mirror of https://github.com/triqs/dft_tools
226 lines
8.5 KiB
Fortran
226 lines
8.5 KiB
Fortran
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c ******************************************************************************
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c
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c TRIQS: a Toolbox for Research in Interacting Quantum Systems
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c
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c Copyright (C) 2011 by L. Pourovskii, V. Vildosola, C. Martins, M. Aichhorn
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c
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c TRIQS is free software: you can redistribute it and/or modify it under the
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c terms of the GNU General Public License as published by the Free Software
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c Foundation, either version 3 of the License, or (at your option) any later
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c version.
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c
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c TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
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c WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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c FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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c details.
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c
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c You should have received a copy of the GNU General Public License along with
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c TRIQS. If not, see <http://www.gnu.org/licenses/>.
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c
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c *****************************************************************************/
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SUBROUTINE orthogonal_h(s1,ndim,inv)
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C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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C %% %%
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C %% This subroutine computes : %%
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C %% - if inv = .FALSE. the square root of the Hermitian matrix s1 %%
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C %% - if inv = .TRUE. the inverse of the square root of the %%
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C %% Hermitian matrix s1 %%
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C %% %%
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C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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C Definiton of the variables :
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C ----------------------------
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USE prnt
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IMPLICIT NONE
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INTEGER :: ndim, INFO, lm, lm1
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COMPLEX(KIND=8), DIMENSION(ndim) :: WORK
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COMPLEX(KIND=8), DIMENSION(ndim,ndim) :: s1
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INTEGER, DIMENSION(ndim,ndim) :: IPIV
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LOGICAL :: inv
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C
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C Calculation of S1^(1/2) or S1^(-1/2):
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C -------------------------------------
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CALL sqrtm(s1,ndim,inv)
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C The resulting matrix is stored in s1.
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RETURN
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END
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SUBROUTINE orthogonal_r(s2,ndim,inv)
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C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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C %% %%
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C %% This subroutine computes : %%
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C %% - if inv = .FALSE. the square root of s1 %%
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C %% - if inv = .TRUE. the inverse of the square root of s2 %%
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C %% where s2 is a real symmetric matrix. %%
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C %% %%
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C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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C Definiton of the variables :
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C ----------------------------
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USE prnt
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IMPLICIT NONE
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INTEGER :: ndim, INFO, lm, lm1
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COMPLEX(KIND=8), DIMENSION(ndim) :: WORK
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COMPLEX(KIND=8), DIMENSION(ndim,ndim) :: s1
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REAL(KIND=8), DIMENSION(ndim,ndim) :: s2
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INTEGER, DIMENSION(ndim,ndim) :: IPIV
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LOGICAL :: inv
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C
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C Calculation of S2^(1/2) or S2^(-1/2):
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C -------------------------------------
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s1=s2
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CALL sqrtm(s1,ndim,inv)
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s2=REAL(s1)
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C The resulting matrix is stored in s2.
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RETURN
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END
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SUBROUTINE sqrtm(cmat,m,inv)
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C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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C %% %%
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C %% This subroutine calculates the square root of a positively %%
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C %% defined Hermitian matrix A=cmat using the decomposition %%
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C %% A=Z*D*Z^H %%
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C %% where D is a diagonal matrix of eigenvalues of A, %%
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C %% Z is matrix of orthonormal eigenvectors of A, %%
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C %% Z^H is its Hermitian conjugate. %%
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C %% Then A^(1/2)=Z*D^(1/2)*Z^H. %%
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C %% Correction: the matrix A is allowed to be negatively defined. %%
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C %% %%
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C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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C Definiton of the variables :
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C ----------------------------
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IMPLICIT NONE
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INTEGER :: m
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COMPLEX(KIND=8), DIMENSION(m,m):: cmat, D, D1
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LOGICAL :: inv
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C Calculation of Z*D^(1/2):
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C -------------------------
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CALL sqrt_eigenvec(cmat,D1,m,inv)
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WRITE(95,*) cmat
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WRITE(95,*) ' '
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WRITE(95,*) D1
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WRITE(95,*) ' '
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C Calculation of A^(1/2)=Z*D^(1/2)*Z^H:
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C -------------------------------------
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D=CONJG(cmat)
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call ZGEMM('N','T',m,m,m,DCMPLX(1.D0,0.D0),D1,
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& m,D,m,DCMPLX(0.D0,0.D0),cmat,m)
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C The resulting matrix is stored in cmat.
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RETURN
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END
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SUBROUTINE sqrt_eigenvec(cmat,D1,m,inv)
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C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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C %% %%
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C %% This subroutine computes : %%
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C %% - if inv = .FALSE. Z*D^(1/2) %%
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C %% - if inv = .TRUE. Z*D^(-1/2) %%
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C %% where Z is a matrix of orthonormal eigenvectors of cmat and %%
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C %% D is the diagonal matrix of cmat's eigenvalues. %%
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C %% %%
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C %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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C Definiton of the variables :
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C ----------------------------
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USE prnt
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IMPLICIT NONE
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LOGICAL :: inv, ifwrite
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INTEGER :: m, INFO, i, j
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INTEGER, PARAMETER :: nwork=40
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C
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COMPLEX(KIND=8), allocatable, DIMENSION(:) :: WORK
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COMPLEX(KIND=8), DIMENSION(m,m) :: cmat, D1
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REAL(KIND=8), DIMENSION(m) :: W
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COMPLEX(KIND=8), DIMENSION(m) :: W_comp
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REAL(KIND=8), allocatable, DIMENSION(:) :: RWORK
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C
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C Finding the eigenvalues and the eigenvectors of cmat :
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C ------------------------------------------------------
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ALLOCATE(rwork(3*m-2))
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ALLOCATE(work(2*m-1))
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CALL ZHEEV('V', 'U', m, cmat, m, W, WORK,2*m-1,RWORK,INFO)
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IF (info.ne.0) THEN
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WRITE(buf,'(a)')
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& 'The subroutine zheev ends with info = ',info
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CALL printout(0)
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WRITE(buf,'(a)')'In sqrt_eigenvec, a pbm occurs in zheev.'
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CALL printout(0)
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WRITE(buf,'(a)')'END OF THE PRGM'
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CALL printout(0)
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STOP
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ENDIF
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C W contains the eigenvalues of cmat.
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W_comp=CMPLX(W,0d0)
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C
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C Checking of the validity of the computation :
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C ---------------------------------------------
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ifwrite=.FALSE.
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DO j=1,m
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C The warning is written only once in the file case.outdmftpr
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IF (ifwrite) EXIT
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C Checking if the eigenvalues are not negative.
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IF (W(j).lt.0.d0) THEN
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WRITE(buf,'(a,i2,a,a)')
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& 'WARNING : An eigenvalue (',j,') of the ',
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& 'overlap matrix is negative.'
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CALL printout(0)
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WRITE(buf,'(a,a)')' The result ',
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& 'of the calculation may thus be wrong.'
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CALL printout(1)
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ifwrite=.TRUE.
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ENDIF
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IF (ABS(W(j)).lt.1.d-12) THEN
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WRITE(buf,'(a,i2,a,a)')
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& 'WARNING : An eigenvalue (',j,') of the ',
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& 'overlap matrix is almost zero.'
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CALL printout(0)
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WRITE(buf,'(a,a)')' The result ',
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& 'of the calculation may thus be wrong.'
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CALL printout(1)
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ifwrite=.TRUE.
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ENDIF
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ENDDO
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C
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C Calculation of Z*D^(1/2) :
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C --------------------------
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C The result is stored in D1.
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IF(.NOT.inv) THEN
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DO i=1,m
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DO j=1,m
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D1(i,j)=cmat(i,j)*SQRT(W_comp(j))
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ENDDO
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ENDDO
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ELSE
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C Calculation of Z*D^(-1/2) :
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C ---------------------------
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C The result is stored in D1.
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DO i=1,m
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DO j=1,m
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IF (ABS(W(j))==0.d0) THEN
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WRITE(buf,'(a,i2,a)')
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& 'An eigenvalue (',j,') of the ',
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& 'overlap matrix has the value 0.'
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CALL printout(0)
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WRITE(buf,'(a)')
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& 'The calculation can not be performed further.'
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CALL printout(0)
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CALL printout(0)
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WRITE(buf,'(a)')'END OF THE PRGM'
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CALL printout(0)
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STOP
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ENDIF
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D1(i,j)=cmat(i,j)/SQRT(W_comp(j))
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ENDDO
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ENDDO
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ENDIF
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C The resulting matrix is stored in D1 and cmat is now Z.
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RETURN
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END
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