798 lines
30 KiB
ReStructuredText
798 lines
30 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
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.. by the `update_README.py` script.
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`a_coef <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/need.irp.f#L251>`_
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Undocumented
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`add_poly <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L302>`_
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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#L330>`_
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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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`apply_rotation <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L367>`_
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Apply the rotation found by find_rotation
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`approx_dble <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L340>`_
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Undocumented
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`b_coef <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/need.irp.f#L256>`_
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Undocumented
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`binom <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L31>`_
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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#L1>`_
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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#L32>`_
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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#L122>`_
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Undocumented
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`dble_fact_even <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L139>`_
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n!!
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`dble_fact_odd <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L183>`_
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n!!
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`dble_logfact <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L217>`_
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n!!
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`ddfact2 <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/need.irp.f#L242>`_
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Undocumented
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`degree_max_integration_lebedev <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/angular_integration.irp.f#L1>`_
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integrate correctly a polynom of order "degree_max_integration_lebedev"
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needed for the angular integration according to LEBEDEV formulae
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`dset_order <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_323#L27>`_
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array A has already been sorted, and iorder has contains the new order of
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elements of A. This subroutine changes the order of x to match the new order of A.
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`dset_order_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_388#L90>`_
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array A has already been sorted, and iorder has contains the new order of
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elements of A. This subroutine changes the order of x to match the new order of A.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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`dsort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_270#L30>`_
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Sort array x(isize).
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`dtranspose <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/transpose.irp.f#L41>`_
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Transpose input matrix A into output matrix B
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`erf0 <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/need.irp.f#L104>`_
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Undocumented
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`extrapolate_data <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/extrapolation.irp.f#L1>`_
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Extrapolate the data to the FCI limit
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`f_integral <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L404>`_
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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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`fact <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L49>`_
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n!
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`fact_inv <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L109>`_
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1/n!
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`find_rotation <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L348>`_
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Find A.C = B
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`gammln <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/need.irp.f#L270>`_
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Undocumented
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`gammp <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/need.irp.f#L132>`_
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Undocumented
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`gaussian_product <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L181>`_
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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#L223>`_
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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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`gcf <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/need.irp.f#L210>`_
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Undocumented
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`get_inverse <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L266>`_
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Returns the inverse of the square matrix A
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`get_pseudo_inverse <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L294>`_
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Find C = A^-1
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`give_explicit_poly_and_gaussian <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L46>`_
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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_double <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L119>`_
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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)
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exp(-(r-A)^2 alpha) exp(-(r-B)^2 beta) exp(-(r-Nucl_center)^2 gama
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.br
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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#L1>`_
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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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`gser <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/need.irp.f#L166>`_
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Undocumented
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`heap_dsort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L312>`_
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Sort array x(isize) using the heap sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`heap_dsort_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L375>`_
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Sort array x(isize) using the heap sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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`heap_i2sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L1008>`_
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Sort array x(isize) using the heap sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`heap_i2sort_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L1071>`_
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Sort array x(isize) using the heap sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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`heap_i8sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L776>`_
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Sort array x(isize) using the heap sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`heap_i8sort_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L839>`_
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Sort array x(isize) using the heap sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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`heap_isort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L544>`_
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Sort array x(isize) using the heap sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`heap_isort_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L607>`_
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Sort array x(isize) using the heap sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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`heap_sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L80>`_
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Sort array x(isize) using the heap sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`heap_sort_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L143>`_
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Sort array x(isize) using the heap sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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`hermite <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L536>`_
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Hermite polynomial
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`i2radix_sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_605#L423>`_
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Sort integer array x(isize) using the radix sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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iradix should be -1 in input.
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`i2set_order <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_323#L102>`_
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array A has already been sorted, and iorder has contains the new order of
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elements of A. This subroutine changes the order of x to match the new order of A.
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`i2set_order_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_388#L261>`_
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array A has already been sorted, and iorder has contains the new order of
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elements of A. This subroutine changes the order of x to match the new order of A.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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`i2sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_291#L34>`_
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Sort array x(isize).
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`i8radix_sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_605#L213>`_
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Sort integer array x(isize) using the radix sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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iradix should be -1 in input.
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`i8radix_sort_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_605#L843>`_
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Sort integer array x(isize) using the radix sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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iradix should be -1 in input.
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`i8set_order <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_323#L77>`_
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array A has already been sorted, and iorder has contains the new order of
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elements of A. This subroutine changes the order of x to match the new order of A.
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`i8set_order_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_388#L204>`_
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array A has already been sorted, and iorder has contains the new order of
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elements of A. This subroutine changes the order of x to match the new order of A.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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`i8sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_291#L18>`_
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Sort array x(isize).
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`insertion_dsort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L234>`_
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Sort array x(isize) using the insertion sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`insertion_dsort_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_388#L59>`_
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Sort array x(isize) using the insertion sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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`insertion_i2sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L930>`_
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Sort array x(isize) using the insertion sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`insertion_i2sort_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_388#L230>`_
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Sort array x(isize) using the insertion sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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`insertion_i8sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L698>`_
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Sort array x(isize) using the insertion sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`insertion_i8sort_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_388#L173>`_
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Sort array x(isize) using the insertion sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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`insertion_isort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L466>`_
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Sort array x(isize) using the insertion sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`insertion_isort_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_388#L116>`_
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Sort array x(isize) using the insertion sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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`insertion_sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L2>`_
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Sort array x(isize) using the insertion sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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`insertion_sort_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_388#L2>`_
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Sort array x(isize) using the insertion sort algorithm.
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iorder in input should be (1,2,3,...,isize), and in output
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contains the new order of the elements.
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This is a version for very large arrays where the indices need
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to be in integer*8 format
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|
`inv_int <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L248>`_
|
|
1/i
|
|
|
|
|
|
`iradix_sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_605#L3>`_
|
|
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.
|
|
|
|
|
|
`iradix_sort_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_605#L633>`_
|
|
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.
|
|
|
|
|
|
`iset_order <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_323#L52>`_
|
|
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.
|
|
|
|
|
|
`iset_order_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_388#L147>`_
|
|
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
|
|
|
|
|
|
`isort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_291#L2>`_
|
|
Sort array x(isize).
|
|
iorder in input should be (1,2,3,...,isize), and in output
|
|
contains the new order of the elements.
|
|
|
|
|
|
`lapack_diag <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L446>`_
|
|
Diagonalize matrix H
|
|
.br
|
|
H is untouched between input and ouptut
|
|
.br
|
|
eigevalues(i) = ith lowest eigenvalue of the H matrix
|
|
.br
|
|
eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
|
|
.br
|
|
|
|
|
|
`lapack_diag_s2 <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L514>`_
|
|
Diagonalize matrix H
|
|
.br
|
|
H is untouched between input and ouptut
|
|
.br
|
|
eigevalues(i) = ith lowest eigenvalue of the H matrix
|
|
.br
|
|
eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
|
|
.br
|
|
|
|
|
|
`lapack_diagd <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L379>`_
|
|
Diagonalize matrix H
|
|
.br
|
|
H is untouched between input and ouptut
|
|
.br
|
|
eigevalues(i) = ith lowest eigenvalue of the H matrix
|
|
.br
|
|
eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
|
|
.br
|
|
|
|
|
|
`lapack_partial_diag <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L580>`_
|
|
Diagonalize matrix H
|
|
.br
|
|
H is untouched between input and ouptut
|
|
.br
|
|
eigevalues(i) = ith lowest eigenvalue of the H matrix
|
|
.br
|
|
eigvectors(i,j) = <i|psi_j> where i is the basis function and psi_j is the j th eigenvector
|
|
.br
|
|
|
|
|
|
`logfact <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L77>`_
|
|
n!
|
|
|
|
|
|
`lowercase <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L364>`_
|
|
Transform to lower case
|
|
|
|
|
|
`map_load_from_disk <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/map_functions.irp.f#L66>`_
|
|
Undocumented
|
|
|
|
|
|
`map_save_to_disk <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/map_functions.irp.f#L1>`_
|
|
Undocumented
|
|
|
|
|
|
`matrix_vector_product <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L661>`_
|
|
performs u1 =! performs u1 +( u0 * matrix)
|
|
|
|
|
|
`multiply_poly <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L261>`_
|
|
Multiply two polynomials
|
|
D(t) =! D(t) +( B(t)*C(t))
|
|
|
|
|
|
`n_points_integration_angular_lebedev <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/angular_integration.irp.f#L11>`_
|
|
Number of points needed for the angular integral
|
|
|
|
|
|
`normalize <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L318>`_
|
|
Normalizes vector u
|
|
|
|
|
|
`nproc <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L274>`_
|
|
Number of current OpenMP threads
|
|
|
|
|
|
`ortho_canonical <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L45>`_
|
|
Compute C_new=C_old.U.s^-1/2 canonical orthogonalization.
|
|
.br
|
|
overlap : overlap matrix
|
|
.br
|
|
LDA : leftmost dimension of overlap array
|
|
.br
|
|
N : Overlap matrix is NxN (array is (LDA,N) )
|
|
.br
|
|
C : Coefficients of the vectors to orthogonalize. On exit,
|
|
orthogonal vectors
|
|
.br
|
|
LDC : leftmost dimension of C
|
|
.br
|
|
m : Coefficients matrix is MxN, ( array is (LDC,N) )
|
|
.br
|
|
|
|
|
|
`ortho_lowdin <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L182>`_
|
|
Compute C_new=C_old.S^-1/2 orthogonalization.
|
|
.br
|
|
overlap : overlap matrix
|
|
.br
|
|
LDA : leftmost dimension of overlap array
|
|
.br
|
|
N : Overlap matrix is NxN (array is (LDA,N) )
|
|
.br
|
|
C : Coefficients of the vectors to orthogonalize. On exit,
|
|
orthogonal vectors
|
|
.br
|
|
LDC : leftmost dimension of C
|
|
.br
|
|
M : Coefficients matrix is MxN, ( array is (LDC,N) )
|
|
.br
|
|
|
|
|
|
`ortho_qr <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L123>`_
|
|
Orthogonalization using Q.R factorization
|
|
.br
|
|
A : matrix to orthogonalize
|
|
.br
|
|
LDA : leftmost dimension of A
|
|
.br
|
|
n : Number of rows of A
|
|
.br
|
|
m : Number of columns of A
|
|
.br
|
|
|
|
|
|
`ortho_qr_unblocked <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L155>`_
|
|
Orthogonalization using Q.R factorization
|
|
.br
|
|
A : matrix to orthogonalize
|
|
.br
|
|
LDA : leftmost dimension of A
|
|
.br
|
|
n : Number of rows of A
|
|
.br
|
|
m : Number of columns of A
|
|
.br
|
|
|
|
|
|
`overlap_a_b_c <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/one_e_integration.irp.f#L35>`_
|
|
Undocumented
|
|
|
|
|
|
`overlap_gaussian_x <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/one_e_integration.irp.f#L1>`_
|
|
.. math::
|
|
.br
|
|
\sum_{-infty}^{+infty} (x-A_x)^ax (x-B_x)^bx exp(-alpha(x-A_x)^2) exp(-beta(x-B_X)^2) dx
|
|
.br
|
|
|
|
|
|
`overlap_gaussian_xyz <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/one_e_integration.irp.f#L113>`_
|
|
.. math::
|
|
.br
|
|
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
|
|
.br
|
|
|
|
|
|
`overlap_x_abs <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/one_e_integration.irp.f#L175>`_
|
|
.. math ::
|
|
.br
|
|
\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
|
|
.br
|
|
|
|
|
|
`phi_angular_integration_lebedev <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/angular_integration.irp.f#L41>`_
|
|
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 !!
|
|
|
|
|
|
`progress_active <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/progress.irp.f#L29>`_
|
|
Current status for displaying progress bars. Global variable.
|
|
|
|
|
|
`progress_bar <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/progress.irp.f#L27>`_
|
|
Current status for displaying progress bars. Global variable.
|
|
|
|
|
|
`progress_timeout <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/progress.irp.f#L28>`_
|
|
Current status for displaying progress bars. Global variable.
|
|
|
|
|
|
`progress_title <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/progress.irp.f#L31>`_
|
|
Current status for displaying progress bars. Global variable.
|
|
|
|
|
|
`progress_value <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/progress.irp.f#L30>`_
|
|
Current status for displaying progress bars. Global variable.
|
|
|
|
|
|
`quick_dsort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L262>`_
|
|
Sort array x(isize) using the quicksort algorithm.
|
|
iorder in input should be (1,2,3,...,isize), and in output
|
|
contains the new order of the elements.
|
|
|
|
|
|
`quick_i2sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L958>`_
|
|
Sort array x(isize) using the quicksort algorithm.
|
|
iorder in input should be (1,2,3,...,isize), and in output
|
|
contains the new order of the elements.
|
|
|
|
|
|
`quick_i8sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L726>`_
|
|
Sort array x(isize) using the quicksort algorithm.
|
|
iorder in input should be (1,2,3,...,isize), and in output
|
|
contains the new order of the elements.
|
|
|
|
|
|
`quick_isort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L494>`_
|
|
Sort array x(isize) using the quicksort algorithm.
|
|
iorder in input should be (1,2,3,...,isize), and in output
|
|
contains the new order of the elements.
|
|
|
|
|
|
`quick_sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L30>`_
|
|
Sort array x(isize) using the quicksort algorithm.
|
|
iorder in input should be (1,2,3,...,isize), and in output
|
|
contains the new order of the elements.
|
|
|
|
|
|
`rec__quicksort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L43>`_
|
|
Undocumented
|
|
|
|
|
|
`rec_d_quicksort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L275>`_
|
|
Undocumented
|
|
|
|
|
|
`rec_i2_quicksort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L971>`_
|
|
Undocumented
|
|
|
|
|
|
`rec_i8_quicksort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L739>`_
|
|
Undocumented
|
|
|
|
|
|
`rec_i_quicksort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L507>`_
|
|
Undocumented
|
|
|
|
|
|
`recentered_poly2 <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L359>`_
|
|
Recenter two polynomials
|
|
|
|
|
|
`rint <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L432>`_
|
|
.. math::
|
|
.br
|
|
\int_0^1 dx \exp(-p x^2) x^n
|
|
.br
|
|
|
|
|
|
`rint1 <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L592>`_
|
|
Standard version of rint
|
|
|
|
|
|
`rint_large_n <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L561>`_
|
|
Version of rint for large values of n
|
|
|
|
|
|
`rint_sum <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/integration.irp.f#L480>`_
|
|
Needed for the calculation of two-electron integrals.
|
|
|
|
|
|
`rinteg <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/need.irp.f#L46>`_
|
|
Undocumented
|
|
|
|
|
|
`rintgauss <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/need.irp.f#L30>`_
|
|
Undocumented
|
|
|
|
|
|
`run_progress <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/progress.irp.f#L45>`_
|
|
Display a progress bar with documentation of what is happening
|
|
|
|
|
|
`sabpartial <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/need.irp.f#L2>`_
|
|
Undocumented
|
|
|
|
|
|
`set_order <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_323#L2>`_
|
|
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.
|
|
|
|
|
|
`set_order_big <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_388#L33>`_
|
|
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
|
|
|
|
|
|
`set_zero_extra_diag <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L637>`_
|
|
Undocumented
|
|
|
|
|
|
`sort <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_270#L2>`_
|
|
Sort array x(isize).
|
|
iorder in input should be (1,2,3,...,isize), and in output
|
|
contains the new order of the elements.
|
|
|
|
|
|
`sorted_dnumber <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L441>`_
|
|
Returns the number of sorted elements
|
|
|
|
|
|
`sorted_i2number <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L1137>`_
|
|
Returns the number of sorted elements
|
|
|
|
|
|
`sorted_i8number <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L905>`_
|
|
Returns the number of sorted elements
|
|
|
|
|
|
`sorted_inumber <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L673>`_
|
|
Returns the number of sorted elements
|
|
|
|
|
|
`sorted_number <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/sort.irp.f_template_238#L209>`_
|
|
Returns the number of sorted elements
|
|
|
|
|
|
`start_progress <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/progress.irp.f#L1>`_
|
|
Starts the progress bar
|
|
|
|
|
|
`stop_progress <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/progress.irp.f#L19>`_
|
|
Stop the progress bar
|
|
|
|
|
|
`svd <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/LinearAlgebra.irp.f#L1>`_
|
|
Compute A = U.D.Vt
|
|
.br
|
|
LDx : leftmost dimension of x
|
|
.br
|
|
Dimsneion of A is m x n
|
|
.br
|
|
|
|
|
|
`theta_angular_integration_lebedev <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/angular_integration.irp.f#L40>`_
|
|
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 !!
|
|
|
|
|
|
`transpose <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/transpose.irp.f#L2>`_
|
|
Transpose input matrix A into output matrix B
|
|
|
|
|
|
`u_dot_u <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L304>`_
|
|
Compute <u|u>
|
|
|
|
|
|
`u_dot_v <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L290>`_
|
|
Compute <u|v>
|
|
|
|
|
|
`wall_time <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L259>`_
|
|
The equivalent of cpu_time, but for the wall time.
|
|
|
|
|
|
`weights_angular_integration_lebedev <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/angular_integration.irp.f#L42>`_
|
|
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 !!
|
|
|
|
|
|
`write_git_log <http://github.com/LCPQ/quantum_package/tree/master/src/Utils/util.irp.f#L234>`_
|
|
Write the last git commit in file iunit.
|
|
|