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FortranDriver

Fortran Library FotranDriverDLL

Compiled with IFX and exports functions that are mostly wrappers to Fortran functions.

For example, below is the code that wraps the Fortran native matrix multiplication intrinsic.

Legacy style fortran exports

subroutine call_mul_array_mm(n,m,k,A,x,b)
!DEC$ ATTRIBUTES DLLEXPORT :: call_mul_array_mm
!DEC$ ATTRIBUTES ALIAS: 'call_mul_array_mm' :: call_mul_array_mm
!DEC$ ATTRIBUTES VALUE     :: n, m, k
!DEC$ ATTRIBUTES REFERENCE :: A, b, x
integer, intent(in)       :: n,m,k
real(real64), intent(in)  :: A(n,m), x(m,k)
real(real64), intent(out) :: b(n,k)
    
    b = matmul(A, x)    
            
end subroutine

and Modern style fortran exports

subroutine call_mul_array_mm(n,m,k,A,x,b) bind(c)
!DEC$ ATTRIBUTES DLLEXPORT :: call_mul_array_mm
integer, intent(in), value :: n,m,k
real(real64), intent(in)   :: A(n,m), x(m,k)
real(real64), intent(out)  :: b(n,k)
    
    b = matmul(A, x)    
            
end subroutine

For matrix inversion, solution of system of equations and for determinant evaluation the Fortran library does a direct evaluation for systems with n <= 4 or otherwise it uses a LUP decomposition for higher dimensional systems.

Some of the exported functions are

  • array_rand_v(integer, real, real, real(:))
  • call_elem_array_v(integer, integer, real, real(:))
  • call_add_array_v(integer, real(:), real(:), real(:))
  • call_sub_array_v(integer, real(:), real(:), real(:))
  • call_scale_array_v(integer, real, real(:), real(:))
  • call_inner_array_v(integer, real(:), real(:), real)
  • call_mul_array_mv(integer, integer, real(:,:), real(:), real(:))
  • call_mul_array_vm(integer, integer, real(:), real(:,:), real(:))
  • call_solve_array_mv(integer, integer, real(:,:), real(:), real(:))
  • array_rand_m(integer, integer, real, real, real(:,:))
  • call_array_diag_m(integer, real(:), real(:,:))
  • call_array_scalar_m(integer, integer, real, real(:,:))
  • call_add_array_m(integer, integer, real(:,:), real(:,:), real(:,:))
  • call_sub_array_m(integer, integer, real(:,:), real(:,:), real(:,:))
  • call_scale_array_m(integer, integer, real, real(:,:), real(:,:))
  • call_determinant_array_m(integer, real(:,:), real)
  • call_transpose_array_m(integer, integer, real(:,:), real(:,:))
  • call_mul_array_mm(integer, integer, integer, real(:,:), real(:,:), real(:,:))
  • call_solve_array_mm(integer, integer, integer, real(:,:), real(:,:), real(:,:))
  • array_inverse_m(integer, real(:,:), real(:,:))

C# Console App FortranDriverCS

The corresponding imported functions are

  • array_rand_v(int, double, double, double[]);
  • call_elem_array_v(int, int, double, double[]);
  • call_add_array_v(int, double[], double[], double[]);
  • call_sub_array_v(int, double[], double[], double[]);
  • call_scale_array_v(int, double, double[], double[]);
  • call_inner_array_v(int, double[], double[], out double);
  • call_mul_array_mv(int, int, double[,], double[], double[]);
  • call_mul_array_vm(int, int, double[], double[,], double[]);
  • call_solve_array_mv(int, int, double[,], double[], double[]);
  • array_rand_m(int, int, double, double, double[,]);
  • call_array_diag_m(int, double[], double[,]);
  • call_array_scalar_m(int, int, double, double[,]);
  • call_add_array_m(int, int, double[,], double[,], double[,]);
  • call_sub_array_m(int, int, double[,], double[,], double[,]);
  • call_scale_array_m(int, int, double, double[,], double[,]);
  • call_determinant_array_m(int, double[,], out double);
  • call_transpose_array_m(int, int, double[,], double[,]);
  • call_mul_array_mm(int, int, int, double[,], double[,], double[,]);
  • call_solve_array_mm(int, int, int, double[,], double[,], double[,]);
  • array_inverse_m(int, double[,], double[,]);

FVector and FMatrix

All of the above imports are neatly wrapped inside a vector and matrix classes that store the values in a way that is compatible with Fortran (column-major arrays) and defines corresponding methods and operators.

FVectors

  • FVector Elemental(int, int, double)
  • FVector Random(int, double, double)
  • double Dot(FVector, FVector)
  • FVector Negate(FVector)
  • FVector Add(FVector, FVector)
  • FVector Subtract(FVector, FVector)
  • FVector Scale(double, FVector)
  • FVector Product(FVector, FMatrix)
  • FVector op_UnaryPlus(FVector)
  • FVector op_Addition(FVector, FVector)
  • FVector op_UnaryNegation(FVector)
  • FVector op_Subtraction(FVector, FVector)
  • FVector op_Multiply(double, FVector)
  • FVector op_Multiply(FVector, double)
  • FVector op_Division(FVector, double)
  • double op_Multiply(FVector, FVector)
  • FVector op_Multiply(FVector, FMatrix)

FMatrix

  • FMatrix Random(int, int, double, double)
  • FMatrix Zero(int)
  • FMatrix Zero(int, int)
  • FMatrix Identity(int)
  • FMatrix Identity(int, int)
  • FMatrix Scalar(int, double)
  • FMatrix Scalar(int, int, double)
  • FMatrix Diagonal(double[])
  • FMatrix Diagonal(int, double[])
  • FMatrix Transpose(FMatrix)
  • FMatrix Negate(FMatrix)
  • FMatrix Add(double, FMatrix)
  • FMatrix Add(FMatrix, double)
  • FMatrix Add(FMatrix, FMatrix)
  • FMatrix Subtract(double, FMatrix)
  • FMatrix Subtract(FMatrix, double)
  • FMatrix Subtract(FMatrix, FMatrix)
  • FMatrix Scale(double, FMatrix)
  • FVector Product(FMatrix, FVector)
  • FMatrix Product(FMatrix, FMatrix)
  • FVector Solve(FMatrix, FVector)
  • FMatrix Solve(FMatrix, FMatrix)
  • double Determinant(FMatrix)
  • FMatrix Inverse(FMatrix)
  • FMatrix op_UnaryPlus(FMatrix)
  • FMatrix op_UnaryNegation(FMatrix)
  • FMatrix op_Addition(double, FMatrix)
  • FMatrix op_Subtraction(double, FMatrix)
  • FMatrix op_Addition(FMatrix, double)
  • FMatrix op_Subtraction(FMatrix, double)
  • FMatrix op_Addition(FMatrix, FMatrix)
  • FMatrix op_Subtraction(FMatrix, FMatrix)
  • FMatrix op_Multiply(double, FMatrix)
  • FMatrix op_Multiply(FMatrix, double)
  • FVector op_Multiply(FMatrix, FVector)
  • FMatrix op_Multiply(FMatrix, FMatrix)
  • FMatrix op_Division(FMatrix, double)
  • FMatrix op_OnesComplement(FMatrix)
  • FVector op_Division(FVector, FMatrix)
  • FMatrix op_Division(FMatrix, FMatrix)
  • FMatrix op_LogicalNot(FMatrix)

Demo/Test code outout

Verbatim the output from the C# test code that does some very basic linear algebra by calling the corresponding method, which in term calls the corresponding Fortran function.

Note that outputs have been rounded to 12 digits and then converted into text using g7 formatting.

Calling Fortran from C#


1. Generate Matrix A in C#
A=
|      1      2      3 |
|      4      5      6 |
|      7      8      9 |
|     10     11     12 |
|     13     14     15 |
|     16     17     18 |
|     19     20     21 |

Step:            1 of  3
Step:            2 of  3
Step:            3 of  3
2. Generate Vector x in C#
x=
|    0.5 |
|      1 |
|    1.5 |

3. Manipulate Matrix A in Fortran
A=
|  1.581  4.845   9.55 |
|  4.863  10.56  18.26 |
|  7.779   16.7  27.98 |
|  10.42  22.92  36.12 |
|  13.89  28.02  45.36 |
|  16.75  34.73  54.77 |
|  19.37  40.75  63.34 |

4. Calculate Vector b in Fortran
b=
|  19.96 |
|  40.39 |
|  62.57 |
|  82.31 |
|    103 |
|  125.3 |
|  145.4 |

5. Calculate Vector x in Fortran
g=
|    0.5 |
|      1 |
|    1.5 |
|      0 |
|      0 |
|      0 |
|      0 |


Testing Native/Fortran Vectors & Matrices
Vector Size =7
Elemental
e =
|           1 |
|           0 |
|           0 |
|           0 |
|           0 |
|           0 |
|           0 |


Random
x =
|     3.53389 |
|  -0.0474646 |
|  -0.0544103 |
|     4.88769 |
|    0.214773 |
|      4.4543 |
|    0.808256 |


Scaling/Negate
n =
|    -3.53389 |
|   0.0474646 |
|   0.0544103 |
|    -4.88769 |
|   -0.214773 |
|     -4.4543 |
|   -0.808256 |


Addition
y =
|     4.53389 |
|  -0.0474646 |
|  -0.0544103 |
|     4.88769 |
|    0.214773 |
|      4.4543 |
|    0.808256 |


Subtraction
z =
|    -2.53389 |
|   0.0474646 |
|   0.0544103 |
|    -4.88769 |
|   -0.214773 |
|     -4.4543 |
|   -0.808256 |


Dot Product
d = -55.92335217964191
Random
A =
|    -0.62464     5.28075     3.70127     2.73815     5.18095     4.92262     1.97883 |
|   -0.716179     2.25109     4.22183     4.06758    0.127354     4.29646   -0.457891 |
|   0.0702138     4.09558     2.90592     2.95752     5.83689   -0.332198     3.72654 |
|     2.20921     4.85445     2.05148     4.04802     2.07399     4.05893     3.54185 |
|     1.95034   -0.731776     1.45102     4.94672   0.0208383     3.75302    0.327344 |
|     3.03146     3.98451     4.83298     2.24488     1.68265     1.87458     4.80515 |
|     1.34869     1.48229   -0.327615     1.00801     3.70934     4.66621     5.05912 |


Matrix/Vector Product
g =
|     35.3627 |
|     35.8086 |
|      17.137 |
|     48.6384 |
|     48.0123 |
|     33.8282 |
|     35.3108 |


Vector/Matrix Product
f =
|     23.6327 |
|     60.8481 |
|     44.3228 |
|     40.9843 |
|     38.6199 |
|     49.9764 |
|     49.6864 |


Matrix/Vector Solve
u =
|     3.53389 |
|  -0.0474646 |
|  -0.0544103 |
|     4.88769 |
|    0.214773 |
|      4.4543 |
|    0.808256 |


Residual
u-x =
|          -0 |
|           0 |
|          -0 |
|           0 |
|          -0 |
|          -0 |
|           0 |


Scalar
S =
|           2           0           0           0           0           0           0 |
|           0           2           0           0           0           0           0 |
|           0           0           2           0           0           0           0 |
|           0           0           0           2           0           0           0 |
|           0           0           0           0           2           0           0 |
|           0           0           0           0           0           2           0 |
|           0           0           0           0           0           0           2 |


Diagonal
D =
|     2.49788           0           0           0           0           0           0 |
|           0     5.42568           0           0           0           0           0 |
|           0           0     5.95427           0           0           0           0 |
|           0           0           0     5.75542           0           0           0 |
|           0           0           0           0   -0.750938           0           0 |
|           0           0           0           0           0     1.96877           0 |
|           0           0           0           0           0           0     2.51319 |


Random
R =
|     4.50354      5.3711     3.54005      5.2476    0.755623     2.32017     1.05255 |
|     4.91874     2.77253     1.00319   -0.588027     4.76002   -0.938255     3.62032 |
|   -0.128475      5.5531     3.72581   -0.908082  -0.0738401     3.72192     4.80324 |
|     3.19735     2.15568     4.19711     1.27234     5.56115   -0.729062     3.71758 |
|     5.53569   -0.156161     2.81046     5.80818     1.62254     4.12428     5.38262 |
|     4.89418     2.24512     2.69301     4.40465     4.62534      2.9859     5.95033 |
|     2.37442     5.84556     3.71649     1.64767     4.02671     0.50351   -0.677844 |


Add
A =
|     7.00142      5.3711     3.54005      5.2476    0.755623     2.32017     1.05255 |
|     4.91874     8.19822     1.00319   -0.588027     4.76002   -0.938255     3.62032 |
|   -0.128475      5.5531     9.68009   -0.908082  -0.0738401     3.72192     4.80324 |
|     3.19735     2.15568     4.19711     7.02776     5.56115   -0.729062     3.71758 |
|     5.53569   -0.156161     2.81046     5.80818    0.871606     4.12428     5.38262 |
|     4.89418     2.24512     2.69301     4.40465     4.62534     4.95467     5.95033 |
|     2.37442     5.84556     3.71649     1.64767     4.02671     0.50351     1.83534 |


Subtract
B =
|     2.00567      5.3711     3.54005      5.2476    0.755623     2.32017     1.05255 |
|     4.91874    -2.65315     1.00319   -0.588027     4.76002   -0.938255     3.62032 |
|   -0.128475      5.5531    -2.22846   -0.908082  -0.0738401     3.72192     4.80324 |
|     3.19735     2.15568     4.19711    -4.48308     5.56115   -0.729062     3.71758 |
|     5.53569   -0.156161     2.81046     5.80818     2.37348     4.12428     5.38262 |
|     4.89418     2.24512     2.69301     4.40465     4.62534     1.01713     5.95033 |
|     2.37442     5.84556     3.71649     1.64767     4.02671     0.50351    -3.19103 |


Scale/Negate
N =
|    -4.50354     -5.3711    -3.54005     -5.2476   -0.755623    -2.32017    -1.05255 |
|    -4.91874    -2.77253    -1.00319    0.588027    -4.76002    0.938255    -3.62032 |
|    0.128475     -5.5531    -3.72581    0.908082   0.0738401    -3.72192    -4.80324 |
|    -3.19735    -2.15568    -4.19711    -1.27234    -5.56115    0.729062    -3.71758 |
|    -5.53569    0.156161    -2.81046    -5.80818    -1.62254    -4.12428    -5.38262 |
|    -4.89418    -2.24512    -2.69301    -4.40465    -4.62534     -2.9859    -5.95033 |
|    -2.37442    -5.84556    -3.71649    -1.64767    -4.02671    -0.50351    0.677844 |


Determinant
d =
-36200.84146176189
Transpose
A_tr =
|     7.00142     4.91874   -0.128475     3.19735     5.53569     4.89418     2.37442 |
|      5.3711     8.19822      5.5531     2.15568   -0.156161     2.24512     5.84556 |
|     3.54005     1.00319     9.68009     4.19711     2.81046     2.69301     3.71649 |
|      5.2476   -0.588027   -0.908082     7.02776     5.80818     4.40465     1.64767 |
|    0.755623     4.76002  -0.0738401     5.56115    0.871606     4.62534     4.02671 |
|     2.32017   -0.938255     3.72192   -0.729062     4.12428     4.95467     0.50351 |
|     1.05255     3.62032     4.80324     3.71758     5.38262     5.95033     1.83534 |


Inverse
A_inv =
|     3.93089     1.63875     2.10649     3.35991    -7.63678     4.87952    -11.2284 |
|    -3.37382    -1.35507    -1.87737    -3.03048     6.77471    -4.36059     9.92826 |
|      2.9805     1.15585     1.70668     2.64829    -5.90924     3.71788    -8.54332 |
|     -3.2229    -1.39087    -1.82862    -2.78981     6.51885    -4.17837     9.45685 |
|     2.17508    0.851885     1.17326      1.9683    -4.54762     2.97656     -6.2984 |
|    -0.64506   -0.406987   -0.395507   -0.738435     1.28146   -0.664938     2.10114 |
|    -2.07703   -0.653442    -1.02572    -1.66869     4.04198    -2.54981     5.50194 |


Check Identity
A_inv*A=
|           1          -0           0           0           0           0           0 |
|          -0           1           0          -0           0          -0          -0 |
|           0          -0           1           0          -0           0           0 |
|          -0          -0          -0           1          -0          -0          -0 |
|           0          -0           0           0           1           0           0 |
|          -0           0          -0          -0           0           1          -0 |
|           0           0          -0          -0           0           0           1 |


A_inv*A-1=
|           0          -0           0           0           0           0           0 |
|          -0           0           0          -0           0          -0          -0 |
|           0          -0           0           0          -0           0           0 |
|          -0          -0          -0          -0          -0          -0          -0 |
|           0          -0           0           0           0           0           0 |
|          -0           0          -0          -0           0          -0          -0 |
|           0           0          -0          -0           0           0          -0 |


Random
Y =
|     5.32029   -0.362404    0.670648 |
|   -0.739317      5.6228   -0.286091 |
|     2.11156   -0.737348     3.17619 |
|   -0.289686   -0.561174    0.598009 |
|     1.71312     2.95986     4.40034 |
|     2.62383     2.68891     5.94585 |
|   -0.918487     2.16345     5.07847 |


Product G=A*Y
G=
|      45.649     32.8607     40.0066 |
|     24.7641     63.3031     37.5406 |
|     21.1416     44.8235     74.7261 |
|     26.4431     26.4663     58.0768 |
|     41.1895     17.0988     71.8502 |
|     44.2477     46.2791     93.8589 |
|     22.2148      45.586      42.743 |


Solve A*U=G
U=
|     5.32029   -0.362404    0.670648 |
|   -0.739317      5.6228   -0.286091 |
|     2.11156   -0.737348     3.17619 |
|   -0.289686   -0.561174    0.598009 |
|     1.71312     2.95986     4.40034 |
|     2.62383     2.68891     5.94585 |
|   -0.918487     2.16345     5.07847 |


Residual
U-Y=
|           0           0           0 |
|          -0          -0          -0 |
|           0           0           0 |
|          -0          -0          -0 |
|           0           0           0 |
|          -0          -0          -0 |
|          -0          -0          -0 |

Fortran

Here is a list of types defined in Fortran that correspond to structs in C#

    type, bind(c) :: vector2
        real(real64) :: data(2)
    end type
    type, bind(c) :: matrix2
        real(real64) :: data(2,2)
    end type
    type, bind(c) :: vector3
        real(real64) :: data(3)
    end type
    type, bind(c) :: matrix3
        real(real64) :: data(3,3)
    end type
    type, bind(c) :: quat4
        real(real64) :: data(4)
    end type

The the corresponding C# structures

public unsafe struct FVector2
{
    fixed double _data[2];
}
public unsafe struct FMatrix2
{
    fixed double _data[2*2];
}
public unsafe struct FVector3
{
    fixed double _data[3];
}
public unsafe struct FMatrix3
{
    fixed double _data[3*3];
}
public unsafe struct FQuat4
{
    fixed double _data[4];
}

The full list of imported Fortran functions defined in C#

  • add_mat2_mat2
  • add_mat2_scalar
  • add_mat3_mat3
  • add_mat3_scalar
  • add_quat4_quat4
  • add_scalar_mat2
  • add_scalar_mat3
  • add_vec2_vec2
  • add_vec3_vec3
  • call_add_array_m
  • call_add_array_v
  • call_array_diag_m
  • call_array_scalar_m
  • call_array_set_column
  • call_array_set_row
  • call_array_zeros_m
  • call_array_zeros_v
  • call_det_array_m
  • call_elem_array_v
  • call_fill_array_m
  • call_inner_array_m
  • call_inner_array_v
  • call_inv_array_m
  • call_mat2_to_array
  • call_mat3_to_array
  • call_mul_array_mm
  • call_mul_array_mv
  • call_mul_array_vm
  • call_outer_array_v
  • call_quat_test_all
  • call_random_array_m
  • call_random_array_v
  • call_reshape_array_mm
  • call_reshape_array_mv
  • call_reshape_array_vm
  • call_round_array_m
  • call_round_array_v
  • call_scale_array_m
  • call_scale_array_v
  • call_slice_array_m
  • call_slice_array_v
  • call_slice_col_array_m
  • call_slice_cols_array_m
  • call_slice_row_array_m
  • call_slice_rows_array_m
  • call_solve_array_mm
  • call_solve_array_mv
  • call_spline_calc_ypp_array
  • call_spline_calc_ypp_domain
  • call_spline_interpolate_array
  • call_spline_interpolate_domain
  • call_spline_interpolate_point
  • call_sub_array_m
  • call_sub_array_v
  • call_test_dowork
  • call_transpose_array_m
  • call_uniform_array_m
  • call_uniform_array_v
  • call_vec2_to_array
  • call_vec3_to_array
  • cross_quat4_quat4
  • cross_scalar_vec2
  • cross_vec2_scalar
  • cross_vec2_vec2
  • cross_vec3_op
  • cross_vec3_vec3
  • determinant_mat2
  • determinant_mat3
  • div_mat2_scalar
  • div_mat3_scalar
  • div_vec2_scalar
  • div_vec3_scalar
  • inner_mat2_mat2
  • inner_mat3_mat3
  • inner_quat4_quat4
  • inner_vec2_vec2
  • inner_vec3_vec3
  • inv_mat2
  • inv_mat3
  • linspace
  • mat2_eye
  • mat2_ones
  • mat2_uniform
  • mat2_values
  • mat2_zeros
  • mat3_eye
  • mat3_ones
  • mat3_rotate_diag
  • mat3_rotate_vec3
  • mat3_uniform
  • mat3_values
  • mat3_zeros
  • mul_mat2_mat2
  • mul_mat2_scalar
  • mul_mat2_vec2
  • mul_mat3_mat3
  • mul_mat3_scalar
  • mul_mat3_vec3
  • mul_quat4_quat4
  • mul_scalar_mat2
  • mul_scalar_mat3
  • mul_scalar_quat4
  • mul_scalar_vec2
  • mul_scalar_vec3
  • mul_vec2_mat2
  • mul_vec2_scalar
  • mul_vec3_mat3
  • mul_vec3_scalar
  • neg_mat2
  • neg_mat3
  • neg_vec2
  • neg_vec3
  • norm_array_m
  • norm_array_v
  • norm_quat4
  • norm_vec2
  • norm_vec3
  • outer_vec2_vec2
  • outer_vec3_vec3
  • quat4_array
  • quat4_axis_angle
  • quat4_conjugate
  • quat4_exp
  • quat4_from_matrix
  • quat4_identity
  • quat4_inverse
  • quat4_normalize
  • quat4_rotate_diag
  • quat4_rotate_vec3
  • quat4_scalar
  • quat4_scalar_vec3
  • quat4_to_axis_angle
  • quat4_to_matrix
  • quat4_uniform
  • quat4_values
  • quat4_vector
  • quat4_zeros
  • rb_get_state
  • rb_set_state
  • rb_state_derivative
  • solve_mat2_mat2
  • solve_mat2_vec2
  • solve_mat3_mat3
  • solve_mat3_vec3
  • sub_mat2_mat2
  • sub_mat2_scalar
  • sub_mat3_mat3
  • sub_mat3_scalar
  • sub_quat4_quat4
  • sub_scalar_mat2
  • sub_scalar_mat3
  • sub_vec2_vec2
  • sub_vec3_vec3
  • trace_mat2
  • trace_mat3
  • transpose_mat2
  • transpose_mat3
  • vec2_ones
  • vec2_to_array
  • vec2_uniform
  • vec2_ux
  • vec2_uy
  • vec2_values
  • vec2_zeros
  • vec3_angle
  • vec3_ones
  • vec3_uniform
  • vec3_ux
  • vec3_uy
  • vec3_uz
  • vec3_values
  • vec3_zeros

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Skeleton code for calling Fortran DLL from C# driver program

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