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179 lines
8.6 KiB
ReStructuredText
179 lines
8.6 KiB
ReStructuredText
============
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Utils Module
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============
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Contains general purpose utilities.
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Documentation
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=============
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.. Do not edit this section. It was auto-generated from the
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.. NEEDED_MODULES file.
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`apply_rotation <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L/subroutine apply_rotation(A,LDA,R,LDR,B,LDB,m,n)/;">`_
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Apply the rotation found by find_rotation
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`find_rotation <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L/subroutine find_rotation(A,LDA,B,m,C,n)/;">`_
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Find A.C = B
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`get_pseudo_inverse <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L/subroutine get_pseudo_inverse(A,m,n,C,LDA)/;">`_
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Find C = A^-1
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`lapack_diag <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L/subroutine lapack_diag(eigvalues,eigvectors,H,nmax,n)/;">`_
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Diagonalize matrix H
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.br
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H is untouched between input and ouptut
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.br
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eigevalues(i) = ith lowest eigenvalue of the H matrix
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.br
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eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
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.br
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`ortho_lowdin <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L/subroutine ortho_lowdin(overlap,LDA,N,C,LDC,m)/;">`_
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Compute C_new=C_old.S^-1/2 canonical orthogonalization.
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.br
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overlap : overlap matrix
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.br
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LDA : leftmost dimension of overlap array
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.br
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N : Overlap matrix is NxN (array is (LDA,N) )
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.br
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C : Coefficients of the vectors to orthogonalize. On exit,
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orthogonal vectors
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.br
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LDC : leftmost dimension of C
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.br
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m : Coefficients matrix is MxN, ( array is (LDC,N) )
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.br
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`add_poly <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/subroutine add_poly(b,nb,c,nc,d,nd)/;">`_
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Add two polynomials
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D(t) =! D(t) +( B(t)+C(t))
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`add_poly_multiply <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/subroutine add_poly_multiply(b,nb,cst,d,nd)/;">`_
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Add a polynomial multiplied by a constant
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D(t) =! D(t) +( cst * B(t))
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`f_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/double precision function F_integral(n,p)/;">`_
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function that calculates the following integral
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\int_{\-infty}^{+\infty} x^n \exp(-p x^2) dx
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`gaussian_product <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/subroutine gaussian_product(a,xa,b,xb,k,p,xp)/;">`_
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Gaussian product in 1D.
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e^{-a (x-x_A)^2} e^{-b (x-x_B)^2} = K_{ab}^x e^{-p (x-x_P)^2}
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`gaussian_product_x <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/subroutine gaussian_product_x(a,xa,b,xb,k,p,xp)/;">`_
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Gaussian product in 1D.
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e^{-a (x-x_A)^2} e^{-b (x-x_B)^2} = K_{ab}^x e^{-p (x-x_P)^2}
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`give_explicit_poly_and_gaussian <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/subroutine give_explicit_poly_and_gaussian(P_new,P_center,p,fact_k,iorder,alpha,beta,a,b,A_center,B_center,dim)/;">`_
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Transforms the product of
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(x-x_A)^a(1) (x-x_B)^b(1) (x-x_A)^a(2) (y-y_B)^b(2) (z-z_A)^a(3) (z-z_B)^b(3) exp(-(r-A)^2 alpha) exp(-(r-B)^2 beta)
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into
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fact_k * [ sum (l_x = 0,i_order(1)) P_new(l_x,1) * (x-P_center(1))^l_x ] exp (- p (x-P_center(1))^2 )
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* [ sum (l_y = 0,i_order(2)) P_new(l_y,2) * (y-P_center(2))^l_y ] exp (- p (y-P_center(2))^2 )
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* [ sum (l_z = 0,i_order(3)) P_new(l_z,3) * (z-P_center(3))^l_z ] exp (- p (z-P_center(3))^2 )
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`give_explicit_poly_and_gaussian_x <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/subroutine give_explicit_poly_and_gaussian_x(P_new,P_center,p,fact_k,iorder,alpha,beta,a,b,A_center,B_center,dim)/;">`_
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Transform the product of
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(x-x_A)^a(1) (x-x_B)^b(1) (x-x_A)^a(2) (y-y_B)^b(2) (z-z_A)^a(3) (z-z_B)^b(3) exp(-(r-A)^2 alpha) exp(-(r-B)^2 beta)
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into
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fact_k (x-x_P)^iorder(1) (y-y_P)^iorder(2) (z-z_P)^iorder(3) exp(-p(r-P)^2)
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`hermite <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/double precision function hermite(n,x)/;">`_
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Hermite polynomial
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`multiply_poly <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/subroutine multiply_poly(b,nb,c,nc,d,nd)/;">`_
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Multiply two polynomials
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D(t) =! D(t) +( B(t)*C(t))
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`recentered_poly2 <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/subroutine recentered_poly2(P_new,x_A,x_P,a,P_new2,x_B,x_Q,b)/;">`_
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Recenter two polynomials
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`rint <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/double precision function rint(n,rho)/;">`_
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.. math::
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.br
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\int_0^1 dx \exp(-p x^2) x^n
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.br
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`rint1 <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/double precision function rint1(n,rho)/;">`_
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Standard version of rint
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`rint_large_n <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/double precision function rint_large_n(n,rho)/;">`_
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Version of rint for large values of n
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`rint_sum <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L/double precision function rint_sum(n_pt_out,rho,d1)/;">`_
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Needed for the calculation of two-electron integrals.
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`overlap_gaussian_x <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/one_e_integration.irp.f#L/double precision function overlap_gaussian_x(A_center,B_center,alpha,beta,power_A,power_B,dim)/;">`_
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.. math::
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.br
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\sum_{-infty}^{+infty} (x-A_x)^ax (x-B_x)^bx exp(-alpha(x-A_x)^2) exp(-beta(x-B_X)^2) dx
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.br
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`overlap_gaussian_xyz <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/one_e_integration.irp.f#L/subroutine overlap_gaussian_xyz(A_center,B_center,alpha,beta,power_A,&>`_
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.. math::
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.br
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S_x = \int (x-A_x)^{a_x} exp(-\alpha(x-A_x)^2) (x-B_x)^{b_x} exp(-beta(x-B_x)^2) dx \\
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S = S_x S_y S_z
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.br
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`overlap_x_abs <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/one_e_integration.irp.f#L/subroutine overlap_x_abs(A_center,B_center,alpha,beta,power_A,power_B,overlap_x,lower_exp_val,dx,nx)/;">`_
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.. math ::
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.br
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\int_{-infty}^{+infty} (x-A_center)^(power_A) * (x-B_center)^power_B * exp(-alpha(x-A_center)^2) * exp(-beta(x-B_center)^2) dx
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.br
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`align_double <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/integer function align_double(n)/;">`_
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Compute 1st dimension such that it is aligned for vectorization.
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`all_utils <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/BEGIN_PROVIDER [ logical, all_utils ]/;">`_
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Dummy provider to provide all utils
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`binom <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/BEGIN_PROVIDER [ double precision, binom, (0:20,0:20) ]/;">`_
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Binomial coefficients
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`binom_func <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/double precision function binom_func(i,j)/;">`_
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.. math ::
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.br
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\frac{i!}{j!(i-j)!}
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.br
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`binom_transp <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/&BEGIN_PROVIDER [ double precision, binom_transp, (0:20,0:20) ]/;">`_
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Binomial coefficients
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`dble_fact <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/double precision function dble_fact(n) result(fact2)/;">`_
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n!!
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`fact <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/double precision function fact(n)/;">`_
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n!
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`fact_inv <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/BEGIN_PROVIDER [ double precision, fact_inv, (128) ]/;">`_
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1/n!
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`inv_int <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/BEGIN_PROVIDER [ double precision, inv_int, (128) ]/;">`_
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1/i
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`normalize <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/subroutine normalize(u,sze)/;">`_
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Normalizes vector u
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u is expected to be aligned in memory.
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`nproc <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/BEGIN_PROVIDER [ integer, nproc ]/;">`_
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Number of current OpenMP threads
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`u_dot_u <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/double precision function u_dot_u(u,sze)/;">`_
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Compute <u|u>
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`u_dot_v <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/double precision function u_dot_v(u,v,sze)/;">`_
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Compute <u|v>
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`wall_time <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/subroutine wall_time(t)/;">`_
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The equivalent of cpu_time, but for the wall time.
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`write_git_log <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L/subroutine write_git_log(iunit)/;">`_
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Write the last git commit in file iunit.
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