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Tensor_Class.fun
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Tensor_Class.fun
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!! Copyright 2010 Fernando M. Cucchietti
!
! This file is part of FortranMPS
!
! FortranMPS is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! FortranMPS is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with Foobar. If not, see <http://www.gnu.org/licenses/>.
!TESTING WHERE WILL THIS APPEAR
test_suite Tensor_Class
!TODO: New tests with all possible combinations of index bonding
! use ErrorHandling
! use Constants
setup
!Set testing mode
MaxErrorAllowed=CriticalError
CALL random_seed()
end setup
teardown
end teardown
test assignments_of_tensor
type(tensor3) :: mps1,mps2
type(tensor4) :: aT4
integer error
print *,'First test'
mps1=new_Tensor(10,2,10)
print *,'Assigned 1'
mps2=mps1
print *,'Assigned 2'
aT4=new_Tensor(20,40,10,20)
! assert_equal_within(mps1.absdiff.mps2, 0.0d0, 1.0e-10)
assert_false(WasThereError())
end test
test tensor3_joinindices_first
type(tensor3) :: aMPS
type(tensor2) :: aMatrix,correct
complex(8) :: data(2,3,4),matrix(6,4)
integer error,i,j,k
print *,'Test: tensor3_joinindices_first'
!initialization
forall (i=1:2 ,j=1:3, k=1:4) data(i,j,k)=ONE*(i+(j-1)*3+(k-1)*4)
aMPS=new_Tensor(data)
matrix=one*Reshape( data, [2*3,4])
correct=new_Tensor(matrix)
aMatrix=aMPS%Joinindices(FiRSTANDSECOND,THiRD)
assert_equal_within(amatrix.absdiff.correct, 0.0d0, 1.0e-8)
correct=new_Tensor(transpose(matrix)) !This will be 4,2*3
aMatrix=JoinindicesOf(aMPS,THiRD,FiRSTANDSECOND)
assert_equal_within(amatrix.absdiff.correct, 0.0d0, 1.0e-8)
assert_false(WasThereError())
end test
test tensor4_joinindices
type(tensor4) :: aTensor
type(tensor2) :: aMatrix,correct
complex(8) :: data(2,3,4,5),matrix(6,20)
integer error,i,j,k,l
print *,'Test: tensor4_joinindices'
!initialization
forall (i=1:2 ,j=1:3, k=1:4, l=1:5) data(i,j,k,l)=ONE*(i+(j-1)*2+(k-1)*3*2+(l-1)*2*3*4)
aTensor=new_Tensor(data)
matrix=one*Reshape( data, [2*3,4*5])
correct=new_Tensor(matrix)
aMatrix=aTensor%Joinindices(FiRSTANDSECOND,THiRDANDFOURTH)
assert_equal_within(amatrix.absdiff.correct, 0.0d0, 1.0e-8)
correct=new_Tensor(transpose(matrix))
aMatrix=aTensor%Joinindices(THiRDANDFOURTH,FiRSTANDSECOND)
assert_equal_within(amatrix.absdiff.correct, 0.0d0, 1.0e-8)
end test
test tensor2_Splitindex
type(tensor3) :: aMPS,correct
type(tensor2) :: aMatrix
complex(8) :: matrixdata(6,4)
integer error,i,j,k
!initialization
forall (i=1:6 ,j=1:4) matrixdata(i,j)=ONE*(i+(j-1)*6)
aMatrix=new_Tensor(matrixdata)
correct=new_Tensor(one*Reshape( matrixdata, [2,3,4]))
aMPS=SplitindexOf(aMatrix,FIRST,2)
assert_equal_within(aMPS.absdiff.correct, 0.0d0, 1.0e-8)
correct=new_Tensor(one*Reshape( matrixdata, [6,2,2]))
aMPS=SplitindexOf(aMatrix,SECOND,2)
assert_equal_within(aMPS.absdiff.correct, 0.0d0, 1.0e-8)
assert_false(WasThereError())
end test
test transpose_of_tensor
integer,parameter :: d1=2,d2=3,d3=4
type(Tensor3) :: aTensor,bTensor,CorrectTensor
complex(8) :: data(d1,d2,d3)
complex(8),allocatable :: correct(:,:,:)
integer :: i,j,k,neworder(3)
forall (i=1:d1, j=1:d2, k=1:d3) data(i,j,k)=one*(i*100+j*10+II*k)
aTensor=new_Tensor(data)
neworder=[3,1,2]
bTensor=ConjugateTranspose(aTensor,neworder)
allocate(correct( d2,d3,d1 ))
forall (i=1:d1, j=1:d2, k=1:d3) correct(j,k,i)=one*(i*100+j*10+II*k)
CorrectTensor=new_Tensor(dconjg(correct))
assert_equal_within(bTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(correct)
neworder=[2,1,3]
bTensor=ConjugateTranspose(aTensor,neworder)
allocate(correct( d2,d1,d3 ))
forall (i=1:d1, j=1:d2, k=1:d3) correct(j,i,k)=one*(i*100+j*10+II*k)
CorrectTensor=new_Tensor(dconjg(correct))
assert_equal_within(bTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(correct)
neworder=[1,3,2]
bTensor=ConjugateTranspose(aTensor,neworder)
allocate(correct( d1,d3,d2 ))
forall (i=1:d1, j=1:d2, k=1:d3) correct(i,k,j)=one*(i*100+j*10+II*k)
CorrectTensor=new_Tensor(dconjg(correct))
assert_equal_within(bTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(correct)
end test
test transpose_of_tensor4
integer,parameter :: d1=2,d2=3,d3=4,d4=5
type(Tensor4) :: aTensor,bTensor,CorrectTensor
complex(8) :: data(d1,d2,d3,d4)
complex(8),allocatable :: correct(:,:,:,:)
integer :: i,j,k,l,neworder(4)
forall (i=1:d1, j=1:d2, k=1:d3, l=1:d4) data(i,j,k,l)=one*(i*1000+j*100+10*II*k+l)
aTensor=new_Tensor(data)
neworder=[1,2,3,4]
bTensor=TensorTranspose(aTensor,neworder)
allocate(correct(d1,d2,d3,d4))
forall (i=1:d1, j=1:d2, k=1:d3, l=1:d4) correct(i,j,k,l)=one*(i*1000+j*100+10*II*k+l)
CorrectTensor=new_Tensor(correct)
assert_equal_within(bTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(correct)
neworder=[4,1,2,3]
bTensor=TensorTranspose(aTensor,neworder)
allocate(correct(d2,d3,d4,d1))
forall (i=1:d1, j=1:d2, k=1:d3, l=1:d4) correct(j,k,l,i)=one*(i*1000+j*100+10*II*k+l)
CorrectTensor=new_Tensor(correct)
assert_equal_within(bTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(correct)
neworder=[3,2,4,1]
bTensor=TensorTranspose(aTensor,neworder)
allocate(correct(d4,d2,d1,d3))
forall (i=1:d1, j=1:d2, k=1:d3, l=1:d4) correct(l,j,i,k)=one*(i*1000+j*100+10*II*k+l)
CorrectTensor=new_Tensor(correct)
assert_equal_within(bTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(correct)
end test
test unfoldings_of_tensor3
integer,parameter :: d1=2,d2=3,d3=4
type(Tensor3) :: aTensor
type(Tensor2) :: unfoldedTensor,CorrectTensor
complex(8) :: data(d1,d2,d3)
complex(8),allocatable :: matrixform(:,:)
integer :: i1,i2,i3
forall (i1=1:d1, i2=1:d2, i3=1:d3) data(i1,i2,i3)=one*(i1*100+i2*10+II*i3)
aTensor=new_Tensor(data)
unfoldedTensor=aTensor.unfold.1
allocate(matrixform( d1,d2*d3 ))
forall (i1=1:d1, i2=1:d2, i3=1:d3) matrixform (i1,(i3-1)*d2+i2)=one*(i1*100+i2*10+II*i3)
CorrectTensor=new_Tensor(matrixform)
assert_equal_within(unfoldedTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(matrixform)
unfoldedTensor=aTensor.unfold.2
allocate(matrixform( d2,d1*d3 ))
forall (i1=1:d1, i2=1:d2, i3=1:d3) matrixform (i2,(i3-1)*d1+i1)=one*(i1*100+i2*10+II*i3)
CorrectTensor=new_Tensor(matrixform)
assert_equal_within(unfoldedTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(matrixform)
unfoldedTensor=aTensor.unfold.3
allocate(matrixform( d3,d1*d2 ))
forall (i1=1:d1, i2=1:d2, i3=1:d3) matrixform (i3,(i1-1)*d2+i2)=one*(i1*100+i2*10+II*i3)
CorrectTensor=new_Tensor(matrixform)
assert_equal_within(unfoldedTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(matrixform)
end test
test unfoldings_of_tensor4
integer,parameter :: d1=2,d2=3,d3=4,d4=3
type(Tensor4) :: aTensor
type(Tensor2) :: unfoldedTensor,CorrectTensor
complex(8) :: data(d1,d2,d3,d4)
complex(8),allocatable :: matrixform(:,:)
integer :: i1,i2,i3,i4
forall (i1=1:d1, i2=1:d2, i3=1:d3, i4=1:d4) data(i1,i2,i3,i4)=one*(i1*1000+i2*100+II*10*i3+i4)
aTensor=new_Tensor(data)
unfoldedTensor=aTensor.unfold.1
allocate(matrixform( d1,d2*d3*d4 ))
forall (i1=1:d1, i2=1:d2, i3=1:d3,i4=1:d4) matrixform (i1,(i4-1)*d2*d3+(i3-1)*d2+i2)=one*(i1*1000+i2*100+II*10*i3+i4)
CorrectTensor=new_Tensor(matrixform)
assert_equal_within(unfoldedTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(matrixform)
unfoldedTensor=aTensor.unfold.2
allocate(matrixform( d2,d1*d3*d4 ))
forall (i1=1:d1, i2=1:d2, i3=1:d3,i4=1:d4) matrixform (i2,(i4-1)*d1*d3+(i3-1)*d1+i1)=one*(i1*1000+i2*100+II*10*i3+i4)
CorrectTensor=new_Tensor(matrixform)
assert_equal_within(unfoldedTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(matrixform)
unfoldedTensor=aTensor.unfold.3
allocate(matrixform( d3,d2*d1*d4 ))
forall (i1=1:d1, i2=1:d2, i3=1:d3,i4=1:d4) matrixform (i3,(i4-1)*d2*d1+(i1-1)*d2+i2)=one*(i1*1000+i2*100+II*10*i3+i4)
CorrectTensor=new_Tensor(matrixform)
assert_equal_within(unfoldedTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(matrixform)
unfoldedTensor=aTensor.unfold.4
allocate(matrixform( d4,d2*d3*d1 ))
forall (i1=1:d1, i2=1:d2, i3=1:d3,i4=1:d4) matrixform (i4,(i1-1)*d2*d3+(i3-1)*d2+i2)=one*(i1*1000+i2*100+II*10*i3+i4)
CorrectTensor=new_Tensor(matrixform)
assert_equal_within(unfoldedTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(matrixform)
end test
test unfoldings_of_tensor5
integer,parameter :: d1=2,d2=3,d3=4,d4=3,d5=2
type(Tensor5) :: aTensor
type(Tensor2) :: unfoldedTensor,CorrectTensor
complex(8) :: data(d1,d2,d3,d4,d5)
complex(8),allocatable :: matrixform(:,:)
integer :: i1,i2,i3,i4,i5
forall (i1=1:d1, i2=1:d2, i3=1:d3, i4=1:d4,i5=1:d5) data(i1,i2,i3,i4,i5)=one*(i1*1000+i2*100+II*10*i3+i4+II*i5)
aTensor=new_Tensor(data)
unfoldedTensor=aTensor.unfold.1
allocate(matrixform( d1,d2*d3*d4*d5 ))
forall (i1=1:d1, i2=1:d2, i3=1:d3,i4=1:d4,i5=1:d5) matrixform (i1,(i5-1)*d2*d3*d4+(i4-1)*d2*d3+(i3-1)*d2+i2)=one*(i1*1000+i2*100+II*10*i3+i4+II*i5)
CorrectTensor=new_Tensor(matrixform)
assert_equal_within(unfoldedTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(matrixform)
unfoldedTensor=aTensor.unfold.2
allocate(matrixform( d2,d1*d3*d4*d5 ))
forall (i1=1:d1, i2=1:d2, i3=1:d3,i4=1:d4,i5=1:d5) matrixform (i2,(i5-1)*d1*d3*d4+(i4-1)*d1*d3+(i3-1)*d1+i1)=one*(i1*1000+i2*100+II*10*i3+i4+II*i5)
CorrectTensor=new_Tensor(matrixform)
assert_equal_within(unfoldedTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(matrixform)
unfoldedTensor=aTensor.unfold.3
allocate(matrixform( d3,d2*d1*d4*d5 ))
forall (i1=1:d1, i2=1:d2, i3=1:d3,i4=1:d4,i5=1:d5) matrixform (i3,(i5-1)*d2*d1*d4+(i4-1)*d2*d1+(i1-1)*d2+i2)=one*(i1*1000+i2*100+II*10*i3+i4+II*i5)
CorrectTensor=new_Tensor(matrixform)
assert_equal_within(unfoldedTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(matrixform)
unfoldedTensor=aTensor.unfold.4
allocate(matrixform( d4,d2*d3*d1*d5 ))
forall (i1=1:d1, i2=1:d2, i3=1:d3,i4=1:d4,i5=1:d5) matrixform (i4,(i5-1)*d2*d3*d1+(i1-1)*d2*d3+(i3-1)*d2+i2)=one*(i1*1000+i2*100+II*10*i3+i4+II*i5)
CorrectTensor=new_Tensor(matrixform)
assert_equal_within(unfoldedTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(matrixform)
unfoldedTensor=aTensor.unfold.5
allocate(matrixform( d5,d2*d3*d1*d4 ))
forall (i1=1:d1, i2=1:d2, i3=1:d3,i4=1:d4,i5=1:d5) matrixform (i5,(i1-1)*d2*d3*d4+(i4-1)*d2*d3+(i3-1)*d2+i2)=one*(i1*1000+i2*100+II*10*i3+i4+II*i5)
CorrectTensor=new_Tensor(matrixform)
assert_equal_within(unfoldedTensor.absdiff.correctTensor, 0.0d0, 1.0e-8)
deallocate(matrixform)
end test
test matrix_product
integer,parameter :: DLeft=6,DRight=8
type(Tensor2) :: mat,mat1, mat2,correct
complex(8) :: data(DLeft,DLeft),data1(DLeft,DRight),data2(DRight,DLeft)
integer i,j
forall (i=1:Dleft ,j=1:Dright) &
& data1(i,j)=one*(exp(II*i*Pi/DLeft)+(j-1)*Dleft)
forall (j=1:Dleft ,i=1:Dright) &
& data2(i,j)=one*(exp(II*i*Pi/100)+(j-1)*DRight*6)
data=matmul(data1, data2)
correct=new_Tensor(data)
mat1=new_Tensor(data1)
mat2=new_Tensor(data2)
mat=mat1*mat2
assert_equal_within(mat .absdiff. correct, 0.0d0, 1.0e-10)
end test
test Singular_Value_Decomposition
integer,parameter :: LeftDimension=6,RightDimension=8
type(Tensor2) :: aMatrix,theU,theVt
type(Tensor2) :: theSigma
complex(8) :: data(LeftDimension,RightDimension)
integer :: i,j,k
print *,'Test: Singular_Value_Decomposition'
!Input value is somewhat regular, perhaps try with random data at some point
forall (i=1:LeftDimension ,j=1:RightDimension) &
& data(i,j)=one*(exp(II*i*Pi/LeftDimension)+(j-1)*LeftDimension)
!Input value is somewhat regular, perhaps try with random data at some point
aMatrix=new_Tensor(data)
call aMatrix%SVD(theU,theSigma,theVt)
!Now test if the three output matrices form the original one
assert_equal_within(aMatrix.absdiff.(theU*(theSigma*theVt)), 0.0d0, 1.0e-10)
assert_false(WasThereError())
end test
test Singular_Value_Decomposition_T3
integer,parameter :: LeftDimension=3,RightDimension=3,CenterDimension=3
type(Tensor3) :: theTensor,theCore,correctCore,reconstructed
type(Tensor2) :: theUmatrices(3),correctUs(3)
complex(8) :: data(LeftDimension,CenterDimension,RightDimension),correctcenter(LeftDimension,CenterDimension,RightDimension)
complex(8) :: correctmatrices(3,LeftDimension,CenterDimension),signchange(3,LeftDimension,CenterDimension)
integer :: n
!Order needs to be changed so that it is the same as the example 4 from
!De Lathauwer et al. A multilinear singular value decomposition. SIAM Journal on Matrix Analysis and Applications (2000) vol. 21 (4) pp. 1253-1278
data= reshape ( ONE*[0.9073d0, 0.7158d0, -0.3698d0, 1.7842d0, 1.6970d0, 0.0151d0, 2.1236d0, -0.0740d0, 1.4429d0, &
& 0.8924d0, -0.4898d0, 2.4288d0, 1.7753d0, -1.5077d0, 4.0337d0, -0.6631d0, 1.9103d0, -1.7495d0, &
& 2.1488d0, 0.3054d0, 2.3753d0, 4.2495d0, 0.3207d0, 4.7146d0, 1.8260d0, 2.1335d0, -0.2716d0], [LeftDimension,CenterDimension,RightDimension], ORDER=[3,2,1])
correctCenter = reshape ( [ 8.7088d0, 0.0489d0, -0.2797d0, 0.1066d0, 3.2737d0, 0.3223d0, -0.0033d0, -0.1797d0, -0.2222d0, &
& -0.0256d0, 3.2546d0, -0.2853d0, 3.1965d0, -0.2130d0, 0.7829d0, 0.2948d0, -0.0378d0, -0.3704d0, &
& 0.0000d0, 0.0000d0, 0.0000d0, 0.0000d0, 0.0000d0, 0.0000d0, 0.0000d0, 0.0000d0, 0.0000d0], [LeftDimension,CenterDimension,RightDimension], ORDER=[3,2,1])
theTensor=new_Tensor(data)
correctCore=new_Tensor(correctCenter)
correctmatrices(1,:,:) = reshape([0.1121d0, 0.5771d0, 0.8090d0, -0.7739d0, 0.5613d0, -0.2932d0,-0.6233d0, -0.5932d0, 0.5095d0], [3,3] )
correctmatrices(2,:,:) = reshape([0.4624d0,0.8866d0, -0.0072d0,0.0102d0, -0.0135d0, -0.9999d0,0.8866d0,-0.4623d0, 0.0152d0], [3,3] )
correctmatrices(3,:,:) = reshape([0.6208d0, -0.0575d0, 0.7819d0, -0.4986d0, -0.7986d0, 0.3371d0, 0.6050d0, -0.5992d0, -0.5244d0], [3,3])
signchange=ZERO
!Each computed matrix shows up with a sign (hopefully compensated by the core tensor sign)
!But for the test I have to fix this by hand
signchange(1,1,1)=-ONE
signchange(1,2,2)=-ONE
signchange(1,3,3)=ONE
signchange(2,1,1)=-ONE
signchange(2,2,2)=ONE
signchange(2,3,3)=ONE
signchange(3,1,1)=-ONE
signchange(3,2,2)=ONE
signchange(3,3,3)=-ONE
do n=1,3
correctUs(n)=new_Tensor(matmul(correctmatrices(n,:,:),signchange(n,:,:)))
enddo
call theTensor%SVD(theCore,theUmatrices)
!See if all matrices are allright
assert_equal_within(correctUs(1).absdiff.(theUMatrices(1)), 0.0d0, 1.0e-3)
assert_equal_within(correctUs(2).absdiff.theUMatrices(2), 0.0d0, 1.0e-3)
assert_equal_within(correctUs(3).absdiff.theUMatrices(3), 0.0d0, 1.0e-3)
! call theCore%Print('Core Info')
! assert_equal_within(correctCore.absdiff.theCore, 0.0d0, 1.0e-10)
reconstructed=nModeProduct(theUMatrices(3),nModeProduct(theUMatrices(2),nModeProduct(theUMatrices(1),theCore,FIRST),SECOND),THIRD)
!Now test if the three output matrices form the original one
assert_equal_within(theTensor.absdiff. reconstructed, 0.0d0, 1.0e-10)
assert_false(WasThereError())
end test
test Singular_Value_Decomposition_T4
integer,parameter :: dim1=3,dim2=4,dim3=2,dim4=3,dim5=2
type(Tensor4) :: theTensor,theCore,correctCore,reconstructed
type(Tensor2) :: theUmatrices(4)
theTensor=new_Tensor(dim1,dim2,dim3,dim4)
call theTensor%SVD(theCore,theUmatrices)
reconstructed=nModeProduct(theUMatrices(4),nModeProduct(theUMatrices(3), &
& nModeProduct(theUMatrices(2),nModeProduct(theUMatrices(1),theCore,FIRST),SECOND),THIRD),FOURTH)
assert_equal_within(theTensor.absdiff. reconstructed, 0.0d0, 1.0e-4)
assert_false(WasThereError())
end test
test Singular_Value_Decomposition_T5
integer,parameter :: dim1=3,dim2=4,dim3=2,dim4=3,dim5=2
type(Tensor5) :: theTensor,theCore,correctCore,reconstructed
type(Tensor2) :: theUmatrices(5)
complex(8) :: data(dim1,dim2,dim3,dim4,dim5)
integer :: i,j,k,l,m
data=ZERO
forall (i=1:dim1 ,j=1:dim2,k=1:dim3, l=1:dim4, m=1:dim5) &
& data(i,j,k,l,m)=one*(exp(II*i*Pi/dim1)+(j-1)*dim4+l*k)
! do i=1,dim5
! data(:,:,:,:,i)=ZERO
! enddo
theTensor=new_Tensor(data)
! theTensor=new_Tensor(dim1,dim2,dim3,dim4,dim5)
call theTensor%SVD(theCore,theUmatrices)
reconstructed=nModeProduct(theUMatrices(5),nModeProduct(theUMatrices(4),nModeProduct(theUMatrices(3), &
& nModeProduct(theUMatrices(2),nModeProduct(theUMatrices(1),theCore,FIRST),SECOND),THIRD),FOURTH),FIFTH)
assert_equal_within(theTensor.absdiff. reconstructed, 0.0d0, 1.0e-4)
assert_false(WasThereError())
end test
test Right_Compactification
type(Tensor3) :: T_Tensor
type(Tensor2) :: T_Compacted,T_Matrix,T_Correct
integer,parameter :: DleftT=4, DrightT=3,spinT=2
complex(8) :: data(DleftT,DrightT,spinT)
complex(8) :: matrix(DrightT,DrightT)
complex(8) :: CorrectResult(DleftT,DleftT)
integer n,i,j,k,s
do i=1,DleftT
do j=1,DrightT
do s=1,spinT
data(i,j,s)=one*(i+(j-1)*DleftT+(s-1)*DrightT)
enddo
enddo
enddo
do i=1,DrightT
do j=1,DrightT
matrix(i,j)=(ii**i+(j-1)*DrightT)
enddo
enddo
CorrectResult=one*reshape([3072 - 312*ii, 3528 - 312*ii, 3984 - 312*ii, 4440 - 312*ii, 3384 - &
& 360*ii, 3888 - 360*ii, 4392 - 360*ii, 4896 - 360*ii, 3696 - &
& 408*ii, 4248 - 408*ii, 4800 - 408*ii, 5352 - 408*ii, 4008 - &
& 456*ii, 4608 - 456*ii, 5208 - 456*ii, 5808 - 456*ii], [DleftT,DleftT] )
T_Tensor=new_Tensor(data)
T_Matrix=new_Tensor(matrix)
T_Correct=new_Tensor(CorrectResult)
T_Compacted=CompactRight(T_Matrix,T_Tensor,Conjugate(T_Tensor),THiRD)
assert_equal_within(T_Compacted.absdiff.T_Correct, 0.0d0, 1.0e-8)
end test
test Left_Compactification
!
! Mathematica code: NOTiCE THE TRANSPOSE TO GET THE ORDER RiGHT
! With[{DL = 3, DR = 4, spin = 2},
! At = Table[
! DR*(s - 1) + (j - 1)*DL + i, {s, 1, 2}, {i, 1, DL}, {j, 1, DR}];
! mat = Table[i^i + (j - 1)*DL, {i, 1, DL}, {j, 1, DL}]];
! Flatten[Transpose[LProduct[At, At, mat]]]
!
type(Tensor3) :: T_Tensor
type(Tensor2) :: T_Compacted,T_Matrix,T_Correct
integer,parameter :: DleftT=3, DrightT=4,spinT=2
complex(8) :: matrix(DleftT,DleftT)
complex(8) :: CorrectResult(DrightT,DrightT)
complex(8) :: data(DleftT,DrightT,spinT)
integer n,i,j,k,s
do i=1,DleftT
do j=1,DrightT
do s=1,spinT
data(i,j,s)=one*(i+(j-1)*DleftT+(s-1)*DrightT)
enddo
enddo
enddo
do i=1,DleftT
do j=1,DleftT
matrix(i,j)=(ii**i+(j-1)*DleftT)
enddo
enddo
CorrectResult=one*reshape([1104 - 48*ii, 1788 - 48*ii, 2472 - 48*ii, 3156 - 48*ii, 1680 - &
& 84*ii, 2796 - 84*ii, 3912 - 84*ii, 5028 - 84*ii, 2256 - 120*ii, 3804 - &
& 120*ii, 5352 - 120*ii, 6900 - 120*ii, 2832 - 156*ii, 4812 - &
& 156*ii, 6792 - 156*ii, 8772 - 156*ii], [DrightT,DrightT] )
T_Tensor=new_Tensor(data)
T_Matrix=new_Tensor(matrix)
T_Correct=new_Tensor(CorrectResult)
T_Compacted=CompactLeft(T_Matrix,T_Tensor,Conjugate(T_Tensor),THiRD)
assert_equal_within(T_Compacted.absdiff.T_Correct, 0.0d0, 1.0e-8)
end test
test Compact_From_Below_T3_T4
!Mathematica Code:
!
!T3 = Table[a*100 + b*10 + 1.0 c, {a, 1, 2}, {b, 1, 3}, {c, 1, 4}];
!T4 = Table[a*1000 + b*100 + c 10.0 + d I, {a, 1, 2}, {b, 1, 2}, {c, 1, 2}, {d,1, 2}];
!math = Round[
! Flatten[Transpose[T3, {3, 1, 2}].Transpose[
! T4, {2, 3, 1, 4}], {{5}, {3, 1}, {4, 2}}]];
!Flatten[Transpose[math, {3, 2, 1}]]
type(Tensor3) :: aT3,correct,result
type(Tensor4) :: aT4
complex(8) :: origArray(2,3,4), origTensor(2,2,2,2), correctArray(2,6,8)
integer :: i,j,k,l
forall (i=1:2, j=1:3, k=1:4) origArray(i,j,k)=100*i+10*j+k
forall (i=1:2, j=1:2, k=1:2, l=1:2) origTensor(i,j,k,l)=1000*i+100*j+10*k+ii*l
correctArray= ONE*reshape( [359530 + 322 *II, 359530 + 644 *II, 381830 + 342 *II, 381830 + &
& 684 *II, 404130 + 362 *II, 404130 + 724 *II, 681530 + 322 *II, 681530 + &
& 644 *II, 723830 + 342 *II, 723830 + 684 *II, 766130 + 362 *II, 766130 + &
& 724 *II, 361760 + 324 *II, 361760 + 648 *II, 384060 + 344 *II, 384060 + &
& 688 *II, 406360 + 364 *II, 406360 + 728 *II, 685760 + 324 *II, 685760 + &
& 648 *II, 728060 + 344 *II, 728060 + 688 *II, 770360 + 364 *II, 770360 + &
& 728 *II, 363990 + 326 *II, 363990 + 652 *II, 386290 + 346 *II, 386290 + &
& 692 *II, 408590 + 366 *II, 408590 + 732 *II, 689990 + 326 *II, 689990 + &
& 652 *II, 732290 + 346 *II, 732290 + 692 *II, 774590 + 366 *II, 774590 + &
& 732 *II, 366220 + 328 *II, 366220 + 656 *II, 388520 + 348 *II, 388520 + &
& 696 *II, 410820 + 368 *II, 410820 + 736 *II, 694220 + 328 *II, 694220 + &
& 656 *II, 736520 + 348 *II, 736520 + 696 *II, 778820 + 368 *II, 778820 + &
& 736 *II, 391730 + 322 *II, 391730 + 644 *II, 416030 + 342 *II, 416030 + &
& 684 *II, 440330 + 362 *II, 440330 + 724 *II, 713730 + 322 *II, 713730 + &
& 644 *II, 758030 + 342 *II, 758030 + 684 *II, 802330 + 362 *II, 802330 + &
& 724 *II, 394160 + 324 *II, 394160 + 648 *II, 418460 + 344 *II, 418460 + &
& 688 *II, 442760 + 364 *II, 442760 + 728 *II, 718160 + 324 *II, 718160 + &
& 648 *II, 762460 + 344 *II, 762460 + 688 *II, 806760 + 364 *II, 806760 + &
& 728 *II, 396590 + 326 *II, 396590 + 652 *II, 420890 + 346 *II, 420890 + &
& 692 *II, 445190 + 366 *II, 445190 + 732 *II, 722590 + 326 *II, 722590 + &
& 652 *II, 766890 + 346 *II, 766890 + 692 *II, 811190 + 366 *II, 811190 + &
& 732 *II, 399020 + 328 *II, 399020 + 656 *II, 423320 + 348 *II, 423320 + &
& 696 *II, 447620 + 368 *II, 447620 + 736 *II, 727020 + 328 *II, 727020 + &
& 656 *II, 771320 + 348 *II, 771320 + 696 *II, 815620 + 368 *II, 815620 + 736 *II ], [2,6,8] )
aT3=new_Tensor(origArray)
aT4=new_Tensor(origTensor)
correct=new_Tensor(correctArray)
result=CompactBelow(aT3,FIRST,aT4,THIRD,FOURTH)
assert_equal_within(result.absdiff.correct, 0.0d0, 1.0e-8)
end test
test nModeProducts_3
type(Tensor3) :: T3_result,T3_Tensor,T3_Correct
type(Tensor2) :: T_Matrix
integer,parameter :: d1=2,d2=3,d3=4,dNew=5
real(8) :: matrixR(dNew,d2),t3R(d1,d2,d3)
real(8) :: matrixI(dNew,d2),t3I(d1,d2,d3)
complex(8) :: Correct3(d1,dNew,d3)
call random_number(matrixR)
call random_number(matrixI)
call random_number(t3R)
call random_number(t3I)
T_Matrix=new_Tensor(matrixR+II*MatrixI)
T3_Tensor=new_Tensor(t3R+II*t3I)
T3_Correct= TensorTranspose( T_Matrix * TensorTranspose(T3_Tensor,[2,1,3]) ,[2,1,3])
T3_Result=nModeProduct(T_matrix,T3_Tensor,SECOND)
assert_equal_within(T3_result.absdiff.T3_correct, 0.0d0, 1.0e-8)
end test
test nModeProducts_5
type(Tensor5) :: T5_result,T5_Tensor,T5_Correct
type(Tensor2) :: T_Matrix
integer,parameter :: d1=3,d2=3,d3=3,d4=3,d5=3,dNew=3
real(8) :: matrixR(dNew,d3),t5R(d1,d2,d3,d4,d5)
real(8) :: matrixI(dNew,d3),t5I(d1,d2,d3,d4,d5)
call random_number(matrixR)
call random_number(matrixI)
call random_number(t5R)
call random_number(t5I)
T_Matrix=new_Tensor(matrixR+II*MatrixI)
T5_Tensor=new_Tensor(t5R+II*t5I)
T5_Correct= TensorTranspose( T_Matrix * TensorTranspose(T5_Tensor,[1,2,3,4,5]) ,[1,2,3,4,5])
T5_Result= nModeProduct(T_matrix,T5_Tensor,FIRST)
assert_equal_within(T5_result.absdiff.T5_correct, 0.0d0, 1.0e-8)
T5_Correct= TensorTranspose( T_Matrix * TensorTranspose(T5_Tensor,[2,1,3,4,5]) ,[2,1,3,4,5])
T5_Result= nModeProduct(T_matrix,T5_Tensor,SECOND)
assert_equal_within(T5_result.absdiff.T5_correct, 0.0d0, 1.0e-8)
T5_Correct= TensorTranspose( T_Matrix * TensorTranspose(T5_Tensor,[3,2,1,4,5]) ,[3,2,1,4,5])
T5_Result= nModeProduct(T_matrix,T5_Tensor,THIRD)
assert_equal_within(T5_result.absdiff.T5_correct, 0.0d0, 1.0e-8)
T5_Correct= TensorTranspose( T_Matrix * TensorTranspose(T5_Tensor,[4,2,3,1,5]) ,[4,2,3,1,5])
T5_Result= nModeProduct(T_matrix,T5_Tensor,FOURTH)
assert_equal_within(T5_result.absdiff.T5_correct, 0.0d0, 1.0e-8)
T5_Correct= TensorTranspose( T_Matrix * TensorTranspose(T5_Tensor,[5,2,3,4,1]) ,[5,2,3,4,1])
T5_Result= nModeProduct(T_matrix,T5_Tensor,FIFTH)
assert_equal_within(T5_result.absdiff.T5_correct, 0.0d0, 1.0e-8)
end test
test Matrices_times_tensor3s
type(Tensor3) :: T_result,T_Tensor,T_Correct
type(Tensor2) :: T_Matrix
integer,parameter :: left=2,center=3,right=4
complex(8) :: matrixL(center,left),matrixR(right,left)
complex(8) :: CorrectL(center,center,right),correctR(left,center,left)
complex(8) :: tensorarray(left,center,right)
integer n,i,j,k,s
forall (i=1:left, j=1:center, k=1:right) tensorarray(i,j,k)=1000*i+100*j*II+10*k
forall (i=1:center, j=1:left) matrixL(i,j)=127*i+13*j*II
forall (i=1:right, j=1:left) matrixR(i,j)=41*i+7*j*II
do k=1,right
do j=1,center
do i=1,center
correctL(i,j,k)=sum( matrixL(i,:)*tensorarray(:,j,k) )!dot_product(dconjg(matrixL(i,:)),tensorarray(:,j,k))
enddo
enddo
enddo
T_Tensor=new_Tensor(tensorarray)
T_matrix=new_Tensor(matrixL)
T_result=T_matrix*T_Tensor
T_correct=new_Tensor(correctL)
assert_equal_within(T_result.absdiff.T_correct, 0.0d0, 1.0e-8)
do k=1,left
do j=1,center
do i=1,left
correctR(i,j,k)=sum( tensorarray(i,j,:) * matrixR(:,k) )
enddo
enddo
enddo
T_matrix=new_Tensor(matrixR)
T_result=T_Tensor*T_matrix
T_correct=new_Tensor(correctR)
assert_equal_within(T_result.absdiff.T_correct, 0.0d0, 1.0e-8)
end test
test tensor5JoinandSplit
type(tensor5) :: t5, newT5
type(tensor2) :: t2
integer :: dims(5)
dims = [3,2,4,5,2]
t5=new_Tensor(dims(1), dims(2), dims(3), dims(4), dims(5) )
t2=t5%JoinIndices()
newT5=SplitIndexOf(t2,dims)
assert_equal_within(t5.absdiff.newT5, 0.0d0, 1.0e-10)
assert_false(WasThereError())
end test
test xplusWithTensor4
type(tensor4) :: aT4,anotherT4,newT4,correctT4
integer,parameter :: lft=4,rgt=5,ump=2,dwn=3
real(8) :: data1R(lft,rgt),data1I(lft,rgt),data2R(rgt,lft),data2I(rgt,lft)
complex(8) :: fulltensor1(lft,rgt,ump,dwn), fulltensor2(rgt,lft,ump,dwn),correctTensor(lft,lft,ump*ump,dwn*dwn)
integer :: i,j,k,l
do i=1,ump
do j=1,dwn
call random_number(data1R)
call random_number(data1I)
call random_number(data2R)
call random_number(data2I)
fulltensor1(:,:,i,j)=data1R+II*data1I
fulltensor2(:,:,i,j)=data2R+II*data2I
enddo
enddo
correctTensor=ZERO
do i=1,ump
do j=1,ump
do k=1,dwn
do l=1,dwn
correctTensor(:,:,(j-1)*ump+i,(l-1)*dwn+k)=matmul(fulltensor1(:,:,i,k),fulltensor2(:,:,j,l))
enddo
enddo
enddo
enddo
correctT4=new_Tensor(correctTensor)
aT4=new_Tensor(fulltensor1)
anotherT4=new_Tensor(fulltensor2)
newT4=aT4.xplus.anotherT4
assert_equal_within(newT4.absdiff.correctT4,0.0d0,1.0e-10)
end test
test TensorTraceWithTensor4
type(tensor4) :: aT4
type(tensor2) :: aT2,correctT2
integer,parameter :: lft=5,rgt=5,ump=2,dwn=3
real(8) :: dataR(lft,rgt),dataI(lft,rgt)
complex(8) :: fulltensor(lft,rgt,ump,dwn), correctTensor(ump,dwn)
integer :: i,j,k,l
print *,'Test: TensorTraceWithTensor4'
do i=1,ump
do j=1,dwn
call random_number(dataR)
call random_number(dataI)
fulltensor(:,:,i,j)=dataR+II*dataI
enddo
enddo
correctTensor=ZERO
do i=1,ump
do j=1,dwn
do k=1,lft
correctTensor(i,j)=correctTensor(i,j)+ (fulltensor(k,k,i,j))
enddo
enddo
enddo
correctT2=new_Tensor(correctTensor)
aT4=new_Tensor(fulltensor)
aT2=TensorTrace(aT4,THIRDANDFOURTH)
! assert_true(aT2%GetDimensions().equalvector.[ump,dwn])
assert_equal_within(aT2.absdiff.correctT2,0.0d0,1.0e-10)
end test
test LinearSolver
integer,parameter :: lft=5,rgt=2
real(8) :: tempR(lft,lft),tempI(lft,lft),vecR(lft,rgt),vecI(lft,rgt)
complex(8) :: thedata(lft,lft),vectordata(lft,rgt)
type(tensor2) :: matrix,vector,solution,originalMatrix
integer :: errorpoint
call random_number(tempR)
call random_number(tempI)
thedata=tempR+II*tempI
call random_number(vecR)
call random_number(vecI)
vectordata=vecR+II*vecI
vector=new_Tensor(vectorData)
matrix=new_Tensor(thedata)
originalMatrix=new_Tensor(matrix)
solution=SolveLinearProblem(matrix, vector, 1.0d-8 )
assert_equal_within( matrix * solution.absdiff.vector,0.0d0,1.0d-8)
!call ZGELSD( thedata, vectordata, 1.0d-8 )
end test
end test_suite