qp2/docs/source/modules/utils.rst

.. _module_utils: 
 
.. program:: utils 
 
.. default-role:: option 
 
=====
utils
=====

Contains general purpose utilities (sorting, maps, etc).

 
 
 
Providers 
--------- 
 
.. c:var:: binom


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        double precision, allocatable	:: binom	(0:40,0:40)
        double precision, allocatable	:: binom_transp	(0:40,0:40)


    Binomial coefficients

    Needed by:

    .. hlist::
       :columns: 3

       * :c:data:`binom_int`

 
.. c:var:: binom_int


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        integer*8, allocatable	:: binom_int	(0:40,0:40)
        integer*8, allocatable	:: binom_int_transp	(0:40,0:40)


    Binomial coefficients, as integers*8

    Needs:

    .. hlist::
       :columns: 3

       * :c:data:`binom`


 
.. c:var:: binom_int_transp


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        integer*8, allocatable	:: binom_int	(0:40,0:40)
        integer*8, allocatable	:: binom_int_transp	(0:40,0:40)


    Binomial coefficients, as integers*8

    Needs:

    .. hlist::
       :columns: 3

       * :c:data:`binom`


 
.. c:var:: binom_transp


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        double precision, allocatable	:: binom	(0:40,0:40)
        double precision, allocatable	:: binom_transp	(0:40,0:40)


    Binomial coefficients

    Needed by:

    .. hlist::
       :columns: 3

       * :c:data:`binom_int`

 
.. c:var:: degree_max_integration_lebedev


    File : :file:`utils/angular_integration.irp.f`

    .. code:: fortran

        integer	:: degree_max_integration_lebedev	


    integrate correctly a polynom of order "degree_max_integration_lebedev"
    needed for the angular integration according to LEBEDEV formulae

    Needed by:

    .. hlist::
       :columns: 3

       * :c:data:`n_points_integration_angular_lebedev`
       * :c:data:`theta_angular_integration_lebedev`

 
.. c:function:: dtranspose:


    File : :file:`utils/transpose.irp.f`

    .. code:: fortran

        recursive subroutine dtranspose(A,LDA,B,LDB,d1,d2)


    Transpose input matrix A into output matrix B

    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`dtranspose`
       * :c:func:`h_s2_u_0_nstates_openmp`
       * :c:func:`h_s2_u_0_nstates_zmq`
       * :c:func:`h_s2_u_0_two_e_nstates_openmp`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`dtranspose`

 
.. c:var:: fact_inv


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        double precision, allocatable	:: fact_inv	(128)


    1/n!


 
.. c:function:: i2radix_sort:


    File : :file:`utils/sort.irp.f_template_644`

    .. code:: fortran

        recursive subroutine i2radix_sort(x,iorder,isize,iradix)


    Sort integer array x(isize) using the radix sort algorithm.
    iorder in input should be (1,2,3,...,isize), and in output
    contains the new order of the elements.
    iradix should be -1 in input.

    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`get_mo_two_e_integrals_erf_i1j1`
       * :c:func:`get_mo_two_e_integrals_erf_ij`
       * :c:func:`get_mo_two_e_integrals_i1j1`
       * :c:func:`get_mo_two_e_integrals_ij`
       * :c:func:`i2radix_sort`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`i2radix_sort`
       * :c:func:`insertion_i2sort`

 
.. c:function:: i8radix_sort:


    File : :file:`utils/sort.irp.f_template_644`

    .. code:: fortran

        recursive subroutine i8radix_sort(x,iorder,isize,iradix)


    Sort integer array x(isize) using the radix sort algorithm.
    iorder in input should be (1,2,3,...,isize), and in output
    contains the new order of the elements.
    iradix should be -1 in input.

    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`get_mo_two_e_integrals_erf_i1j1`
       * :c:func:`get_mo_two_e_integrals_erf_ij`
       * :c:func:`get_mo_two_e_integrals_i1j1`
       * :c:func:`get_mo_two_e_integrals_ij`
       * :c:func:`i8radix_sort`
       * :c:data:`psi_bilinear_matrix_transp_values`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`i8radix_sort`
       * :c:func:`insertion_i8sort`

 
.. c:function:: i8radix_sort_big:


    File : :file:`utils/sort.irp.f_template_644`

    .. code:: fortran

        recursive subroutine i8radix_sort_big(x,iorder,isize,iradix)


    Sort integer array x(isize) using the radix sort algorithm.
    iorder in input should be (1,2,3,...,isize), and in output
    contains the new order of the elements.
    iradix should be -1 in input.

    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`i8radix_sort_big`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`i8radix_sort_big`
       * :c:func:`insertion_i8sort_big`

 
.. c:var:: inv_int


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        double precision, allocatable	:: inv_int	(128)


    1/i


 
.. c:function:: iradix_sort:


    File : :file:`utils/sort.irp.f_template_644`

    .. code:: fortran

        recursive subroutine iradix_sort(x,iorder,isize,iradix)


    Sort integer array x(isize) using the radix sort algorithm.
    iorder in input should be (1,2,3,...,isize), and in output
    contains the new order of the elements.
    iradix should be -1 in input.

    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`get_mo_two_e_integrals_erf_i1j1`
       * :c:func:`get_mo_two_e_integrals_erf_ij`
       * :c:func:`get_mo_two_e_integrals_i1j1`
       * :c:func:`get_mo_two_e_integrals_ij`
       * :c:func:`iradix_sort`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`insertion_isort`
       * :c:func:`iradix_sort`

 
.. c:function:: iradix_sort_big:


    File : :file:`utils/sort.irp.f_template_644`

    .. code:: fortran

        recursive subroutine iradix_sort_big(x,iorder,isize,iradix)


    Sort integer array x(isize) using the radix sort algorithm.
    iorder in input should be (1,2,3,...,isize), and in output
    contains the new order of the elements.
    iradix should be -1 in input.

    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`iradix_sort_big`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`insertion_isort_big`
       * :c:func:`iradix_sort_big`

 
.. c:var:: n_points_integration_angular_lebedev


    File : :file:`utils/angular_integration.irp.f`

    .. code:: fortran

        integer	:: n_points_integration_angular_lebedev	


    Number of points needed for the angular integral

    Needs:

    .. hlist::
       :columns: 3

       * :c:data:`degree_max_integration_lebedev`

    Needed by:

    .. hlist::
       :columns: 3

       * :c:data:`theta_angular_integration_lebedev`

 
.. c:var:: nproc


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        integer	:: nproc	


    Number of current OpenMP threads

    Needed by:

    .. hlist::
       :columns: 3

       * :c:data:`ao_two_e_integrals_erf_in_map`
       * :c:data:`ao_two_e_integrals_in_map`
       * :c:data:`h_apply_buffer_allocated`
       * :c:data:`n_det`
       * :c:data:`nthreads_davidson`
       * :c:data:`nthreads_pt2`

 
.. c:function:: overlap_gaussian_xyz:


    File : :file:`utils/one_e_integration.irp.f`

    .. code:: fortran

        subroutine overlap_gaussian_xyz(A_center,B_center,alpha,beta,power_A,&
      power_B,overlap_x,overlap_y,overlap_z,overlap,dim)


    .. math::
    
       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 \\
       S = S_x S_y S_z
    

    Called by:

    .. hlist::
       :columns: 3

       * :c:data:`ao_coef_normalization_libint_factor`
       * :c:data:`ao_coef_normalized`
       * :c:data:`ao_deriv2_x`
       * :c:data:`ao_deriv_1_x`
       * :c:data:`ao_dipole_x`
       * :c:data:`ao_overlap`
       * :c:data:`ao_spread_x`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`gaussian_product_x`
       * :c:func:`give_explicit_poly_and_gaussian`

 
.. c:var:: phi_angular_integration_lebedev


    File : :file:`utils/angular_integration.irp.f`

    .. code:: fortran

        double precision, allocatable	:: theta_angular_integration_lebedev	(n_points_integration_angular_lebedev)
        double precision, allocatable	:: phi_angular_integration_lebedev	(n_points_integration_angular_lebedev)
        double precision, allocatable	:: weights_angular_integration_lebedev	(n_points_integration_angular_lebedev)


    Theta phi values together with the weights values for the angular integration :
    integral [dphi,dtheta] f(x,y,z) = 4 * pi * sum (1<i<n_points_integration_angular_lebedev) f(xi,yi,zi)
    Note that theta and phi are in DEGREES !!

    Needs:

    .. hlist::
       :columns: 3

       * :c:data:`degree_max_integration_lebedev`
       * :c:data:`n_points_integration_angular_lebedev`


 
.. c:var:: qp_max_mem


    File : :file:`utils/memory.irp.f`

    .. code:: fortran

        integer	:: qp_max_mem	


    Maximum memory in Gb

    Needs:

    .. hlist::
       :columns: 3

       * :c:data:`mpi_master`

    Needed by:

    .. hlist::
       :columns: 3

       * :c:data:`pt2_j`
       * :c:data:`pt2_w`

 
.. c:function:: rec__quicksort:


    File : :file:`utils/sort.irp.f_template_261`

    .. code:: fortran

        recursive subroutine rec__quicksort(x, iorder, isize, first, last, level)



    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`quick_sort`
       * :c:func:`rec__quicksort`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`rec__quicksort`

 
.. c:function:: rec_d_quicksort:


    File : :file:`utils/sort.irp.f_template_261`

    .. code:: fortran

        recursive subroutine rec_d_quicksort(x, iorder, isize, first, last, level)



    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`quick_dsort`
       * :c:func:`rec_d_quicksort`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`rec_d_quicksort`

 
.. c:function:: rec_i2_quicksort:


    File : :file:`utils/sort.irp.f_template_261`

    .. code:: fortran

        recursive subroutine rec_i2_quicksort(x, iorder, isize, first, last, level)



    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`quick_i2sort`
       * :c:func:`rec_i2_quicksort`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`rec_i2_quicksort`

 
.. c:function:: rec_i8_quicksort:


    File : :file:`utils/sort.irp.f_template_261`

    .. code:: fortran

        recursive subroutine rec_i8_quicksort(x, iorder, isize, first, last, level)



    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`quick_i8sort`
       * :c:func:`rec_i8_quicksort`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`rec_i8_quicksort`

 
.. c:function:: rec_i_quicksort:


    File : :file:`utils/sort.irp.f_template_261`

    .. code:: fortran

        recursive subroutine rec_i_quicksort(x, iorder, isize, first, last, level)



    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`quick_isort`
       * :c:func:`rec_i_quicksort`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`rec_i_quicksort`

 
.. c:var:: theta_angular_integration_lebedev


    File : :file:`utils/angular_integration.irp.f`

    .. code:: fortran

        double precision, allocatable	:: theta_angular_integration_lebedev	(n_points_integration_angular_lebedev)
        double precision, allocatable	:: phi_angular_integration_lebedev	(n_points_integration_angular_lebedev)
        double precision, allocatable	:: weights_angular_integration_lebedev	(n_points_integration_angular_lebedev)


    Theta phi values together with the weights values for the angular integration :
    integral [dphi,dtheta] f(x,y,z) = 4 * pi * sum (1<i<n_points_integration_angular_lebedev) f(xi,yi,zi)
    Note that theta and phi are in DEGREES !!

    Needs:

    .. hlist::
       :columns: 3

       * :c:data:`degree_max_integration_lebedev`
       * :c:data:`n_points_integration_angular_lebedev`


 
.. c:function:: transpose:


    File : :file:`utils/transpose.irp.f`

    .. code:: fortran

        recursive subroutine transpose(A,LDA,B,LDB,d1,d2)


    Transpose input matrix A into output matrix B

    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`transpose`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`transpose`

 
.. c:var:: weights_angular_integration_lebedev


    File : :file:`utils/angular_integration.irp.f`

    .. code:: fortran

        double precision, allocatable	:: theta_angular_integration_lebedev	(n_points_integration_angular_lebedev)
        double precision, allocatable	:: phi_angular_integration_lebedev	(n_points_integration_angular_lebedev)
        double precision, allocatable	:: weights_angular_integration_lebedev	(n_points_integration_angular_lebedev)


    Theta phi values together with the weights values for the angular integration :
    integral [dphi,dtheta] f(x,y,z) = 4 * pi * sum (1<i<n_points_integration_angular_lebedev) f(xi,yi,zi)
    Note that theta and phi are in DEGREES !!

    Needs:

    .. hlist::
       :columns: 3

       * :c:data:`degree_max_integration_lebedev`
       * :c:data:`n_points_integration_angular_lebedev`


 
 
Subroutines / functions 
----------------------- 
 
.. c:function:: a_coef:


    File : :file:`utils/need.irp.f`

    .. code:: fortran

        double precision function a_coef(n)



 
.. c:function:: add_poly:


    File : :file:`utils/integration.irp.f`

    .. code:: fortran

        subroutine add_poly(b,nb,c,nc,d,nd)


    Add two polynomials
    D(t) =! D(t) +( B(t)+C(t))

 
.. c:function:: add_poly_multiply:


    File : :file:`utils/integration.irp.f`

    .. code:: fortran

        subroutine add_poly_multiply(b,nb,cst,d,nd)


    Add a polynomial multiplied by a constant
    D(t) =! D(t) +( cst * B(t))

    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`general_primitive_integral`
       * :c:func:`general_primitive_integral_erf`

 
.. c:function:: apply_rotation:


    File : :file:`utils/linear_algebra.irp.f`

    .. code:: fortran

        subroutine apply_rotation(A,LDA,R,LDR,B,LDB,m,n)


    Apply the rotation found by find_rotation

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`dgemm`

 
.. c:function:: approx_dble:


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        double precision function approx_dble(a,n)



 
.. c:function:: b_coef:


    File : :file:`utils/need.irp.f`

    .. code:: fortran

        double precision function b_coef(n,u)



 
.. c:function:: binom_func:


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        double precision function binom_func(i,j)


    .. math                       ::
    
      \frac{i!}{j!(i-j)!}
    

 
.. c:function:: check_mem:


    File : :file:`utils/memory.irp.f`

    .. code:: fortran

        subroutine check_mem(rss_in,routine)


    Checks if n gigabytes can be allocated. If not, exit the run.

    Needs:

    .. hlist::
       :columns: 3

       * :c:data:`qp_max_mem`

    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`create_selection_buffer`
       * :c:func:`davidson_diag_hjj_sjj`
       * :c:func:`make_selection_buffer_s2`
       * :c:func:`merge_selection_buffers`
       * :c:func:`pt2_collector`
       * :c:data:`pt2_j`
       * :c:data:`pt2_w`
       * :c:func:`remove_duplicates_in_selection_buffer`
       * :c:func:`run_cipsi`
       * :c:func:`run_slave_main`
       * :c:func:`run_stochastic_cipsi`
       * :c:func:`selection_collector`
       * :c:func:`sort_selection_buffer`
       * :c:func:`testteethbuilding`
       * :c:func:`zmq_pt2`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`resident_memory`

 
.. c:function:: dble_fact:


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        double precision function dble_fact(n)



 
.. c:function:: dble_fact_even:


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        double precision function dble_fact_even(n) result(fact2)


    n!!

 
.. c:function:: dble_fact_odd:


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        double precision function dble_fact_odd(n) result(fact2)


    n!!

 
.. c:function:: dble_logfact:


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        double precision function dble_logfact(n) result(logfact2)


    n!!

 
.. c:function:: ddfact2:


    File : :file:`utils/need.irp.f`

    .. code:: fortran

        double precision function ddfact2(n)



 
.. c:function:: dset_order:


    File : :file:`utils/sort.irp.f_template_347`

    .. code:: fortran

        subroutine dset_order(x,iorder,isize)


    array A has already been sorted, and iorder has contains the new order of
    elements of A. This subroutine changes the order of x to match the new order of A.

    Called by:

    .. hlist::
       :columns: 3

       * :c:data:`ao_coef_normalized_ordered`
       * :c:func:`h_s2_u_0_nstates_openmp`
       * :c:func:`h_s2_u_0_nstates_zmq`
       * :c:func:`h_s2_u_0_two_e_nstates_openmp`
       * :c:data:`psi_bilinear_matrix_transp_values`
       * :c:data:`psi_bilinear_matrix_values`

 
.. c:function:: dset_order_big:


    File : :file:`utils/sort.irp.f_template_412`

    .. code:: fortran

        subroutine dset_order_big(x,iorder,isize)


    array A has already been sorted, and iorder has contains the new order of
    elements of A. This subroutine changes the order of x to match the new order of A.
    This is a version for very large arrays where the indices need
    to be in integer*8 format

 
.. c:function:: dsort:


    File : :file:`utils/sort.irp.f_template_293`

    .. code:: fortran

        subroutine dsort(x,iorder,isize)


    Sort array x(isize).
    iorder in input should be (1,2,3,...,isize), and in output
    contains the new order of the elements.

    Called by:

    .. hlist::
       :columns: 3

       * :c:data:`ao_coef_normalized_ordered`
       * :c:func:`make_selection_buffer_s2`
       * :c:data:`psi_det_sorted`
       * :c:func:`reorder_core_orb`
       * :c:func:`sort_by_fock_energies`
       * :c:func:`sort_selection_buffer`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`insertion_dsort`
       * :c:func:`quick_dsort`

 
.. c:function:: erf0:


    File : :file:`utils/need.irp.f`

    .. code:: fortran

        double precision function erf0(x)



 
.. c:function:: extrapolate_data:


    File : :file:`utils/extrapolation.irp.f`

    .. code:: fortran

        subroutine extrapolate_data(N_data, data, pt2, output)


    Extrapolate the data to the FCI limit

    Called by:

    .. hlist::
       :columns: 3

       * :c:data:`extrapolated_energy`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`get_pseudo_inverse`

 
.. c:function:: f_integral:


    File : :file:`utils/integration.irp.f`

    .. code:: fortran

        double precision function F_integral(n,p)


    function that calculates the following integral
    \int_{\-infty}^{+\infty} x^n \exp(-p x^2) dx

 
.. c:function:: fact:


    File : :file:`utils/util.irp.f`

    .. code:: fortran

        double precision function fact(n)


    n!

 
.. c:function:: find_rotation:


    File : :file:`utils/linear_algebra.irp.f`

    .. code:: fortran

        subroutine find_rotation(A,LDA,B,m,C,n)


    Find A.C = B

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`dgemm`
       * :c:func:`get_pseudo_inverse`

 
.. c:function:: gammln:


    File : :file:`utils/need.irp.f`

    .. code:: fortran

        double precision function gammln(xx)



 
.. c:function:: gammp:


    File : :file:`utils/need.irp.f`

    .. code:: fortran

        double precision function gammp(a,x)



    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`gcf`
       * :c:func:`gser`

 
.. c:function:: gaussian_product:


    File : :file:`utils/integration.irp.f`

    .. code:: fortran

        subroutine gaussian_product(a,xa,b,xb,k,p,xp)


    Gaussian product in 1D.
    e^{-a (x-x_A)^2} e^{-b (x-x_B)^2} = K_{ab}^x e^{-p (x-x_P)^2}

    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`give_explicit_poly_and_gaussian`
       * :c:func:`give_explicit_poly_and_gaussian_double`

 
.. c:function:: gaussian_product_x:


    File : :file:`utils/integration.irp.f`

    .. code:: fortran

        subroutine gaussian_product_x(a,xa,b,xb,k,p,xp)


    Gaussian product in 1D.
    e^{-a (x-x_A)^2} e^{-b (x-x_B)^2} = K_{ab}^x e^{-p (x-x_P)^2}

    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`overlap_gaussian_xyz`

 
.. c:function:: gcf:


    File : :file:`utils/need.irp.f`

    .. code:: fortran

        subroutine gcf(gammcf,a,x,gln)



    Called by:

    .. hlist::
       :columns: 3

       * :c:func:`gammp`

 
.. c:function:: get_inverse:


    File : :file:`utils/linear_algebra.irp.f`

    .. code:: fortran

        subroutine get_inverse(A,LDA,m,C,LDC)


    Returns the inverse of the square matrix A

    Called by:

    .. hlist::
       :columns: 3

       * :c:data:`ao_ortho_canonical_coef_inv`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`dgetrf`
       * :c:func:`dgetri`

 
.. c:function:: get_pseudo_inverse:


    File : :file:`utils/linear_algebra.irp.f`

    .. code:: fortran

        subroutine get_pseudo_inverse(A,LDA,m,n,C,LDC)


    Find C = A^-1

    Called by:

    .. hlist::
       :columns: 3

       * :c:data:`ao_cart_to_sphe_inv`
       * :c:func:`extrapolate_data`
       * :c:func:`find_rotation`
       * :c:data:`s_inv`

    Calls:

    .. hlist::
       :columns: 3

       * :c:func:`dgesvd`