = d1fvector(fvectest,vec,q,nf) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"---Hessian matrix---" - Hmat = Hessian(fstest,q(1:3)) - do i=1,3 - write(*,"(A,i0)") "row:",i - write(*,*) Hmat(i,:) - end do - write(*,*) - - print*,"---Gradient---" - GV = gradient(fstest,q(1:3)) - do i=1,3 - write(*,*) GV(i) - end do -end program main diff --git a/GNU_Linux/ifx_case/prec_real64/LibDualzn64/diff_mod.mod b/GNU_Linux/ifx_case/prec_real64/LibDualzn64/diff_mod.mod deleted file mode 100644 index c141158686b708ed8e832a9ae544200d846e56d4..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 9691 zcmd5?OK%)S5bjBA>^v5mI3$4pnPk0rU`QOJ2y#Fg$7{zMZFarhc;!SwPEarq$U`LI z#9sg+6mdWia6yOzM-W^P`2$=yA#s5NATIoY9QeNKshOUK*Y?`pq*pUN-Bn%vb#+xu zPxls#XRhos=7cfkoma+2Um87Ww&D4^9^Aq-cH-!$KL7XW?zi|%9wyIb8+P9sO1}K| z;^M;9>z9u%o*Xsh%GA`t*?QUZg$N!Cxyr|DlpeWwLh8y!pnppgg86oFVwmbNaDAU12q_IRu)}M=U2uw=x+yn}j8n<4k}t zAjZNnvT`cC0m{4WZ8ODah^>~{jLNuTu4T5Mq7=0c1b(oG{aHK_Dd&O0U;zb}#5%1g zPBqJh!zi|7riu+2^}&cg*ert-Rb;#KQ$w~2>FJ-2+Q$#XU7RnQUgqd_ZoFFJ?Ly7a zHeleAd}ALJu>D*RaBrjV|s>^MZ10+!`3=-Y{D=PdWjihHPoH069R5IFrN!) zei~*Hu}X+?x`7K**$ZYMfwL2sono@~9jh+JG`MC=of<5SJ#Da@poGEFk&E+YJG1jb zg56@mP0DTq>%z<1t&I%r?Uvy*#~?bjTN|BY<*VHSN*C-lz+i0BN!M~Jr;hXOc3T4H zI@oO>UGcUICTk0^>Xf|zi*R+5w&#hCXv{R$A>&w7g@=TGmmZOtqww?a@>37mczL1?)6W0S@K)Nr^*J z^bRF!<5D`F`g=&rMz*+xecCD6G7Eqw!Gr|>b%8)i$*Dj}<3P%G=Nq4dC{Ypy*meQ1 z3moehNGZ?IHurp-tjK{UnlQp!wpf$Ya0MY3JKy1iaJLwP#SZ}U1kRA?4 zzR6sa7_d@bo<;>s_*rHRLxmJ;vZlP@^@ZWit^rS= zT*t+Fb!@Hy8J(7*L0Tdm2}}K^ysG6fLDD-kD5|O2c?g9HTFb%Z@?KQiF**xoR~emz zRSjEydKF7}icax3Il<)l8Ya!P7g6Tw7u%f3)F3;xY}$bfRIR80LvfLIqP$Kq*>-sm zVDFkSMF!z#zn(-DOWdp>^bGZdlb-b2ezQ`q^+kTxYwhbtJC`p{d5MHxyC0NdW8&;g zb)NB>K0A!87ryye=%Z?lu5VHfQ#;>Q9?tMIWW9%rFHx3X_6lATR~>*UL*HvxydIBq zO^ge9buN$lO#ZxB@-VUJSTs+?t`&bGajNoSmtAS8bk3HYF~+U~C_OTB3ozGT<&1IWI!<8_4wHoV8yA+TjOYIXUu+OTF{JTc5Tto0^vb`sXC z3h4R#*jV|pWklvY8;<;hEl4<$x0-~b7dU+la}?Q9k>D6;8y$txp4qKF6RJU>Q%|89 zxu8&Um120KvblhGk@@q}E)k5yBX63@9oCC3_+yM(K5W<)KnuXXMwh&2MHHGj3 z={0$?>#Md~uE)`$(=AuF#rmf!Tdq0@K6(srNoq56YXNPCJ_Z?`4xMc`dg$Cr{1O*m zaSZy4*NThRr1TR?Ra~#*x_#-!jl{v=Z0L{DAli^skX$%F;^+tnBy_Tpra z*1#11iGmY(3zWzf^zRj-?){+t4Qixrmr7-GETy; 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mIKMAr;ZkyaUCo7D zu@E(P4-ZGndo6liX2-yeLZ*pzKM$H3*ghMF9TinJP8*#26zzqVqgY%L@!EwjA4 z@5W{iRk40;5(1>E=ISc4s*2dJF)E`KCB`iHODzYhf|@50$lH>vI)uH4jjx=M>Im=_ zF`Zu6+|~>*Toqn8i6C4Zg4)AAOPf{1LL2Larnz<`kM1G+`w{a@U%nqPk>d9GVey^SI`ffW+6R1BPLOW(X;!!(T$p6W! z6Gh66TXO$>i^cl%{{dqz(K*OoV9-(<_GL+F{{95Zd+lJM_GhpuZo~Z~Z{H8K{gc47 z{nAQ1VQGRDl4AM(2#V3itnr1$pY^4B?5o#xpFNFO!(M+?T$=xL0PX9%a{XXfqh+@6 z7OMXY>f>X(vSHR^eu8ZFD6??7+;K`R1E*=A1b*LDJ}Bl4zcYu5)@aoy^k$#_zzS=v#@T9JgO1 zmpo<;izd{+^?WXt+q;Xi#(ksJbZ%PbiF!Us6}wzCs)l7cM^;IYMDLwd1v}%}UQC=n z05?I$SxNSF=5r2rSzN^xwQ0z!H%4`Iz&ibxC_E$!UeRrJc86(Cx_8W z&87fIk*=N3klWLW|n8aoL}z||pIk#ohKgj6kjXyF+Z#8`u2O#wv; ziG%Kv%&3mVO$_f?W>R|3jp}&XwJ^Nnu|+JhIlSYsMJx;rb}WjQsJCQN+1^~sOBkf* z{>U};sV-m0OEB<;wvNWft2d+drd!-!m|dYAV2@F?oIT5~*#*-no5!>YTt~&8LbDVd zJi85M6`ftfEE(oLZ32G*rve?5oS2Wd%@1}B>uqo!pjq7i!?mY+W!4D}sj#vcA1e;l qx55(tPhXme$1aVD|H((=ynKT82+hJY{9iuaBGwA1WND87Rr&#Le_(q6 diff --git a/GNU_Linux/ifx_case/prec_real64/examples/create_exec.sh b/GNU_Linux/ifx_case/prec_real64/examples/create_exec.sh deleted file mode 100755 index 13113b7..0000000 --- a/GNU_Linux/ifx_case/prec_real64/examples/create_exec.sh +++ /dev/null @@ -1,13 +0,0 @@ -#!/bin/bash - -#Check if at least one argument (the source file) is provided -if [ "$#" -lt 1 ]; then - echo "Usage: $0 [output_executable_name]" - exit 1 -fi - -#Use the provided source file and output executable name or default to "a.out" -SOURCE_FILE=$1 -OUTPUT_NAME=${2:-a.out} - -ifx -I../LibDualzn64 -o "$OUTPUT_NAME" "$SOURCE_FILE" -L../LibDualzn64 -ldualzn diff --git a/GNU_Linux/ifx_case/prec_real64/examples/ex1.f90 b/GNU_Linux/ifx_case/prec_real64/examples/ex1.f90 deleted file mode 100644 index 55005f6..0000000 --- a/GNU_Linux/ifx_case/prec_real64/examples/ex1.f90 +++ /dev/null @@ -1,37 +0,0 @@ -!ifx -I../LibDualzn64 -o e1 ex1.f90 -L../LibDualzn64 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - - call set_order(5) !before anything we set the 'order' to work with - - z0 = (1.1_prec,2.2_prec) - r = 0 !we initialize the dual number to 0 - - !we set the 0-th and 1-th components. If dual numbers are used to - !calculate D^n f(z0) then r must be of the form r = r0 + 1*eps_1 - r%f(0) = z0 - r%f(1) = 1 - - fval = sin(r)**log(r*r) - - !writing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - print*,fval%f(k) - end do - - - deallocate(r%f) - deallocate(fval%f) -end program main - - - - diff --git a/GNU_Linux/ifx_case/prec_real64/examples/ex2.f90 b/GNU_Linux/ifx_case/prec_real64/examples/ex2.f90 deleted file mode 100644 index 41e2177..0000000 --- a/GNU_Linux/ifx_case/prec_real64/examples/ex2.f90 +++ /dev/null @@ -1,52 +0,0 @@ -!ifx -I../LibDualzn64 -o e2 ex2.f90 -L../LibDualzn64 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - real :: t1,t2 - - call set_order(15) !we set the order to work with - - !since a dualzn numbers is an allocatable entity, do not forget to - !initialize it - r = 0 !<--- initializing r to 0 - r%f(0) = (1.1_prec,0.0_prec) - r%f(1) = 1 !since we want to differentiate, r = r0 +1*eps_1 - !all the other components are 0 as r was initialized to 0 - - call cpu_time(t1) - fval = ftest(r) - call cpu_time(t2) - - !Computing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - write(*,"(i0,a,f0.1,a,e17.10)") k,"-th derivative at x = ", & - real(r%f(0)),":",real(fval%f(k)) - end do - - print*,"elapsed time (s):",t2-t1 - deallocate(r%f) - deallocate(fval%f) - -contains - function ftest(x) result(fr) - type(dualzn), intent(in) :: x - type(dualzn) :: fr - integer :: k - - !nested function f(x) = sin(x) * exp(-x^2), f(f(...(f(x))...)) - !applied 1000 times - fr = sin(x)*exp(-x*x) - do k=1, 1000-1 - fr = sin(fr)*exp(-fr*fr) - end do - end function ftest -end program main - - diff --git a/README.md b/README.md index d504aed..a64ba61 100644 --- a/README.md +++ b/README.md @@ -2,37 +2,18 @@ **DNAOAD** (Dual Number Arbitrary Order Automatic Differentiation) is a Fortran implementation of dual numbers for arbitrary order automatic differentiation. -## 🧪 Running Examples +## 🧪 Building & Running Examples -To run the examples, navigate to the `examples` directory and use a terminal. For example: +To build and run the examples we recommend installing the fortran package manger ([fpm][https://fpm.fortran-lang.org/index.html]) first. Then the examples can by executed by simply running, for example -```sh -sh create_exec.sh ex1.f90 +```bash +fpm run --example ex1 ``` -On **Windows**, use: - -```bat -create_exec.bat ex1.f90 -``` - -> **Note:** Alternatively (and this is the recommended method), you can manually compile and run the source files. - -## ⚙️ Manual Compilation - -The examples in the `SourcesF` folder can be compiled directly using the **Intel Fortran** compiler: - -```sh -ifx ex3.f90 -``` - -If you're using **gfortran**, use the `SourcesF_gfortran` folder instead. +from the command line. ## 📖 More Information -For further details, see **Section 4** of the article: +For further details, see the article: 📎 [https://doi.org/10.48550/arXiv.2501.04159](https://doi.org/10.48550/arXiv.2501.04159) - - - diff --git a/SourcesF/diff_mod.f90 b/SourcesF/diff_mod.f90 deleted file mode 100644 index 58883ed..0000000 --- a/SourcesF/diff_mod.f90 +++ /dev/null @@ -1,178 +0,0 @@ -module diff_mod - use precision_mod !Depending on how to link, it will set prec to be - !real64 or real128 - use dualzn_mod - implicit none - - private - public :: d1fscalar, d2fscalar, d1fvector - public :: Jacobian, Hessian, gradient - - !Abstract interfaces for functions passed as arguments to other - !functions. - ! - !Interface for a scalar dual function f: D^m --> D (similar to - !f: R^m --> R) - abstract interface - function fsdual(xd) result(frsd) - use dualzn_mod - type(dualzn), intent(in), dimension(:) :: xd - type(dualzn) :: frsd - end function fsdual - end interface - - !Interface for a vector dual function f: D^m --> D^n - interface - function fvecdual(xd) result(frd) - use dualzn_mod - type(dualzn), intent(in), dimension(:) :: xd - type(dualzn), allocatable, dimension(:) :: frd - end function fvecdual - end interface - - interface d2fscalar - module procedure d2fscalarvv - module procedure d2fscalaruv - end interface d2fscalar - !--------------------------------------------------------------------- - -contains - !Hessian operator - function Hessian(fsd,qcmplx) result(Hmat) - procedure(fsdual) :: fsd - complex(prec), intent(in), dimension(:) :: qcmplx - complex(prec), dimension(size(qcmplx),size(qcmplx)) :: Hmat - - complex(prec), dimension(size(qcmplx)) :: ei, ej - integer :: i,j,m - - m = size(qcmplx) - - Hmat = 0 - do i=1,m - ei = 0 - ei(i) = 1 - Hmat(i,i) = d2fscalarvv(fsd,ei,qcmplx) - end do - - do i=1, m - ei = 0 - ei(i) = 1 - do j=i+1,m - ej = 0 - ej(j) = 1 - Hmat(i,j) = 0.5_prec * (d2fscalar(fsd,ei + ej,qcmplx) - Hmat(i,i) & - Hmat(j,j)) - Hmat(j,i) = Hmat(i,j) - end do - end do - end function Hessian - - !d2fscalaruv(f,u,v,q) gives the second-order directional derivative - !of the scalar function f: D^m --> D, where f = f(q), along vectors u - !and v, evaluated at point q - function d2fscalaruv(fsd,x,y,q) result(fr) - procedure(fsdual) :: fsd - complex(prec), intent(in), dimension(:) :: x, y, q - complex(prec) :: fr - - if(all(x == y)) then - fr = d2fscalarvv(fsd,x,q) - else - fr = 0.5_prec*(d2fscalarvv(fsd,x + y,q) - d2fscalarvv(fsd,x,q) -& - d2fscalarvv(fsd,y,q)) - end if - end function d2fscalaruv - - !Second-order directional derivative of a scalar function along vector - !v, evaluated at point q - function d2fscalarvv(fsd,v,q) result(fr) - procedure(fsdual) :: fsd - complex(prec), intent(in), dimension(:) :: v, q - complex(prec) :: fr - type(dualzn) :: eps1 - integer :: original_order - - original_order = get_order() - call set_order(2) - eps1 = 0 - eps1%f(1) = 1 - - fr = f_part(fsd(q + eps1*v),2) - call set_order(original_order) - end function d2fscalarvv - - !Jacobian operator: To optimize efficiency, we include the parameter - !'n', representing the dimension of 'fvecd'. - function Jacobian(fvecd,qcmplx,n) result(Jmat) - procedure(fvecdual) :: fvecd - complex(prec), intent(in), dimension(:) :: qcmplx - integer, intent(in) :: n - complex(prec), dimension(n,size(qcmplx)) :: Jmat - - complex(prec), dimension(size(qcmplx),n) :: TrpJmat - complex(prec), dimension(size(qcmplx)) :: ei - integer :: i - - do i = 1,size(qcmplx) - ei = 0 - ei(i) = 1 - TrpJmat(i,:) = d1fvector(fvecd,ei,qcmplx,n) - end do - - Jmat = transpose(TrpJmat) - end function Jacobian - - !First-order directional derivative of a vector function along vector - !v, evaluated at point q. To optimize efficiency, we include the - !parameter 'n', representing the dimension of 'fvecd'. - ! - function d1fvector(fvecd,v,q,n) result(fr) - procedure(fvecdual) :: fvecd - complex(prec), intent(in), dimension(:) :: v, q - integer, intent(in) :: n - complex(prec), dimension(n) :: fr - type(dualzn) :: eps1 - integer :: original_order - - original_order = get_order() - call set_order(1) - eps1 = 0 - eps1%f(1) = 1 - - fr = f_part(fvecd(q + eps1*v),1) - call set_order(original_order) - end function d1fvector - - function gradient(fsd,q) result(fr) - procedure(fsdual) :: fsd - complex(prec), intent(in), dimension(:) :: q - complex(prec), dimension(size(q)) :: fr - complex(prec), dimension(size(q)) :: ei - integer :: i - - do i = 1,size(q) - ei = 0 - ei(i) = 1 - fr(i) = d1fscalar(fsd,ei,q) - end do - end function gradient - - !First-order directional derivative of a scalar function along vector - !v, evaluated at point q - function d1fscalar(fsd,v,q) result(fr) - procedure(fsdual) :: fsd - complex(prec), intent(in), dimension(:) :: v, q - complex(prec) :: fr - type(dualzn) :: eps1 - integer :: original_order - - original_order = get_order() - call set_order(1) - eps1 = 0 - eps1%f(1) = 1 - - fr = f_part(fsd(q + eps1*v),1) - call set_order(original_order) - end function d1fscalar -end module diff_mod diff --git a/SourcesF/ex1.f90 b/SourcesF/ex1.f90 deleted file mode 100644 index 9e60eaf..0000000 --- a/SourcesF/ex1.f90 +++ /dev/null @@ -1,42 +0,0 @@ -include './precision_mod.f90' -include './dualzn_mod.f90' - -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k, local_order - - - call set_order(5) !before anything we set the 'order' to work with - - local_order = get_order() - - z0 = (1.1_prec,2.2_prec) - r = 0 !we initialize the dual number to 0 - - !we set the 0-th and 1-th components. If dual numbers are used to - !calculate D^n f(z0) then r must be of the form r = r0 + 1*eps_1 - r%f(0) = z0 - r%f(1) = 1 - - fval = sin(r)**log(r*r) - - !writing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0, local_order - print*,fval%f(k) - end do - - deallocate(r%f) - deallocate(fval%f) - -end program main - - - - diff --git a/SourcesF/ex2.f90 b/SourcesF/ex2.f90 deleted file mode 100644 index c14b7b7..0000000 --- a/SourcesF/ex2.f90 +++ /dev/null @@ -1,54 +0,0 @@ -include './precision_mod.f90' -include './dualzn_mod.f90' - -program main - use precision_mod - use dualzn_mod - implicit none - - type(dualzn) :: r, fval - integer :: k, local_order - real :: t1,t2 - - - call set_order(15) !we set the order to work with - local_order = get_order() - - !since a dualzn numbers is an allocatable entity, do not forget to - !initialize it - r = 0 !<--- initializing r to 0 - r%f(0) = (1.1_prec,0.0_prec) - r%f(1) = 1 !since we want to differentiate, r = r0 +1*eps_1 - !all the other components are 0 as r was initialized to 0 - - call cpu_time(t1) - fval = ftest(r) - call cpu_time(t2) - - !Computing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0, local_order - write(*,"(i0,a,f0.1,a,e17.10)") k,"-th derivative at x = ", & - real(r%f(0)),":",real(fval%f(k)) - end do - - print*,"elapsed time (s):",t2-t1 - - deallocate(r%f) - deallocate(fval%f) - -contains - function ftest(x) result(fr) - type(dualzn), intent(in) :: x - type(dualzn) :: fr - integer :: k - - !nested function f(x) = sin(x) * exp(-x^2), f(f(...(f(x))...)) - !applied 1000 times - fr = sin(x)*exp(-x*x) - do k=1, 1000-1 - fr = sin(fr)*exp(-fr*fr) - end do - end function ftest -end program main diff --git a/SourcesF/ex3.f90 b/SourcesF/ex3.f90 deleted file mode 100644 index 36d87d5..0000000 --- a/SourcesF/ex3.f90 +++ /dev/null @@ -1,92 +0,0 @@ -include './precision_mod.f90' -include './dualzn_mod.f90' -include './diff_mod.f90' - -!module with example of functions -module function_mod - use dualzn_mod - implicit none - private - - public :: fstest, fvectest - -contains - !Example of scalar function f = sin(x*y*z) + cos(x*y*z) - function fstest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn) :: fr - type(dualzn) :: x,y,z - - x = r(1); y = r(2); z = r(3) - fr = sin(x*y*z) + cos(x*y*z) - end function fstest - - !Example of vector function f = [f1,f2,f3] - !f = fvectest(r) is a function f:D^m ---> Dn - function fvectest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn), allocatable, dimension(:) :: fr - type(dualzn) :: f1,f2,f3 - type(dualzn) :: x,y,z,w - - x = r(1); y = r(2); z = r(3); w = r(4) - - f1 = sin(x*y*z*w) - f2 = cos(x*y*z*w)*sqrt(w/y - x/z) - f3 = sin(log(x*y*z*w)) - - allocate(fr(3)) - fr = [f1,f2,f3] - end function fvectest -end module function_mod - -!----------------------------------------------------------------------- -!main program -program main - use precision_mod - use dualzn_mod - use diff_mod - use function_mod - implicit none - - integer, parameter :: nf =3, mq = 4 - complex(prec), parameter :: ii = (0,1) - complex(prec), dimension(mq) :: q, vec - complex(prec), dimension(nf,mq) :: Jmat - complex(prec), dimension(nf) :: JV - complex(prec), dimension(3) :: GV - complex(prec), dimension(3,3) :: Hmat - integer :: i - - vec = [1.0_prec,2.0_prec,3.0_prec,4.0_prec] - q = vec/10.0_prec + ii - - print*,"Jv using matmul" - Jmat = Jacobian(fvectest, q , nf) - JV = matmul(Jmat,vec) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"Jv using vector directional derivative" - JV = d1fvector(fvectest,vec,q,nf) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"---Hessian matrix---" - Hmat = Hessian(fstest,q(1:3)) - do i=1,3 - write(*,"(A,i0)") "row:",i - write(*,*) Hmat(i,:) - end do - write(*,*) - - print*,"---Gradient---" - GV = gradient(fstest,q(1:3)) - do i=1,3 - write(*,*) GV(i) - end do -end program main diff --git a/SourcesF_gfortran/Readme.txt b/SourcesF_gfortran/Readme.txt deleted file mode 100644 index 3d09cc5..0000000 --- a/SourcesF_gfortran/Readme.txt +++ /dev/null @@ -1,2 +0,0 @@ -The addition of dualzn numbers is implemented as an elemental operation, which allows expressions like xvec + yvec for dualzn vectors. However, the gfortran compiler produces errors when such expressions are passed directly as arguments to a function (e.g., f(x + y)). In such cases, gfortran requires the result to be stored in an intermediate variable before being passed. To avoid this issue, a dedicated function for adding dual vectors is defined in the diff_mod.f90 file. - diff --git a/SourcesF_gfortran/dualzn_mod.f90 b/SourcesF_gfortran/dualzn_mod.f90 deleted file mode 100644 index b2259b5..0000000 --- a/SourcesF_gfortran/dualzn_mod.f90 +++ /dev/null @@ -1,1816 +0,0 @@ -!Dual numbers to order n of complex components -!This can be used to compute first, second,... nth order derivatives -!F. Pe~nu~nuri -!UADY, Merida Yucatan Mexico -!2024 -! - -module dualzn_mod - use precision_mod - implicit none - - private - !--------------------------------------------------------------------- - !Some Module variables - !Default order, can be modified with set_order - integer, protected :: order = 1 - real(prec), public, parameter :: Pi = 4.0_prec*atan(1.0_prec) - !--------------------------------------------------------------------- - - !dual number definition to any order - type, public :: dualzn - complex(prec), allocatable, dimension(:) :: f - end type dualzn - - public :: set_order, get_order, initialize_dualzn, f_part - public :: binomial, BellY, Dnd - public :: Mset_fpart - public :: xto_dzn - public :: itodn, realtodn, cmplxtodn - - public :: inv, sin, cos, tan, exp, log, sqrt, asin, acos, atan, asinh - public :: acosh, atanh, sinh, cosh, tanh, absx, atan2 - public :: conjg, sum, product, matmul - - public :: assignment (=) - public :: operator(*), operator(/), operator(+), operator(-) - public :: operator(**), operator(==), operator(/=) - - !equal assignment - interface assignment (=) - module procedure igualz16_dzn !dualzn <--- complex16 - module procedure igualz8_dzn !dualzn <--- complex8 - module procedure igualz4_dzn !dualzn <--- complex4 - module procedure igualr16_dzn !dualzn <--- real16 - module procedure igualr8_dzn !dualzn <--- real8 - module procedure igualr4_dzn !dualzn <--- real4 - module procedure iguali8_dzn !dualzn <--- integer8 - module procedure iguali4_dzn !dualzn <--- integer4 - end interface assignment (=) - !--------------------------------------------------------------------- - - !functions to change from integer, real and complex numbers to dual - ! can use xto_dzn instead - interface itodn - module procedure i4todn - module procedure i8todn - end interface itodn - - interface realtodn - module procedure r4todn - module procedure r8todn - module procedure r16todn - end interface realtodn - - interface cmplxtodn - module procedure c4todn - module procedure c8todn - module procedure c16todn - end interface cmplxtodn - !--------------------------------------------------------------------- - - !Logical equal operator - interface operator (==) - module procedure eq_dzn - end interface operator (==) - !--------------------------------------------------------------------- - - !Logical not equal operator - interface operator (/=) - module procedure noteq_dzn - end interface operator (/=) - !--------------------------------------------------------------------- - - !overloaded operators - interface operator(*) - module procedure timesdX - module procedure timesXd - end interface operator(*) - - interface operator(/) - module procedure divdX - module procedure divXd - end interface operator(/) - - interface operator (+) - module procedure masd !unary - module procedure sumadX - module procedure sumaXd - end interface operator (+) - - interface operator (-) - module procedure menosd !unary - module procedure restadX - module procedure restaXd - end interface operator (-) - - interface operator(**) - module procedure powerdX - module procedure powerXd - end interface operator(**) - !--------------------------------------------------------------------- - !some matrix and vector operations - interface sum - module procedure sumR2dzn !sum(dual_rank2,dir) - module procedure sumR20dzn !sum(dual_rank2) - module procedure sumR1dzn !sum(dual_rank1) - end interface sum - !--------------------------------------------------------------------- - - !product for dual - interface product - module procedure prodR2dzn !product(dual_rank2,dir) - module procedure prodR20dzn !product(dual_rank2) - module procedure prodR1dzn !product(dual_rank1) - end interface product - !--------------------------------------------------------------------- - - interface matmul - module procedure MtimesdX - module procedure Mtimesc128d - module procedure Mtimesc64d - module procedure Mtimesc32d - module procedure Mtimesr128d - module procedure Mtimesr64d - module procedure Mtimesr32d - module procedure Mtimesi64d - module procedure Mtimesi32d - end interface matmul - !--------------------------------------------------------------------- - - !overloaded functions - interface conjg - module procedure conjg_dzn - end interface conjg - - interface atan2 - module procedure atan2d_ - end interface atan2 - - interface tanh - module procedure tanhd - end interface tanh - - interface cosh - module procedure coshd - end interface cosh - - interface sinh - module procedure sinhd - end interface sinh - - interface atanh - module procedure atanhd - end interface atanh - - interface acosh - module procedure acoshd - end interface acosh - - interface asinh - module procedure asinhd - end interface asinh - - interface atan - module procedure atand_ - ! Fortran 2008 standard for 2 argument atan: - module procedure atan2d_ - end interface atan - - interface acos - module procedure acosd_ - end interface acos - - interface asin - module procedure asind_ - end interface asin - - interface log - module procedure logd - end interface log - - interface exp - module procedure expd - end interface exp - - interface sqrt - module procedure sqrtd - end interface sqrt - - interface sin - module procedure sind_ - end interface sin - - interface cos - module procedure cosd_ - end interface cos - - interface tan - module procedure tand_ - end interface tan - !--------------------------------------------------------------------- - - !interface to define a function of complex variable returning a dual - !variable - !f:z --> dual - abstract interface - pure function funzdual(z_val) result(f_result) - use precision_mod - import :: dualzn - complex(prec), intent(in) :: z_val - type(dualzn) :: f_result - end function funzdual - end interface - !--------------------------------------------------------------------- - - !Functions -contains - !to set the order for dual numbers - subroutine set_order(new_order) - integer, intent(in) :: new_order - if(new_order<1) then - stop "order must be greater than 0" - end if - order = new_order - end subroutine set_order - - !check the order for dual numbers - pure function get_order() result(order_value) - integer :: order_value - order_value = order - end function get_order - !--------------------------------------------------------------------- - - !Assignment, equal operator - !dualzn <--- complex16 - elemental subroutine igualz16_dzn(A, z) - type(dualzn), intent(out) :: A - complex(real128), intent(in) :: z - - A = cmplxtodn(z) - end subroutine igualz16_dzn - - !dualzn <--- complex8 - elemental subroutine igualz8_dzn(A, z) - type(dualzn), intent(out) :: A - complex(real64), intent(in) :: z - - A = cmplxtodn(z) - end subroutine igualz8_dzn - - !dualzn <--- complex4 - elemental subroutine igualz4_dzn(A, z) - type(dualzn), intent(out) :: A - complex(real32), intent(in) :: z - - A = cmplxtodn(z) - end subroutine igualz4_dzn - !--------------------------------------------------------------------- - - !dualzn <--- real16 - elemental subroutine igualr16_dzn(A, x) - type(dualzn), intent(out) :: A - real(real128), intent(in) :: x - - A = realtodn(x) - end subroutine igualr16_dzn - - !dualzn <--- real8 - elemental subroutine igualr8_dzn(A, x) - type(dualzn), intent(out) :: A - real(real64), intent(in) :: x - - A = realtodn(x) - end subroutine igualr8_dzn - - !dualzn <--- real4 - elemental subroutine igualr4_dzn(A, x) - type(dualzn), intent(out) :: A - real(real32), intent(in) :: x - - A = realtodn(x) - end subroutine igualr4_dzn - !--------------------------------------------------------------------- - - !dualzn <--- integer8 - elemental subroutine iguali8_dzn(A, ix) - type(dualzn), intent(out) :: A - integer(int64), intent(in) :: ix - - A = itodn(ix) - end subroutine iguali8_dzn - - !dualzn <--- integer4 - elemental subroutine iguali4_dzn(A, ix) - type(dualzn), intent(out) :: A - integer(int32), intent(in) :: ix - - A = itodn(ix) - end subroutine iguali4_dzn - !--------------------------------------------------------------------- - - !to initialize a dual number to zero - elemental subroutine initialize_dualzn(zdn) - type(dualzn), intent(out) :: zdn - - allocate(zdn%f(0:order)) !notice, it will be order+1 components - zdn%f=(0.0_prec,0.0_prec) - end subroutine initialize_dualzn - !--------------------------------------------------------------------- - - !to extract the f%(k) part of a dual number or array of duals - elemental function f_part(x,k) result(fr) - type(dualzn), intent(in) :: x - integer, intent(in) :: k - complex(prec) :: fr - - fr = x%f(k) - end function f_part - !--------------------------------------------------------------------- - - !Logical equal operator - elemental function eq_dzn(lhs, rhs) result(fr) - type (dualzn), intent(in) :: lhs, rhs - logical :: fr - logical :: eqfk - integer :: k - - fr = .true. - do k=0,order - eqfk = lhs%f(k) == rhs%f(k) - if(.not. eqfk) then - fr = .false. - exit - end if - end do - end function eq_dzn - !--------------------------------------------------------------------- - !Logical not equal operator - elemental function noteq_dzn(lhs, rhs) result(f_res) - type (dualzn), intent(in) :: lhs, rhs - logical :: f_res - - f_res = .not.(lhs == rhs) - end function noteq_dzn - !--------------------------------------------------------------------- - - ! Converts a value (integer, real, complex, dualzn) `X` to a dualzn - ! number. - elemental function xto_dzn(X) result(fr) - class(*), intent(in) :: X - type(dualzn) :: fr - - call initialize_dualzn(fr) - - select type (X) - type is (dualzn) - fr = X - return - type is (complex(kind=real128)) - fr%f(0) = cmplx(X, kind=prec) - type is (complex(kind=real64)) - fr%f(0) = cmplx(X, kind=prec) - type is (complex(kind=real32)) - fr%f(0) = cmplx(X, kind=prec) - type is (real(kind=real128)) - fr%f(0) = cmplx(X, 0.0_prec, kind=prec) - type is (real(kind=real64)) - fr%f(0) = cmplx(X, 0.0_prec, kind=prec) - type is (real(kind=real32)) - fr%f(0) = cmplx(X, 0.0_prec, kind=prec) - type is (integer(kind=int64)) - fr%f(0) = cmplx(X, 0.0_prec, kind=prec) - type is (integer(kind=int32)) - fr%f(0) = cmplx(X, 0.0_prec, kind=prec) - class default - continue - end select - end function xto_dzn - - !the beolow functions are private, use xto_dzn instead - elemental function c16todn(x) result(fr) - complex(real128), intent(in) :: x - type(dualzn) :: fr - - call initialize_dualzn(fr) - fr%f(0)=cmplx(x,kind=prec) - end function c16todn - - elemental function c8todn(x) result(fr) - complex(real64), intent(in) :: x - type(dualzn) :: fr - - call initialize_dualzn(fr) - fr%f(0)=cmplx(x,kind=prec) - end function c8todn - - elemental function c4todn(x) result(fr) - complex(real32), intent(in) :: x - type(dualzn) :: fr - - call initialize_dualzn(fr) - fr%f(0)=cmplx(x,kind=prec) - end function c4todn - !--------------------------------------------------------------------- - - elemental function r16todn(x) result(fr) - real(real128), intent(in) :: x - type(dualzn) :: fr - - call initialize_dualzn(fr) - fr%f(0)=real(x,kind=prec) - end function r16todn - - elemental function r8todn(x) result(fr) - real(real64), intent(in) :: x - type(dualzn) :: fr - - call initialize_dualzn(fr) - fr%f(0)=real(x,kind=prec) - end function r8todn - - elemental function r4todn(x) result(fr) - real(real32), intent(in) :: x - type(dualzn) :: fr - - call initialize_dualzn(fr) - fr%f(0)=real(x,kind=prec) - end function r4todn - !--------------------------------------------------------------------- - - elemental function i4todn(ix) result(fr) - integer(int32), intent(in) :: ix - type(dualzn) :: fr - - call initialize_dualzn(fr) - fr%f(0)=real(ix,kind=prec) - end function i4todn - - elemental function i8todn(ix) result(fr) - integer(int64), intent(in) :: ix - type(dualzn) :: fr - - call initialize_dualzn(fr) - fr%f(0)=real(ix,kind=prec) - end function i8todn - !--------------------------------------------------------------------- - - !dual + class - elemental function sumadX(B,X) result(fr) - class(*), intent(in) :: X - type(dualzn), intent(in) :: B - type(dualzn) :: fr - type(dualzn) :: Xd - - select type (X) - type is (dualzn) - Xd = X - type is(complex(kind=real128)) - Xd = cmplxtodn(X) - type is (complex(kind=real64)) - Xd =cmplxtodn(X) - type is (complex(kind=real32)) - Xd =cmplxtodn(X) - type is (real(kind=real128)) - Xd = realtodn(X) - type is (real(kind=real64)) - Xd = realtodn(X) - type is (real(kind=real32)) - Xd = realtodn(X) - type is (integer(kind=int64)) - Xd = itodn(X) - type is (integer(kind=int32)) - Xd = itodn(X) - end select - fr = sumad(B,Xd) - end function sumadX - !--------------------------------------------------------------------- - - !class + dual - elemental function sumaXd(XX,BB) result(fr) - class(*), intent(in) :: XX - type(dualzn), intent(in) :: BB - type(dualzn) :: fr - type(dualzn) :: Xd - - select type (XX) - type is (dualzn) - Xd = XX - type is(complex(kind=real128)) - Xd = cmplxtodn(XX) - type is (complex(kind=real64)) - Xd =cmplxtodn(XX) - type is (complex(kind=real32)) - Xd =cmplxtodn(XX) - type is (real(kind=real128)) - Xd = realtodn(XX) - type is (real(kind=real64)) - Xd = realtodn(XX) - type is (real(kind=real32)) - Xd = realtodn(XX) - type is (integer(kind=int64)) - Xd = itodn(XX) - type is (integer(kind=int32)) - Xd = itodn(XX) - end select - fr = sumad(Xd, BB) - end function sumaXd - !--------------------------------------------------------------------- - - !A+B - elemental function sumad(A,B) result(fr) - type(dualzn), intent(in) :: A,B - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - do k=0,order - fr%f(k) = A%f(k) + B%f(k) - end do - end function sumad - !--------------------------------------------------------------------- - - !+dualzn (unary) - elemental function masd(A) result(fr) - type(dualzn), intent(in) :: A - type(dualzn) :: fr - - fr = A - end function masd - !--------------------------------------------------------------------- - - !dual - class - elemental function restadX(B,X) result(fr) - class(*), intent(in) :: X - type(dualzn), intent(in) :: B - type(dualzn) :: fr - type(dualzn) :: Xd - - select type (X) - type is (dualzn) - Xd = X - type is(complex(kind=real128)) - Xd = cmplxtodn(X) - type is (complex(kind=real64)) - Xd =cmplxtodn(X) - type is (complex(kind=real32)) - Xd =cmplxtodn(X) - type is (real(kind=real128)) - Xd = realtodn(X) - type is (real(kind=real64)) - Xd = realtodn(X) - type is (real(kind=real32)) - Xd = realtodn(X) - type is (integer(kind=int64)) - Xd = itodn(X) - type is (integer(kind=int32)) - Xd = itodn(X) - end select - fr = restad(B,Xd) - end function restadX - !--------------------------------------------------------------------- - - !class - dual - elemental function restaXd(XX,BB) result(fr) - class(*), intent(in) :: XX - type(dualzn), intent(in) :: BB - type(dualzn) :: fr - type(dualzn) :: Xd - - select type (XX) - type is (dualzn) - Xd = XX - type is(complex(kind=real128)) - Xd = cmplxtodn(XX) - type is (complex(kind=real64)) - Xd =cmplxtodn(XX) - type is (complex(kind=real32)) - Xd =cmplxtodn(XX) - type is (real(kind=real128)) - Xd = realtodn(XX) - type is (real(kind=real64)) - Xd = realtodn(XX) - type is (real(kind=real32)) - Xd = realtodn(XX) - type is (integer(kind=int64)) - Xd = itodn(XX) - type is (integer(kind=int32)) - Xd = itodn(XX) - end select - fr = restad(Xd, BB) - end function restaXd - !--------------------------------------------------------------------- - - !-dualzn (unary) - elemental function menosd(A) result(fr) - type(dualzn), intent(in) :: A - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - do k=0,order - fr%f(k) = -A%f(k) - end do - end function menosd - - !A-B - elemental function restad(A,B) result(fr) - type(dualzn), intent(in) :: A,B - type(dualzn) :: fr - - fr = -B+A - end function restad - !--------------------------------------------------------------------- - - !dual**class - elemental function powerdX(B, X) result(fr) - class(*), intent(in) :: X - type(dualzn), intent(in) :: B - type(dualzn) :: fr - - select type (X) - type is (dualzn) - fr = powerd(B, X) - type is (integer(kind=int64)) - fr = power_dint8(B, X) - type is (integer(kind=int32)) - fr = power_dint(B, X) - class default - fr = powerd(B, xto_dzn(X)) - end select - end function powerdX - !--------------------------------------------------------------------- - - !class**dual (X**B) - elemental function powerXd(XX,BB) result(fr) - class(*), intent(in) :: XX - type(dualzn), intent(in) :: BB - type(dualzn) :: fr - - select type (XX) - type is (dualzn) - fr = powerd(XX, BB) - class default - fr = powerd(xto_dzn(XX),BB) - end select - end function powerXd -!--------------------------------------------------------------------- - - function MtimesdX(A,X) result(fr) - type(dualzn), intent(in), dimension(:,:) :: A - class(*), intent(in), dimension(:,:) :: X - type(dualzn), dimension(size(A,1),size(X,2)) :: fr - type(dualzn), dimension(size(X,1),size(X,2)) :: Xd - - select type (X) - type is (dualzn) - Xd = X - type is(complex(kind=real128)) - Xd = X - type is(complex(kind=real64)) - Xd = X - type is(complex(kind=real32)) - Xd = X - type is(real(kind=real128)) - Xd = X - type is(real(kind=real64)) - Xd = X - type is(real(kind=real32)) - Xd = X - type is(integer(kind=int64)) - Xd = X - type is(integer(kind=int32)) - Xd = X - end select - fr = Mtimesd(A,Xd) - !fr = Mtimesd_LbnzRule(A,Xd) - end function MtimesdX - !--------------------------------------------------------------------- - - !cmplx*dual - function Mtimesc128d(X,B) result(fr) - complex(real128), intent(in), dimension(:,:) :: X - type(dualzn), intent(in), dimension(:,:) :: B - type(dualzn), dimension(size(X,1),size(B,2)) :: fr - type(dualzn), dimension(size(X,1),size(X,2)) :: Xd - - Xd = X - - fr = Mtimesd(Xd,B) - !fr = Mtimesd_LbnzRule(Xd,B) - end function Mtimesc128d - - - function Mtimesc64d(X,B) result(fr) - complex(real64), intent(in), dimension(:,:) :: X - type(dualzn), intent(in), dimension(:,:) :: B - type(dualzn), dimension(size(X,1),size(B,2)) :: fr - type(dualzn), dimension(size(X,1),size(X,2)) :: Xd - - Xd = X - - fr = Mtimesd(Xd,B) - !fr = Mtimesd_LbnzRule(Xd,B) - end function Mtimesc64d - - function Mtimesc32d(X,B) result(fr) - complex(real32), intent(in), dimension(:,:) :: X - type(dualzn), intent(in), dimension(:,:) :: B - type(dualzn), dimension(size(X,1),size(B,2)) :: fr - type(dualzn), dimension(size(X,1),size(X,2)) :: Xd - - Xd = X - - fr = Mtimesd(Xd,B) - !fr = Mtimesd_LbnzRule(Xd,B) - end function Mtimesc32d - !--------------------------------------------------------------------- - - !real*dual - function Mtimesr128d(X,B) result(fr) - real(real128), intent(in), dimension(:,:) :: X - type(dualzn), intent(in), dimension(:,:) :: B - type(dualzn), dimension(size(X,1),size(B,2)) :: fr - type(dualzn), dimension(size(X,1),size(X,2)) :: Xd - - Xd = X - - fr = Mtimesd(Xd,B) - !fr = Mtimesd_LbnzRule(Xd,B) - end function Mtimesr128d - - function Mtimesr64d(X,B) result(fr) - real(real64), intent(in), dimension(:,:) :: X - type(dualzn), intent(in), dimension(:,:) :: B - type(dualzn), dimension(size(X,1),size(B,2)) :: fr - type(dualzn), dimension(size(X,1),size(X,2)) :: Xd - - Xd = X - - fr = Mtimesd(Xd,B) - !fr = Mtimesd_LbnzRule(Xd,B) - end function Mtimesr64d - - function Mtimesr32d(X,B) result(fr) - real(real32), intent(in), dimension(:,:) :: X - type(dualzn), intent(in), dimension(:,:) :: B - type(dualzn), dimension(size(X,1),size(B,2)) :: fr - type(dualzn), dimension(size(X,1),size(X,2)) :: Xd - - Xd = X - - fr = Mtimesd(Xd,B) - !fr = Mtimesd_LbnzRule(Xd,B) - end function Mtimesr32d - !--------------------------------------------------------------------- - - function Mtimesi64d(X,B) result(fr) - integer(real64), intent(in), dimension(:,:) :: X - type(dualzn), intent(in), dimension(:,:) :: B - type(dualzn), dimension(size(X,1),size(B,2)) :: fr - type(dualzn), dimension(size(X,1),size(X,2)) :: Xd - - Xd = X - - fr = Mtimesd(Xd,B) - !fr = Mtimesd_LbnzRule(Xd,B) - end function Mtimesi64d - - function Mtimesi32d(X,B) result(fr) - integer(real32), intent(in), dimension(:,:) :: X - type(dualzn), intent(in), dimension(:,:) :: B - type(dualzn), dimension(size(X,1),size(B,2)) :: fr - type(dualzn), dimension(size(X,1),size(X,2)) :: Xd - - Xd = X - - fr = Mtimesd(Xd,B) - !fr = Mtimesd_LbnzRule(Xd,B) - end function Mtimesi32d - !--------------------------------------------------------------------- - - !direct implementation of dual matrix multiplication - function Mtimesd(A,B) result(fr) - type(dualzn), intent(in), dimension(:,:) :: A, B - type(dualzn), dimension(size(A,1),size(B,2)) :: fr - integer :: i, j, k, m, n, p, q - - m = size(A,1) - n = size(A,2) - p = size(B,1) - q = size(B,2) - - if (n /= p) then - print*,"Error: Matrix dimensions do not align for multiplication" - return - end if - - call initialize_dualzn(fr) - - do i = 1, m - do j = 1, q - do k = 1, n - fr(i,j) = fr(i,j) + A(i,k)*B(k,j) - end do - end do - end do - end function Mtimesd - !................... - - - !to set the dual-k component to cm in matrix A - subroutine Mset_fpart(k,cm,A) - integer, intent(in) :: k - complex(prec),intent(in), dimension(:,:) :: cm - type(dualzn), intent(inout), dimension(size(cm,1),size(cm,1)) :: A - integer :: i,j - - do i=1,size(cm,1) - do j=1,size(cm,2) - A(i,j)%f(k) = cm(i,j) - end do - end do - end subroutine Mset_fpart - !--------------------------------------------------------------------- - - !A**B - elemental function powerd(A,B) result(fr) - type(dualzn), intent(in) :: A, B - type(dualzn) :: fr - type(dualzn) :: intdual - integer :: iaux - logical :: BIQ - - iaux = int(real(B%f(0))) - intdual = itodn(iaux) - - BIQ = intdual == B - - if(BIQ) then - fr = A**iaux - else - fr = expd(B*logd(A)) - end if - end function powerd - - !A**n (n integer) - elemental function power_dint(A,n) result(fr) - type(dualzn), intent(in) :: A - integer, intent(in) :: n - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - fr%f=(0.0_prec,0.0_prec) - - if(A==itodn(1)) then - fr=A - return - elseif(A==itodn(0) .and. n>0)then - fr=A - return - end if - - !0**0 ---> 1 - if(n==0) then - fr%f(0) = (1.0_prec,0.0_prec) - elseif(n>=1) then - fr%f(0) = (1.0_prec,0.0_prec) - do k=1,n - fr = fr*A - end do - elseif(n<0) then - fr%f(0) = (1.0_prec,0.0_prec) - do k=1,-n - fr = fr*A - end do - fr = inv(fr) - end if - end function power_dint - !--------------------------------------------------------------------- - - !A**n (n integer) - elemental function power_dint8(A,n) result(fr) - type(dualzn), intent(in) :: A - integer(int64), intent(in) :: n - type(dualzn) :: fr - integer(int64) :: k - - allocate(fr%f(0:order)) - fr%f=(0.0_prec,0.0_prec) - - if(A==itodn(1)) then - fr=A - return - elseif(A==itodn(0) .and. n>0)then - fr=A - return - end if - - !0**0 ---> 1 - if(n==0) then - fr%f(0) = (1.0_prec,0.0_prec) - elseif(n>=1) then - fr%f(0) = (1.0_prec,0.0_prec) - do k=1,n - fr = fr*A - end do - elseif(n<0) then - fr%f(0) = (1.0_prec,0.0_prec) - do k=1,-n - fr = fr*A - end do - fr = inv(fr) - end if - end function power_dint8 - !--------------------------------------------------------------------- - - - !chain rule, D^n (f(g)) - recursive pure function Dnd(fc,gdual,n) result(dnfc) - procedure(funzdual) :: fc - type(dualzn), intent(in) :: gdual - integer, intent(in) :: n - complex(prec) :: dnfc - type(dualzn) :: fvd - complex(prec) :: g0, suma - complex(prec), allocatable, dimension(:) :: xvg - integer :: k, j - - g0 = gdual%f(0) - fvd = fc(g0) - if(n==0) then - dnfc = fvd%f(0) - else - suma = 0 - do k=1,n - allocate(xvg(1:n-k+1)) - do j=1,n-k+1 - xvg(j) = gdual%f(j) - end do - suma = suma + fvd%f(k)*BellY(n,k,xvg) - deallocate(xvg) - end do - dnfc = suma - end if - end function Dnd - !--------------------------------------------------------------------- - - !dual/class - elemental function divdX(B,X) result(fr) - class(*), intent(in) :: X - type(dualzn), intent(in) :: B - type(dualzn) :: fr - type(dualzn) :: Xd - - select type (X) - type is (dualzn) - Xd = X - type is(complex(kind=real128)) - Xd = cmplxtodn(X) - type is (complex(kind=real64)) - Xd =cmplxtodn(X) - type is (complex(kind=real32)) - Xd =cmplxtodn(X) - type is (real(kind=real128)) - Xd = realtodn(X) - type is (real(kind=real64)) - Xd = realtodn(X) - type is (real(kind=real32)) - Xd = realtodn(X) - type is (integer(kind=int64)) - Xd = itodn(X) - type is (integer(kind=int32)) - Xd = itodn(X) - end select - fr = divd(B,Xd) - end function divdX - !--------------------------------------------------------------------- - - !class/dual - elemental function divXd(XX,BB) result(fr) - class(*), intent(in) :: XX - type(dualzn), intent(in) :: BB - type(dualzn) :: fr - type(dualzn) :: Xd - - select type (XX) - type is (dualzn) - Xd = XX - type is(complex(kind=real128)) - Xd = cmplxtodn(XX) - type is (complex(kind=real64)) - Xd =cmplxtodn(XX) - type is (complex(kind=real32)) - Xd =cmplxtodn(XX) - type is (real(kind=real128)) - Xd = realtodn(XX) - type is (real(kind=real64)) - Xd = realtodn(XX) - type is (real(kind=real32)) - Xd = realtodn(XX) - type is (integer(kind=int64)) - Xd = itodn(XX) - type is (integer(kind=int32)) - Xd = itodn(XX) - end select - fr = divd(Xd, BB) - end function divXd - !--------------------------------------------------------------------- - - !A/B - elemental function divd(A,B) result(fr) - type(dualzn), intent(in) :: A, B - type(dualzn) :: fr - - fr = A*inv(B) - end function divd - !--------------------------------------------------------------------- - - !dual*class - elemental function timesdX(B,X) result(fr) - class(*), intent(in) :: X - type(dualzn), intent(in) :: B - type(dualzn) :: fr - type(dualzn) :: Xd - - select type (X) - type is (dualzn) - Xd = X - type is(complex(kind=real128)) - Xd = cmplxtodn(X) - type is (complex(kind=real64)) - Xd =cmplxtodn(X) - type is (complex(kind=real32)) - Xd =cmplxtodn(X) - type is (real(kind=real128)) - Xd = realtodn(X) - type is (real(kind=real64)) - Xd = realtodn(X) - type is (real(kind=real32)) - Xd = realtodn(X) - type is (integer(kind=int64)) - Xd = itodn(X) - type is (integer(kind=int32)) - Xd = itodn(X) - end select - fr = timesd(B,Xd) - end function timesdX - !--------------------------------------------------------------------- - - !class*dual - elemental function timesXd(XX,BB) result(fr) - class(*), intent(in) :: XX - type(dualzn), intent(in) :: BB - type(dualzn) :: fr - type(dualzn) :: Xd - - select type (XX) - type is (dualzn) - Xd = XX - type is(complex(kind=real128)) - Xd = cmplxtodn(XX) - type is (complex(kind=real64)) - Xd =cmplxtodn(XX) - type is (complex(kind=real32)) - Xd =cmplxtodn(XX) - type is (real(kind=real128)) - Xd = realtodn(XX) - type is (real(kind=real64)) - Xd = realtodn(XX) - type is (real(kind=real32)) - Xd = realtodn(XX) - type is (integer(kind=int64)) - Xd = itodn(XX) - type is (integer(kind=int32)) - Xd = itodn(XX) - end select - fr = timesd(Xd, BB) - end function timesXd - !--------------------------------------------------------------------- - - !A*B - elemental function timesd(A,B) result(fr) - type(dualzn), intent(in) :: A, B - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - do k=0,order - fr%f(k)=timesdzn(A,B,k) - end do - end function timesd - - pure function timesdzn(A,B,k) result(fr) - type(dualzn), intent(in) :: A, B - integer, intent(in) :: k - complex(prec) :: fr - integer :: i - - fr=0.0_prec - do i=0,k - fr=fr+binomial(k,i)*A%f(i)*B%f(k-i) - end do - end function timesdzn - !--------------------------------------------------------------------- - - !inverse function - elemental function inv(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = Dnd(invzdn,g,k) - end do - end function inv - - pure function invzdn(z) result(fr) - complex(prec), intent(in) :: z - type(dualzn) :: fr - integer :: k,signo - - allocate(fr%f(0:order)) - - signo=1 - do k=0,order - fr%f(k)=signo*gamma(real(k+1,kind=prec))/(z**(k+1)) - signo=-signo - end do - end function invzdn - !--------------------------------------------------------------------- - - !acos function - elemental function acosd_(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = Dnd(acoszdn,g,k) - end do - end function acosd_ - - pure function acoszdn(z) result(fr) - complex(prec), intent(in) :: z - type(dualzn) :: fr - integer :: k, i - complex(prec) :: sumterm, sqz - type(dualzn) :: sqzdn, zdn - - allocate(fr%f(0:order)) - fr%f(0) = acos(z) - if (order == 0) return - - fr%f(1) = -1.0_prec/sqrt(1.0_prec - z**2) - if (order == 1) return - - call initialize_dualzn(zdn) - zdn%f(0) = z - zdn%f(1) = 1.0_prec - - sqz = sqrt(1.0_prec-z*z) - sqzdn = sqrt(realtodn(1.0_prec) - zdn*zdn) - do k=2,order - sumterm = 0.0_prec - do i=1,k-1 - sumterm = sumterm + binomial(k-1,i)*sqzdn%f(i)*fr%f(k-i)/sqz - end do - fr%f(k) = -sumterm - end do - end function acoszdn - !--------------------------------------------------------------------- - - !asin function - elemental function asind_(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = Dnd(asinzdn,g,k) - end do - end function asind_ - - pure function asinzdn(z) result(fr) - complex(prec), intent(in) :: z - type(dualzn) :: fr - integer :: k, i - complex(prec) :: sumterm, sqz - type(dualzn) :: sqzdn, zdn - - allocate(fr%f(0:order)) - fr%f(0) = asin(z) - if (order == 0) return - - fr%f(1) = 1.0_prec/sqrt(1.0_prec - z**2) - if (order == 1) return - - call initialize_dualzn(zdn) - zdn%f(0) = z - zdn%f(1) = 1.0_prec - - sqz = sqrt(1.0_prec-z*z) - sqzdn = sqrt(realtodn(1.0_prec) - zdn*zdn) - do k=2,order - sumterm = 0.0_prec - do i=1,k-1 - sumterm = sumterm + binomial(k-1,i)*sqzdn%f(i)*fr%f(k-i)/sqz - end do - fr%f(k) = -sumterm - end do - end function asinzdn - !--------------------------------------------------------------------- - - !atan function - elemental function atand_(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = Dnd(atanzdn,g,k) - end do - end function atand_ - - pure function atanzdn(z) result(fr) - complex(prec), intent(in) :: z - type(dualzn) :: fr - integer :: k, i - complex(prec) :: sumterm, den - type(dualzn) :: auxdn - - allocate(fr%f(0:order)) - fr%f(0) = atan(z) - - if (order == 0) return - - fr%f(1) = 1.0_prec/(1.0_prec + z**2) - if (order == 1) return - - den = 1.0_prec + z*z - - call initialize_dualzn(auxdn) - auxdn%f(0) = den - auxdn%f(1) = 2.0_prec * z - auxdn%f(2) = 2.0_prec - - do k=2,order - sumterm = 0.0_prec - do i=1,k-1 - sumterm = sumterm + binomial(k-1,i)*auxdn%f(i)*fr%f(k-i)/den - end do - fr%f(k) = -sumterm - end do - end function atanzdn - !--------------------------------------------------------------------- - - !asinh function - elemental function asinhd(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = Dnd(asinhzdn,g,k) - end do - end function asinhd - - pure function asinhzdn(z) result(fr) - complex(prec), intent(in) :: z - type(dualzn) :: fr - integer :: k, i - complex(prec) :: sumterm, den - type(dualzn) :: auxdn, zdn - - allocate(fr%f(0:order)) - fr%f(0) = asinh(z) - if (order == 0) return - - fr%f(1) = 1.0_prec/sqrt(1.0_prec + z**2) - if (order == 1) return - - den = sqrt(1.0_prec + z*z) - - call initialize_dualzn(zdn) - zdn%f(0) = z - zdn%f(1) = 1.0_prec - - auxdn = sqrt(realtodn(1.0_prec) + zdn*zdn) - - do k=2,order - sumterm = 0.0_prec - do i=1,k-1 - sumterm = sumterm + binomial(k-1,i)*auxdn%f(i)*fr%f(k-i)/den - end do - fr%f(k) = -sumterm - end do - end function asinhzdn - !--------------------------------------------------------------------- - - !acosh function - elemental function acoshd(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = Dnd(acoshzdn,g,k) - end do - end function acoshd - - pure function acoshzdn(z) result(fr) - complex(prec), intent(in) :: z - type(dualzn) :: fr - integer :: k, i - complex(prec) :: sumterm, den - type(dualzn) :: auxdn, zdn, onedn - - allocate(fr%f(0:order)) - fr%f(0) = acosh(z) - if (order == 0) return - - !do not 'simplify' they are complex - den = sqrt(z - 1.0_prec) * sqrt(1.0_prec + z) - fr%f(1) = 1.0_prec/den - if (order == 1) return - - call initialize_dualzn(zdn) - zdn%f(0) = z - zdn%f(1) = 1.0_prec - - onedn = realtodn(1.0_prec) - auxdn = sqrt(zdn - onedn) * sqrt(zdn + onedn) - do k=2,order - sumterm = 0.0_prec - do i=1,k-1 - sumterm = sumterm + binomial(k-1,i)*auxdn%f(i)*fr%f(k-i)/den - end do - fr%f(k) = -sumterm - end do - end function acoshzdn - !--------------------------------------------------------------------- - - !atanh function - elemental function atanhd(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = Dnd(atanhzdn,g,k) - end do - end function atanhd - - pure function atanhzdn(z) result(fr) - complex(prec), intent(in) :: z - type(dualzn) :: fr - integer :: k, i - complex(prec) :: sumterm, den - type(dualzn) :: auxdn - - allocate(fr%f(0:order)) - fr%f(0) = atanh(z) - - if (order == 0) return - - !do not 'simplify' they are complex - den = 1.0_prec - z*z - fr%f(1) = 1.0_prec/den - if (order == 1) return - - call initialize_dualzn(auxdn) - auxdn%f(0) = den - auxdn%f(1) = -2.0_prec * z - auxdn%f(2) = -2.0_prec - - do k=2,order - sumterm = 0.0_prec - do i=1,k-1 - sumterm = sumterm + binomial(k-1,i)*auxdn%f(i)*fr%f(k-i)/den - end do - fr%f(k) = -sumterm - end do - end function atanhzdn - !--------------------------------------------------------------------- - - !atan2d function - elemental function atan2d_(y,x) result(fr) - type(dualzn), intent(in) :: y, x - type(dualzn) :: fr - complex(prec) :: x0, y0 - - fr = atan(y/x) - x0 = x%f(0) - y0 = y%f(0) - fr%f(0) = atan2_z(y0,x0) - end function atan2d_ - - !Atan2 for complex arguments - elemental function atan2_z(zy,zx) result (f_res) - complex(prec), intent(in) :: zy, zx - complex(prec) :: f_res - complex(prec), parameter :: ii = cmplx(0,1,prec) - complex(prec) :: num, den, divnd, t1, t2 - real(prec) :: x1, x2, y1, y2 - complex(prec) :: x1c, x2c, y1c, y2c - - x1 = real(zx,kind=prec) - x2 = aimag(zx) - - y1 = real(zy,kind=prec) - y2 = aimag(zy) - - x1c = x1 - x2c = x2 - y1c = y1 - y2c = y2 - - num = x1c + ii*x2c + ii*(y1c + ii*y2c) - den = sqrt((x1c + ii*x2c)**2 + (y1c + ii*y2c)**2) - divnd = num/den; - t1 = atan2(aimag(divnd),real(divnd,kind=prec)) - t2 = ii*log(sqrt((x2c + y1c)**2 + (x1c - y2c)**2)/((2.0_prec*x1c*& - x2c + 2.0_prec*y1c*y2c)**2 + (x1c**2 - x2c**2 + y1c**2 - & - y2c**2)**2)**0.25_prec) - - f_res = t1 - t2 - end function atan2_z - !--------------------------------------------------------------------- - - !sinh function - elemental function sinhd(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - fr = (exp(g)-exp(-g)) - do k=0,order - fr%f(k) = 0.5_prec*fr%f(k) - end do - end function sinhd - !--------------------------------------------------------------------- - - !cosh function - elemental function coshd(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - fr = (exp(g)+exp(-g)) - do k=0,order - fr%f(k) = 0.5_prec*fr%f(k) - end do - end function coshd - !--------------------------------------------------------------------- - - !tanh function - elemental function tanhd(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - - fr = (exp(g) - exp(-g))/(exp(g) + exp(-g)) - end function tanhd - !--------------------------------------------------------------------- - - !absx = sqrt(z*z) is not sqrt(z*conjg(z)) - elemental function absx(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - complex(prec) :: g0 - integer :: k - - g0 = g%f(0) - - fr = g - do k=0,order - fr%f(k) = g%f(k) * g0/sqrt(g0*g0) - end do - end function absx - !--------------------------------------------------------------------- - - !conjg - !notice tat the conjugation operation is not differentiable. In the - !below definitions we mean (df)* not d(f*) - elemental function conjg_dzn(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - call initialize_dualzn(fr) - do k=0, order - fr%f(k) = conjg(g%f(k)) - end do - end function conjg_dzn - !-------------------------------------------------------------------- - - !sum(AR2,dir) for rank2 arrays - !the result is given as array of rank 1 - function sumR2dzn(AR2,dir) result(fr) - type(dualzn), intent(in), dimension(:,:) :: AR2 - integer, intent(in) :: dir - type(dualzn), dimension(size(AR2,2/dir)) :: fr - complex(prec), dimension(size(AR2,2/dir)) :: sAk - complex(prec), dimension(size(AR2,1),size(AR2,2)) :: Ak - integer :: k,j, dimfr - - call initialize_dualzn(fr) - dimfr = size(AR2,2/dir) - - do k=0,order - Ak = f_part(AR2,k) - sAk = sum(Ak,dir) - do j=1,dimfr - fr(j)%f(k) = sAk(j) - end do - end do - end function sumR2dzn - !--------------------------------------------------------------------- - - !sum for Rank 2 array - function sumR20dzn(AR2) result(fr) - type(dualzn), intent(in), dimension(:,:) :: AR2 - type(dualzn) :: fr - complex(prec), dimension(size(AR2,1),size(AR2,2)) :: Azaux - integer :: k - - call initialize_dualzn(fr) - do k=0,order - Azaux = f_part(AR2,k) - fr%f(k) = sum(Azaux) - end do - end function sumR20dzn - !--------------------------------------------------------------------- - - !sum for Rank 1 array - function sumR1dzn(AR1) result(fr) - type(dualzn), intent(in), dimension(:) :: AR1 - type(dualzn) :: fr - complex(prec), dimension(size(AR1)) :: Azaux - integer :: k - - call initialize_dualzn(fr) - do k=0,order - Azaux = f_part(AR1,k) - fr%f(k) = sum(Azaux) - end do - end function sumR1dzn - !--------------------------------------------------------------------- - - !product(AR2,dir) for Rank 2 array - function prodR2dzn(AR2,dir) result(fr) - type(dualzn), intent(in), dimension(:,:) :: AR2 - integer, intent(in) :: dir - type(dualzn), dimension(size(AR2,2/dir)) :: fr - type(dualzn), dimension(size(AR2,dir)) :: vkdir - integer :: k - - if(dir==1) then - do k = 1, size(AR2,2) - vkdir = AR2(:,k) - fr(k) = prodR1dzn(vkdir) - end do - else if(dir==2) then - do k = 1, size(AR2,1) - vkdir = AR2(k,:) - fr(k) = prodR1dzn(vkdir) - end do - else - stop 'use 1 (2) to collapse rows (columns) in product function' - end if - end function prodR2dzn - - !product for Rank 2 array - function prodR20dzn(AR2) result(fr) - type(dualzn), intent(in), dimension(:,:) :: AR2 - type(dualzn) :: fr - integer :: k, m - - m=size(AR2,1) - fr = 1.0_prec - do k=1,m - fr = fr*prodR1dzn(AR2(k,:)) - end do - end function prodR20dzn - - !product for Rank 1 array - function prodR1dzn(x) result(fr) - type(dualzn), intent(in), dimension(:) :: x - type(dualzn) :: fr - integer :: k - - fr = 1.0_prec - do k=1,size(x) - fr = fr*x(k) - end do - end function prodR1dzn - !--------------------------------------------------------------------- - - !log function - elemental function logd(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = Dnd(logzdn,g,k) - end do - end function logd - - pure function logzdn(z) result(fr) - complex(prec), intent(in) :: z - type(dualzn) :: fr - integer :: k, signo - - allocate(fr%f(0:order)) - fr%f(0) = log(z) - - signo = 1 - do k=1,order - fr%f(k) = signo*gamma(real(k,kind=prec))/(z**k) - signo = -signo - end do - end function logzdn - !--------------------------------------------------------------------- - - !exp function - elemental function expd(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = Dnd(expzdn,g,k) - end do - end function expd - - pure function expzdn(z) result(fr) - complex(prec), intent(in) :: z - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = exp(z) - end do - end function expzdn - !--------------------------------------------------------------------- - - !sin function - elemental function sind_(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = Dnd(sinzdn,g,k) - end do - end function sind_ - - pure function sinzdn(z) result(fr) - complex(prec), intent(in) :: z - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = sin(z + k*Pi/2) - end do - end function sinzdn - !--------------------------------------------------------------------- - - !cos function - elemental function cosd_(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = Dnd(coszdn,g,k) - end do - end function cosd_ - - pure function coszdn(z) result(fr) - complex(prec), intent(in) :: z - type(dualzn) :: fr - integer :: k - - allocate(fr%f(0:order)) - - do k=0,order - fr%f(k) = cos(z + k*Pi/2) - end do - end function coszdn - !--------------------------------------------------------------------- - - !tan function - elemental function tand_(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - - fr = sind_(g)*inv(cosd_(g)) - end function tand_ - !--------------------------------------------------------------------- - - !sqrt function - elemental function sqrtd(g) result(fr) - type(dualzn), intent(in) :: g - type(dualzn) :: fr - - fr = g**(0.5_prec) - end function sqrtd - !--------------------------------------------------------------------- - - !Combinations - !m!/((m-n)! * n!) - pure function binomial(m, n) result(binom) - integer, intent(in) :: m, n - real(prec) :: binom - integer :: j - - if (n == 0 .or. n == m) then - binom = 1.0 - else - binom = 1.0 - do j = 1, n - binom = binom*(m-j+1)/j - end do - endif - end function binomial - - pure function BellY(n, k, x) result(result_value) - integer, intent(in) :: n, k - complex(prec), dimension(:), intent(in) :: x - complex(prec) :: result_value - complex(prec), dimension(n+1,k+1) :: dp - complex(prec) :: sum_val - complex(prec), dimension(:), allocatable :: newx - integer :: nn, kk, ii, LX, nx - - dp = 0.0 - dp(1, 1) = 1.0 - - do nn = 1, n - dp(nn+1, 1) = 0.0 - end do - - do kk = 1, k - dp(1, kk+1) = 0.0 - end do - - !special cases - if (n == 0 .and. k == 0) then - result_value = 1.0 - return - elseif (size(x) == 0) then - result_value = 0.0 - return - end if - - !Main loop to compute BellY[n, k, x] - do nn = 1, n - do kk = 1, k - LX = size(x) - nx = max(nn - kk + 1, LX) - if (nx > 0) then - allocate(newx(nx)) - newx = 0.0 - newx(1:LX) = x - sum_val = 0.0 - do ii = 0, nn - kk - sum_val = sum_val + binomial(nn - 1, ii) * & - newx(ii + 1)*dp(nn - ii, kk) - end do - dp(nn + 1, kk + 1) = sum_val - deallocate(newx) - end if - end do - end do - - result_value = dp(n + 1, k + 1) - end function BellY -end module dualzn_mod diff --git a/SourcesF_gfortran/ex3.f90 b/SourcesF_gfortran/ex3.f90 deleted file mode 100644 index 36d87d5..0000000 --- a/SourcesF_gfortran/ex3.f90 +++ /dev/null @@ -1,92 +0,0 @@ -include './precision_mod.f90' -include './dualzn_mod.f90' -include './diff_mod.f90' - -!module with example of functions -module function_mod - use dualzn_mod - implicit none - private - - public :: fstest, fvectest - -contains - !Example of scalar function f = sin(x*y*z) + cos(x*y*z) - function fstest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn) :: fr - type(dualzn) :: x,y,z - - x = r(1); y = r(2); z = r(3) - fr = sin(x*y*z) + cos(x*y*z) - end function fstest - - !Example of vector function f = [f1,f2,f3] - !f = fvectest(r) is a function f:D^m ---> Dn - function fvectest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn), allocatable, dimension(:) :: fr - type(dualzn) :: f1,f2,f3 - type(dualzn) :: x,y,z,w - - x = r(1); y = r(2); z = r(3); w = r(4) - - f1 = sin(x*y*z*w) - f2 = cos(x*y*z*w)*sqrt(w/y - x/z) - f3 = sin(log(x*y*z*w)) - - allocate(fr(3)) - fr = [f1,f2,f3] - end function fvectest -end module function_mod - -!----------------------------------------------------------------------- -!main program -program main - use precision_mod - use dualzn_mod - use diff_mod - use function_mod - implicit none - - integer, parameter :: nf =3, mq = 4 - complex(prec), parameter :: ii = (0,1) - complex(prec), dimension(mq) :: q, vec - complex(prec), dimension(nf,mq) :: Jmat - complex(prec), dimension(nf) :: JV - complex(prec), dimension(3) :: GV - complex(prec), dimension(3,3) :: Hmat - integer :: i - - vec = [1.0_prec,2.0_prec,3.0_prec,4.0_prec] - q = vec/10.0_prec + ii - - print*,"Jv using matmul" - Jmat = Jacobian(fvectest, q , nf) - JV = matmul(Jmat,vec) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"Jv using vector directional derivative" - JV = d1fvector(fvectest,vec,q,nf) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"---Hessian matrix---" - Hmat = Hessian(fstest,q(1:3)) - do i=1,3 - write(*,"(A,i0)") "row:",i - write(*,*) Hmat(i,:) - end do - write(*,*) - - print*,"---Gradient---" - GV = gradient(fstest,q(1:3)) - do i=1,3 - write(*,*) GV(i) - end do -end program main diff --git a/SourcesF_gfortran/precision_mod.f90 b/SourcesF_gfortran/precision_mod.f90 deleted file mode 100644 index c7a6948..0000000 --- a/SourcesF_gfortran/precision_mod.f90 +++ /dev/null @@ -1,7 +0,0 @@ -module precision_mod - use iso_fortran_env, only: int32, int64, real32, real64, real128 - implicit none - - integer, parameter :: prec = real64 - !integer, parameter :: prec = real128 -end module precision_mod diff --git a/Windows/gfortranCase/prec_real128/LibDualzn128/diff_mod.mod b/Windows/gfortranCase/prec_real128/LibDualzn128/diff_mod.mod deleted file mode 100644 index 45e332b52a127ed99068926733592971440f01d0..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 3411 zcmV-Z4XpAXiwFP!000003hiCna^koaeb-m$4e~IjEX&tN2b@0C5TFcXCg+8s13Ar9 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zqxr#o<7iW8=OC8R00gTb@Cy*EfWQqByPl*=!Kfp+#xw|?$9?bKn^DGuz8Lv#p}D%G zzP$`pv@=5)1rv#iTvBw00B-1Se=zL(t{=5V&YO3i*Wt(U!>u~ED`j9^V$@?bbNRQ9 zK1qg4(>h3Gxma=CevmY+cQZ%cp [output_executable_name] - exit /b 1 -) - -:: Use the provided source file and output executable name or default to "a.exe" -set "SOURCE_FILE=%~1" -set "OUTPUT_NAME=%~2" - -if "%OUTPUT_NAME%"=="" ( - set "OUTPUT_NAME=a.exe" -) - -:: Run the compilation command -gfortran -I../LibDualzn128 -o "%OUTPUT_NAME%" "%SOURCE_FILE%" -L../LibDualzn128 -ldualzn - - diff --git a/Windows/gfortranCase/prec_real128/examples/ex1.f90 b/Windows/gfortranCase/prec_real128/examples/ex1.f90 deleted file mode 100644 index 7d9f062..0000000 --- a/Windows/gfortranCase/prec_real128/examples/ex1.f90 +++ /dev/null @@ -1,35 +0,0 @@ -!gfortran -I../LibDualzn128 -o e1 ex1.f90 -L../LibDualzn128 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - - call set_order(5) !before anything we set the 'order' to work with - - z0 = (1.1_prec,2.2_prec) - r = 0 !we initialize the dual number to 0 - - !we set the 0-th and 1-th components. If dual numbers are used to - !calculate D^n f(z0) then r must be of the form r = r0 + 1*eps_1 - r%f(0) = z0 - r%f(1) = 1 - - fval = sin(r)**log(r*r) - - !writing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - print*,fval%f(k) - end do - deallocate(r%f) - deallocate(fval%f) -end program main - - - - diff --git a/Windows/gfortranCase/prec_real128/examples/ex2.f90 b/Windows/gfortranCase/prec_real128/examples/ex2.f90 deleted file mode 100644 index 2cc3abe..0000000 --- a/Windows/gfortranCase/prec_real128/examples/ex2.f90 +++ /dev/null @@ -1,52 +0,0 @@ -!gfortran -I../LibDualzn128 -o e2 ex2.f90 -L../LibDualzn128 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - real :: t1,t2 - - call set_order(5) !we set the order to work with - - !since a dualzn numbers is an allocatable entity, do not forget to - !initialize it - r = 0 !<--- initializing r to 0 - r%f(0) = (1.1_prec,0.0_prec) - r%f(1) = 1 !since we want to differentiate, r = r0 +1*eps_1 - !all the other components are 0 as r was initialized to 0 - - call cpu_time(t1) - fval = ftest(r) - call cpu_time(t2) - - !Computing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - write(*,"(i0,a,f0.1,a,e17.10)") k,"-th derivative at x = ", & - real(r%f(0)),":",real(fval%f(k)) - end do - - print*,"elapsed time (s):",t2-t1 - deallocate(r%f) - deallocate(fval%f) - -contains - function ftest(x) result(fr) - type(dualzn), intent(in) :: x - type(dualzn) :: fr - integer :: k - - !nested function f(x) = sin(x) * exp(-x^2), f(f(...(f(x))...)) - !applied 1000 times - fr = sin(x)*exp(-x*x) - do k=1, 1000-1 - fr = sin(fr)*exp(-fr*fr) - end do - end function ftest -end program main - - diff --git a/Windows/gfortranCase/prec_real128/examples/ex3.f90 b/Windows/gfortranCase/prec_real128/examples/ex3.f90 deleted file mode 100644 index 041011e..0000000 --- a/Windows/gfortranCase/prec_real128/examples/ex3.f90 +++ /dev/null @@ -1,90 +0,0 @@ -!gfortran -I../LibDualzn128 -o ExDO ex3.f90 -L../LibDualzn128 -ldualzn - -!module with example of functions -module function_mod - use dualzn_mod - implicit none - private - - public :: fstest, fvectest - -contains - !Example of scalar function f = sin(x*y*z) + cos(x*y*z) - function fstest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn) :: fr - type(dualzn) :: x,y,z - - x = r(1); y = r(2); z = r(3) - fr = sin(x*y*z) + cos(x*y*z) - end function fstest - - !Example of vector function f = [f1,f2,f3] - !f = fvectest(r) is a function f:D^m ---> Dn - function fvectest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn), allocatable, dimension(:) :: fr - type(dualzn) :: f1,f2,f3 - type(dualzn) :: x,y,z,w - - x = r(1); y = r(2); z = r(3); w = r(4) - - f1 = sin(x*y*z*w) - f2 = cos(x*y*z*w)*sqrt(w/y - x/z) - f3 = sin(log(x*y*z*w)) - - allocate(fr(3)) - fr = [f1,f2,f3] - end function fvectest -end module function_mod - -!----------------------------------------------------------------------- -!main program -program main - use precision_mod - use dualzn_mod - use diff_mod - use function_mod - implicit none - - integer, parameter :: nf =3, mq = 4 - complex(prec), parameter :: ii = (0,1) - complex(prec), dimension(mq) :: q, vec - complex(prec), dimension(nf,mq) :: Jmat - complex(prec), dimension(nf) :: JV - complex(prec), dimension(3) :: GV - complex(prec), dimension(3,3) :: Hmat - integer :: i - - vec = [1.0_prec,2.0_prec,3.0_prec,4.0_prec] - q = vec/10.0_prec + ii - - print*,"Jv using matmul" - Jmat = Jacobian(fvectest, q , nf) - JV = matmul(Jmat,vec) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"Jv using vector directional derivative" - JV = d1fvector(fvectest,vec,q,nf) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"---Hessian matrix---" - Hmat = 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[output_executable_name] - exit /b 1 -) - -:: Use the provided source file and output executable name or default to "a.exe" -set "SOURCE_FILE=%~1" -set "OUTPUT_NAME=%~2" - -if "%OUTPUT_NAME%"=="" ( - set "OUTPUT_NAME=a.exe" -) - -:: Run the compilation command -gfortran -I../LibDualzn64 -o "%OUTPUT_NAME%" "%SOURCE_FILE%" -L../LibDualzn64 -ldualzn - - diff --git a/Windows/gfortranCase/prec_real64/examples/ex1.f90 b/Windows/gfortranCase/prec_real64/examples/ex1.f90 deleted file mode 100644 index dbe9810..0000000 --- a/Windows/gfortranCase/prec_real64/examples/ex1.f90 +++ /dev/null @@ -1,35 +0,0 @@ -!gfortran -I../LibDualzn64 -o e1 ex1.f90 -L../LibDualzn64 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - - call set_order(5) !before anything we set the 'order' to work with - - z0 = (1.1_prec,2.2_prec) - r = 0 !we initialize the dual number to 0 - - !we set the 0-th and 1-th components. If dual numbers are used to - !calculate D^n f(z0) then r must be of the form r = r0 + 1*eps_1 - r%f(0) = z0 - r%f(1) = 1 - - fval = sin(r)**log(r*r) - - !writing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - print*,fval%f(k) - end do - deallocate(r%f) - deallocate(fval%f) -end program main - - - - diff --git a/Windows/gfortranCase/prec_real64/examples/ex2.f90 b/Windows/gfortranCase/prec_real64/examples/ex2.f90 deleted file mode 100644 index ccee209..0000000 --- a/Windows/gfortranCase/prec_real64/examples/ex2.f90 +++ /dev/null @@ -1,52 +0,0 @@ -!gfortran -I../LibDualzn64 -o e2 ex2.f90 -L../LibDualzn64 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - real :: t1,t2 - - call set_order(5) !we set the order to work with - - !since a dualzn numbers is an allocatable entity, do not forget to - !initialize it - r = 0 !<--- initializing r to 0 - r%f(0) = (1.1_prec,0.0_prec) - r%f(1) = 1 !since we want to differentiate, r = r0 +1*eps_1 - !all the other components are 0 as r was initialized to 0 - - call cpu_time(t1) - fval = ftest(r) - call cpu_time(t2) - - !Computing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - write(*,"(i0,a,f0.1,a,e17.10)") k,"-th derivative at x = ", & - real(r%f(0)),":",real(fval%f(k)) - end do - - print*,"elapsed time (s):",t2-t1 - deallocate(r%f) - deallocate(fval%f) - -contains - function ftest(x) result(fr) - type(dualzn), intent(in) :: x - type(dualzn) :: fr - integer :: k - - !nested function f(x) = sin(x) * exp(-x^2), f(f(...(f(x))...)) - !applied 1000 times - fr = sin(x)*exp(-x*x) - do k=1, 1000-1 - fr = sin(fr)*exp(-fr*fr) - end do - end function ftest -end program main - - diff --git a/Windows/gfortranCase/prec_real64/examples/ex3.f90 b/Windows/gfortranCase/prec_real64/examples/ex3.f90 deleted file mode 100644 index 73fdc70..0000000 --- a/Windows/gfortranCase/prec_real64/examples/ex3.f90 +++ /dev/null @@ -1,90 +0,0 @@ -!gfortran -I../LibDualzn64 -o e3 ex3.f90 -L../LibDualzn64 -ldualzn - -!module with example of functions -module function_mod - use dualzn_mod - implicit none - private - - public :: fstest, fvectest - -contains - !Example of scalar function f = sin(x*y*z) + cos(x*y*z) - function fstest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn) :: fr - type(dualzn) :: x,y,z - - x = r(1); y = r(2); z = r(3) - fr = sin(x*y*z) + cos(x*y*z) - end function fstest - - !Example of vector function f = [f1,f2,f3] - !f = fvectest(r) is a function f:D^m ---> Dn - function fvectest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn), allocatable, dimension(:) :: fr - type(dualzn) :: f1,f2,f3 - type(dualzn) :: x,y,z,w - - x = r(1); y = r(2); z = r(3); w = r(4) - - f1 = sin(x*y*z*w) - f2 = cos(x*y*z*w)*sqrt(w/y - x/z) - f3 = sin(log(x*y*z*w)) - - allocate(fr(3)) - fr = [f1,f2,f3] - end function fvectest -end module function_mod - -!----------------------------------------------------------------------- -!main program -program main - use precision_mod - use dualzn_mod - use diff_mod - use function_mod - implicit none - - integer, parameter :: nf =3, mq = 4 - complex(prec), parameter :: ii = (0,1) - complex(prec), dimension(mq) :: q, vec - complex(prec), dimension(nf,mq) :: Jmat - complex(prec), dimension(nf) :: JV - complex(prec), dimension(3) :: GV - complex(prec), dimension(3,3) :: Hmat - integer :: i - - vec = [1.0_prec,2.0_prec,3.0_prec,4.0_prec] - q = vec/10.0_prec + ii - - print*,"Jv using matmul" - Jmat = Jacobian(fvectest, q , nf) - JV = matmul(Jmat,vec) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"Jv using vector directional derivative" - JV = d1fvector(fvectest,vec,q,nf) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"---Hessian matrix---" - Hmat = Hessian(fstest,q(1:3)) - do i=1,3 - write(*,"(A,i0)") "row:",i - write(*,*) Hmat(i,:) - end do - write(*,*) - - print*,"---Gradient---" - GV = gradient(fstest,q(1:3)) - do i=1,3 - write(*,*) GV(i) - end do -end program main diff --git a/Windows/ifxCase/prec_real128/LibDualzn128/diff_mod.mod b/Windows/ifxCase/prec_real128/LibDualzn128/diff_mod.mod deleted file mode 100644 index 54e9ddd12f1d6f9469412a62581918043a6f2a64..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 9912 zcmd5?OK%)S5blX>?7XmvLkJ0wN!HHG;5bGBVhL%ST|3^$-nG5)%87)WM2Uk7lMoRGM{0U~}w4t!sA_e{_1WW63gLa%0ex~sbS>+Y)R znx5UMJaybx>J6pTdvEpkz20|P?ZER7&A6G=f2z07KEM0Hqw9Po50j^}4ZCkMlCRFq z&dw|>UG1Gc-KPr0;o+IFazV8k1kV_*!pY%EesFYfQsJpOls{jdRObfs>k{TJR zRG6Qg94r)vO6S$}Yl}gl-?ngu;5*OB$F^jJo`EI_KCrNV2cygS}@l?#Vht*RzeMio<4wG|cJVf#Sf2YcC{#uJiK9w-bNu+t^6ZopLJ zhARcdVdSc^Qn?8k_2G~|Xp%w7RMd9oCx)yiq`7S*Y#%)kcW%0%T9~8Tslm~1-Y%9D zb>o2H^p(Oob(oUQnq|zfs<1$DN;P*{7Tfi+7`Ck=#}*9puoqh~R%5zr>x6(?3d~mw 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"a.exe" -set "SOURCE_FILE=%~1" -set "OUTPUT_NAME=%~2" - -if "%OUTPUT_NAME%"=="" ( - set "OUTPUT_NAME=a.exe" -) - -:: Run the compilation command -ifx -o "%OUTPUT_NAME%" "%SOURCE_FILE%" -I../LibDualzn128 ../LibDualzn128/libdualzn.lib - diff --git a/Windows/ifxCase/prec_real128/examples/ex1.f90 b/Windows/ifxCase/prec_real128/examples/ex1.f90 deleted file mode 100644 index b8bbb11..0000000 --- a/Windows/ifxCase/prec_real128/examples/ex1.f90 +++ /dev/null @@ -1,37 +0,0 @@ -!ifx -I../LibDualzn128 -o e1 ex1.f90 -L../LibDualzn128 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - - call set_order(5) !before anything we set the 'order' to work with - - z0 = (1.1_prec,2.2_prec) - r = 0 !we initialize the dual number to 0 - - !we set the 0-th and 1-th components. If dual numbers are used to - !calculate D^n f(z0) then r must be of the form r = r0 + 1*eps_1 - r%f(0) = z0 - r%f(1) = 1 - - fval = sin(r)**log(r*r) - - !writing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - print*,fval%f(k) - end do - - deallocate(r%f) - deallocate(fval%f) - -end program main - - - - diff --git a/Windows/ifxCase/prec_real128/examples/ex2.f90 b/Windows/ifxCase/prec_real128/examples/ex2.f90 deleted file mode 100644 index 00296b7..0000000 --- a/Windows/ifxCase/prec_real128/examples/ex2.f90 +++ /dev/null @@ -1,52 +0,0 @@ -!ifx -I../LibDualzn128 -o e2 ex2.f90 -L../LibDualzn128 -ldualzn -program main - use precision_mod - use dualzn_mod - implicit none - - complex(prec) :: z0 - type(dualzn) :: r, fval - integer :: k - real :: t1,t2 - - call set_order(5) !we set the order to work with - - !since a dualzn numbers is an allocatable entity, do not forget to - !initialize it - r = 0 !<--- initializing r to 0 - r%f(0) = (1.1_prec,0.0_prec) - r%f(1) = 1 !since we want to differentiate, r = r0 +1*eps_1 - !all the other components are 0 as r was initialized to 0 - - call cpu_time(t1) - fval = ftest(r) - call cpu_time(t2) - - !Computing the derivatives, from the 0th derivative up to the - !order-th derivative. - print*,"derivatives" - do k=0,order - write(*,"(i0,a,f0.1,a,e17.10)") k,"-th derivative at x = ", & - real(r%f(0)),":",real(fval%f(k)) - end do - - print*,"elapsed time (s):",t2-t1 - deallocate(r%f) - deallocate(fval%f) - -contains - function ftest(x) result(fr) - type(dualzn), intent(in) :: x - type(dualzn) :: fr - integer :: k - - !nested function f(x) = sin(x) * exp(-x^2), f(f(...(f(x))...)) - !applied 1000 times - fr = sin(x)*exp(-x*x) - do k=1, 1000-1 - fr = sin(fr)*exp(-fr*fr) - end do - end function ftest -end program main - - diff --git a/Windows/ifxCase/prec_real128/examples/ex3.f90 b/Windows/ifxCase/prec_real128/examples/ex3.f90 deleted file mode 100644 index d1fe232..0000000 --- a/Windows/ifxCase/prec_real128/examples/ex3.f90 +++ /dev/null @@ -1,90 +0,0 @@ -!ifx -I../LibDualzn128 -o e3 ex3.f90 -L../LibDualzn128 -ldualzn - -!module with example of functions -module function_mod - use dualzn_mod - implicit none - private - - public :: fstest, fvectest - -contains - !Example of scalar function f = sin(x*y*z) + cos(x*y*z) - function fstest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn) :: fr - type(dualzn) :: x,y,z - - x = r(1); y = r(2); z = r(3) - fr = sin(x*y*z) + cos(x*y*z) - end function fstest - - !Example of vector function f = [f1,f2,f3] - !f = fvectest(r) is a function f:D^m ---> Dn - function fvectest(r) result(fr) - type(dualzn), intent(in), dimension(:) :: r - type(dualzn), allocatable, dimension(:) :: fr - type(dualzn) :: f1,f2,f3 - type(dualzn) :: x,y,z,w - - x = r(1); y = r(2); z = r(3); w = r(4) - - f1 = sin(x*y*z*w) - f2 = cos(x*y*z*w)*sqrt(w/y - x/z) - f3 = sin(log(x*y*z*w)) - - allocate(fr(3)) - fr = [f1,f2,f3] - end function fvectest -end module function_mod - -!----------------------------------------------------------------------- -!main program -program main - use precision_mod - use dualzn_mod - use diff_mod - use function_mod - implicit none - - integer, parameter :: nf =3, mq = 4 - complex(prec), parameter :: ii = (0,1) - complex(prec), dimension(mq) :: q, vec - complex(prec), dimension(nf,mq) :: Jmat - complex(prec), dimension(nf) :: JV - complex(prec), dimension(3) :: GV - complex(prec), dimension(3,3) :: Hmat - integer :: i - - vec = [1.0_prec,2.0_prec,3.0_prec,4.0_prec] - q = vec/10.0_prec + ii - - print*,"Jv using matmul" - Jmat = Jacobian(fvectest, q , nf) - JV = matmul(Jmat,vec) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"Jv using vector directional derivative" - JV = d1fvector(fvectest,vec,q,nf) - do i=1,nf - write(*,*) JV(i) - end do - write(*,*) - - print*,"---Hessian matrix---" - Hmat = Hessian(fstest,q(1:3)) - do i=1,3 - write(*,"(A,i0)") "row:",i - write(*,*) Hmat(i,:) - end do - write(*,*) - - print*,"---Gradient---" - GV = gradient(fstest,q(1:3)) - do i=1,3 - write(*,*) GV(i) - end do -end program main diff --git a/Windows/ifxCase/prec_real64/LibDualzn64/diff_mod.mod b/Windows/ifxCase/prec_real64/LibDualzn64/diff_mod.mod deleted file mode 100644 index 1b5dd5fba751e6d2687d44109bcc6f41d9837656..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 9912 zcmd5?TW?iG6rN36D3@a^Afl*jI4xH#1%t|i$u8%#^pJ8++e4c|VhRLGKw1bF^4LtaLYxbHw`_fWQOJPp-p37RZ);BY2tv!48 zDVf0R3ypcp81w!+hx*^_KVmkZ{9`+AaXNIkuV2dtKYVbJW%4iuHhW_Cb+P30mu6o^NsimThc|@KD`$(H*#pyCML~VH1xXuk-(3(QlG`+NCgE7g9Vg)65F()Jk+cj z4x>CND^(toQSWm6QJV}>rXsH{%naF1NPFk7>z@>eyF67j9n7J2Vqm0~x6^e)+t?m+ zhQ?r>y5pM7+GWhCCRd?2W7;<iJO!`3!(timvN1*sKdGp0M=CIs9HV7?a9!Ys@* zVwK=>x`7W<*-NG?g|iiytzxqFolISVse8$oS~XZ2d)8pNKq-TzBbTQnz?Dx433iJG zHyOK)tP4NdZf#^(*lyQT>GIhv#rX!Ib_*ygV7HNI=S>&gHKYsnAyQ-`>r*(F!EPg` 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