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rbmat.f90
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!============================================!
! !
! Linear Algebra and LU Decomposition !
! for the !
! Direct Numerical Simulation (DNS) !
! of a turbulent channel flow !
! !
!============================================!
!
! Author: Dr. Davide Gatti
! Date : 28/Jul/2015
!
MODULE rbmat
USE, intrinsic :: iso_c_binding
!- Overload division operator -!
!------------------------------!
INTERFACE operator (.bs.)
PROCEDURE LLUdiv
END INTERFACE OPERATOR (.bs.)
INTERFACE operator (.bsr.)
PROCEDURE LLU5div
END INTERFACE OPERATOR (.bsr.)
CONTAINS
!- in-place LU Decomposition of a real square matrix -!
!-----------------------Doolittle---------------------!
SUBROUTINE LUdecompD(A)
real(C_DOUBLE), intent(inout) :: A(:,:)
integer(C_INT) :: HI
real(C_DOUBLE) :: piv
HI=SIZE(A,1)
DO i=1,HI
FORALL (j=i:HI) A(i,j)=A(i,j)-sum(A(i,1:i-1)*A(1:i-1,j))
piv=1/A(i,i)
FORALL (j=i+1:HI) A(j,i)=(A(j,i)-sum(A(j,1:i-1)*A(1:i-1,i)))*piv
END DO
END SUBROUTINE LUdecompD
!- in-place LU Decomposition of a real square matrix -!
!-------------------------Crout-----------------------!
SUBROUTINE LUdecompC(A)
real(C_DOUBLE), intent(inout) :: A(:,:)
integer(C_INT) :: HI
real(C_DOUBLE) :: piv
HI=SIZE(A,1)
DO k=1,HI
FORALL (i=k:HI) A(i,k)=A(i,k)-sum(A(i,1:k-1)*A(1:k-1,k))
piv=1/A(k,k)
FORALL (j=k+1:HI) A(k,j)=(A(k,j)-sum(A(k,1:k-1)*A(1:k-1,j)))*piv
END DO
END SUBROUTINE LUdecompC
!- in-place LU Decomposition of a real square matrix -!
!-----------------------------------------------------!
SUBROUTINE LUdecomp(A)
real(C_DOUBLE), intent(inout) :: A(:,:)
integer(C_INT) :: HI
real(C_DOUBLE) :: piv
HI=SIZE(A,1)
DO i=HI,2,-1
piv=1.0d0/A(i,i); A(i,i)=piv; A(i,1:i-1)=A(i,1:i-1)*piv
DO k=1,i-1
piv=A(k,i)
A(k,1:i-1)=A(k,1:i-1)-piv*A(i,1:i-1)
!DO j=i-1,1,-1
! A(k,j)=A(k,j)-piv*A(i,j)
!END DO
END DO
END DO
A(1,1)=1.0d0/A(1,1)
END SUBROUTINE LUdecomp
!---- in-place LU Decomposition of a banded matrix ---!
!-----------------------------------------------------!
SUBROUTINE LU5decomp(A)
real(C_DOUBLE), intent(inout) :: A(0:,-2:)
integer(C_INT) :: HI
real(C_DOUBLE) :: piv
HI=SIZE(A,1)-1;
DO i=HI,0,-1
piv=1.0d0/A(i,0); A(i,0)=piv; A(i,-2:-1)=A(i,-2:-1)*piv
DO k=max(-2,-i),-1
piv=A(i+k,-k)
DO j=-1,-2,-1
!A(i+k,M:2*M-1)=A(i+k,M:2*M-1)-piv*A(i,1:M)
A(i+k,j-k)=A(i+k,j-k)-piv*A(i,j)
END DO
END DO
END DO
END SUBROUTINE LU5decomp
!- Left LU division of a square matrix -!
!---------------Doolittle---------------!
SUBROUTINE LeftLUdivD(x,A)
real(C_DOUBLE), intent(inout) :: x(:)
real(C_DOUBLE), intent(in) :: A(:,:)
integer(C_INT) :: HI
HI=SIZE(A,1)
DO k=2,HI
x(k)=x(k)-sum(A(k,1:k-1)*x(1:k-1))
END DO
x(HI)=x(HI)/A(HI,HI)
DO k=HI-1,1,-1
x(k)=(x(k)-sum(A(k,k+1:HI)*x(k+1:HI)))/A(k,k)
END DO
END SUBROUTINE LeftLUdivD
!- Left LU division of a square matrix -!
!-----------------Crout-----------------!
SUBROUTINE LeftLUdivC(x,A)
real(C_DOUBLE), intent(inout) :: x(:)
real(C_DOUBLE), intent(in) :: A(:,:)
integer(C_INT) :: HI
HI=SIZE(A,1)
x(1)=x(1)/A(1,1)
DO i=2,HI
x(i)=(x(i)-sum(A(i,1:i-1)*x(1:i-1)))/A(i,i)
END DO
DO i=HI-1,1,-1
x(i)=x(i)-sum(A(i,i+1:HI)*x(i+1:HI))
END DO
END SUBROUTINE LeftLUdivC
!- Left LU division of a square matrix -!
!---------------------------------------!
SUBROUTINE LeftLUdiv(x,A)
real(C_DOUBLE), intent(inout) :: x(:)
real(C_DOUBLE), intent(in) :: A(:,:)
integer(C_INT) :: HI
HI=SIZE(A,1)
x(HI)=x(HI)*A(HI,HI)
DO i=HI-1,1,-1
x(i)=(x(i)-sum(A(i,i+1:HI)*x(i+1:HI)))*A(i,i)
END DO
DO i=2,HI
x(i)=x(i)-sum(A(i,1:i-1)*x(1:i-1))
END DO
END SUBROUTINE LeftLUdiv
!- Left LU division of a banded matrix -!
!---------------------------------------!
SUBROUTINE LeftLU5div(A,b)
complex(C_DOUBLE_COMPLEX), intent(inout) :: b(:)
real(C_DOUBLE), intent(in) :: A(:,-2:)
integer(C_INT) :: HI
HI=SIZE(A,1)
DO i=HI,1,-1
j=MIN(2,HI-i)
b(i)=(b(i)-sum(A(i,1:j)*b(i+1:i+j)))*A(i,0)
END DO
DO i=1,HI
j=MAX(-2,1-i)
b(i)=b(i)-sum(A(i,j:-1)*b(i+j:i-1))
END DO
END SUBROUTINE LeftLU5div
!- Left LU division of a square matrix -!
!----OPERATOR----Doolittle--------------!
FUNCTION LLUdivD(A,b) RESULT(x)
real(C_DOUBLE), intent(in) :: b(:)
real(C_DOUBLE), intent(in) :: A(:,:)
real(C_DOUBLE), allocatable :: x(:)
integer(C_INT) :: HI
HI=SIZE(A,1)
ALLOCATE(x(1:HI))
x(1)=b(1)
DO k=2,HI
x(k)=b(k)-sum(A(k,1:k-1)*x(1:k-1))
END DO
x(HI)=x(HI)/A(HI,HI)
DO k=HI-1,1,-1
x(k)=(x(k)-sum(A(k,k+1:HI)*x(k+1:HI)))/A(k,k)
END DO
END FUNCTION LLUdivD
!- Left LU division of a square matrix -!
!----OPERATOR-----Crout-----------------!
FUNCTION LLUdivC(A,b) RESULT(x)
real(C_DOUBLE), intent(in) :: b(:)
real(C_DOUBLE), intent(in) :: A(:,:)
real(C_DOUBLE), allocatable :: x(:)
integer(C_INT) :: HI
HI=SIZE(A,1)
ALLOCATE(x(1:HI))
x(1)=b(1)/A(1,1)
DO i=2,HI
x(i)=(b(i)-sum(A(i,1:i-1)*x(1:i-1)))/A(i,i)
END DO
DO i=HI-1,1,-1
x(i)=x(i)-sum(A(i,i+1:HI)*x(i+1:HI))
END DO
END FUNCTION LLUdivC
!- Left LU division of a square matrix -!
!----OPERATOR---------------------------!
FUNCTION LLUdiv(A,b) RESULT(x)
real(C_DOUBLE), intent(in) :: b(:)
real(C_DOUBLE), intent(in) :: A(:,:)
real(C_DOUBLE), allocatable :: x(:)
integer(C_INT) :: HI
HI=SIZE(A,1)
ALLOCATE(x(1:HI))
x(HI)=b(HI)*A(HI,HI)
DO i=HI-1,1,-1
x(i)=(b(i)-sum(A(i,i+1:HI)*x(i+1:HI)))*A(i,i)
END DO
DO i=2,HI
x(i)=x(i)-sum(A(i,1:i-1)*x(1:i-1))
END DO
END FUNCTION LLUdiv
!- Left LU division of a banded matrix -!
!----OPERATOR---------------------------!
FUNCTION LLU5div(A,b) RESULT(x)
real(C_DOUBLE), intent(in) :: b(:)
real(C_DOUBLE), intent(in) :: A(:,-2:)
real(C_DOUBLE), allocatable :: x(:)
integer(C_INT) :: HI
HI=SIZE(A,1)
ALLOCATE(x(1:HI))
DO i=HI,1,-1
j=MIN(2,HI-i)
x(i)=(b(i)-sum(A(i,1:j)*x(i+1:i+j)))*A(i,0)
END DO
DO i=1,HI
j=MAX(-2,1-i)
x(i)=x(i)-sum(A(i,j:-1)*x(i+j:i-1))
END DO
END FUNCTION LLU5div
END MODULE rbmat