dseuss/mpnum

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mpnum/linalg.py

Summary

Maintainability
F
1 wk
Test Coverage

File linalg.py has 454 lines of code (exceeds 250 allowed). Consider refactoring.
Open

# encoding: utf-8

"""Linear algebra with matrix product arrays

Currently, we support computing extremal eigenvalues and eigenvectors
Severity: Minor
Found in mpnum/linalg.py - About 6 hrs to fix

    Function eig has a Cognitive Complexity of 23 (exceeds 5 allowed). Consider refactoring.
    Open

    def eig(mpo, num_sweeps, var_sites=2,
            startvec=None, startvec_rank=None, randstate=None, eigs=None):
        r"""Iterative search for MPO eigenvalues
    
        .. note::
    Severity: Minor
    Found in mpnum/linalg.py - About 3 hrs to fix

    Cognitive Complexity

    Cognitive Complexity is a measure of how difficult a unit of code is to intuitively understand. Unlike Cyclomatic Complexity, which determines how difficult your code will be to test, Cognitive Complexity tells you how difficult your code will be to read and comprehend.

    A method's cognitive complexity is based on a few simple rules:

    • Code is not considered more complex when it uses shorthand that the language provides for collapsing multiple statements into one
    • Code is considered more complex for each "break in the linear flow of the code"
    • Code is considered more complex when "flow breaking structures are nested"

    Further reading

    Function eig_sum has a Cognitive Complexity of 23 (exceeds 5 allowed). Consider refactoring.
    Open

    def eig_sum(mpas, num_sweeps, var_sites=2,
                startvec=None, startvec_rank=None, randstate=None, eigs=None):
        r"""Iterative search for eigenvalues of a sum of MPOs/MPSs
    
        Try to compute the ground state of the sum of the objects in
    Severity: Minor
    Found in mpnum/linalg.py - About 3 hrs to fix

    Cognitive Complexity

    Cognitive Complexity is a measure of how difficult a unit of code is to intuitively understand. Unlike Cyclomatic Complexity, which determines how difficult your code will be to test, Cognitive Complexity tells you how difficult your code will be to read and comprehend.

    A method's cognitive complexity is based on a few simple rules:

    • Code is not considered more complex when it uses shorthand that the language provides for collapsing multiple statements into one
    • Code is considered more complex for each "break in the linear flow of the code"
    • Code is considered more complex when "flow breaking structures are nested"

    Further reading

    Function _eig_minimize_locally2 has a Cognitive Complexity of 11 (exceeds 5 allowed). Consider refactoring.
    Open

    def _eig_minimize_locally2(local_op, eigvec_ltens, eigs):
        """Implement the main part of :func:`_eig_minimize_locally`
    
        See :func:`_eig_minimize_locally` for a description.
    
    
    Severity: Minor
    Found in mpnum/linalg.py - About 1 hr to fix

    Cognitive Complexity

    Cognitive Complexity is a measure of how difficult a unit of code is to intuitively understand. Unlike Cyclomatic Complexity, which determines how difficult your code will be to test, Cognitive Complexity tells you how difficult your code will be to read and comprehend.

    A method's cognitive complexity is based on a few simple rules:

    • Code is not considered more complex when it uses shorthand that the language provides for collapsing multiple statements into one
    • Code is considered more complex for each "break in the linear flow of the code"
    • Code is considered more complex when "flow breaking structures are nested"

    Further reading

    Function _eig_sum_minimize_locally has 7 arguments (exceeds 4 allowed). Consider refactoring.
    Open

    def _eig_sum_minimize_locally(
    Severity: Major
    Found in mpnum/linalg.py - About 50 mins to fix

      Function eig_sum has 7 arguments (exceeds 4 allowed). Consider refactoring.
      Open

      def eig_sum(mpas, num_sweeps, var_sites=2,
      Severity: Major
      Found in mpnum/linalg.py - About 50 mins to fix

        Function eig has 7 arguments (exceeds 4 allowed). Consider refactoring.
        Open

        def eig(mpo, num_sweeps, var_sites=2,
        Severity: Major
        Found in mpnum/linalg.py - About 50 mins to fix

          Function _eig_sum_leftvec_add has 6 arguments (exceeds 4 allowed). Consider refactoring.
          Open

          def _eig_sum_leftvec_add(
          Severity: Minor
          Found in mpnum/linalg.py - About 45 mins to fix

            Function _eig_sum_rightvec_add has 6 arguments (exceeds 4 allowed). Consider refactoring.
            Open

            def _eig_sum_rightvec_add(
            Severity: Minor
            Found in mpnum/linalg.py - About 45 mins to fix

              Function _eig_minimize_locally has 5 arguments (exceeds 4 allowed). Consider refactoring.
              Open

              def _eig_minimize_locally(leftvec, mpo_ltens, rightvec, eigvec_ltens,
              Severity: Minor
              Found in mpnum/linalg.py - About 35 mins to fix

                Similar blocks of code found in 2 locations. Consider refactoring.
                Open

                    for i, mpa, ndims, rv in zip(it.count(), mpas, mpas_ndims, rightvec):
                        if ndims == 2:
                            rightvec_out[i] = _eig_rightvec_add(rv, mpa.lt[pos], mps_lten)
                        elif ndims == 1:
                            rightvec_out[i] = _eig_rightvec_add_mps(rv, mpa.lt[pos], mps_lten)
                Severity: Major
                Found in mpnum/linalg.py and 1 other location - About 6 hrs to fix
                mpnum/linalg.py on lines 157..163

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 107.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Similar blocks of code found in 2 locations. Consider refactoring.
                Open

                    for i, mpa, ndims, lv in zip(it.count(), mpas, mpas_ndims, leftvec):
                        if ndims == 2:
                            leftvec_out[i] = _eig_leftvec_add(lv, mpa.lt[pos], mps_lten)
                        elif ndims == 1:
                            leftvec_out[i] = _eig_leftvec_add_mps(lv, mpa.lt[pos], mps_lten)
                Severity: Major
                Found in mpnum/linalg.py and 1 other location - About 6 hrs to fix
                mpnum/linalg.py on lines 169..175

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 107.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Similar blocks of code found in 2 locations. Consider refactoring.
                Open

                            if pos > 0:
                                eigvec.canonicalize(left=pos)
                                rightvecs[pos - 1] = None
                                leftvecs[pos] = _eig_leftvec_add(
                                    leftvecs[pos - 1], mpo.lt[pos - 1], eigvec.lt[pos - 1])
                Severity: Major
                Found in mpnum/linalg.py and 1 other location - About 5 hrs to fix
                mpnum/mparray.py on lines 1082..1086

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 95.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Similar blocks of code found in 2 locations. Consider refactoring.
                Open

                            if pos < nr_sites - var_sites:
                                # We always do this, because we don't do the last site again.
                                eigvec.canonicalize(right=pos_end)
                                leftvecs[pos + 1] = None
                                rightvecs[pos] = _eig_rightvec_add(
                Severity: Major
                Found in mpnum/linalg.py and 1 other location - About 5 hrs to fix
                mpnum/mparray.py on lines 1096..1101

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 89.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Identical blocks of code found in 2 locations. Consider refactoring.
                Open

                    assert not any(rank12 == (1, 1) for rank12 in
                                   zip((1,) + startvec.ranks, startvec.ranks + (1,))), \
                        ('startvec must not contain two consecutive ranks 1, '
                         'ranks including dummy values = (1,) + {!r} + (1,)'
                         .format(startvec.ranks))
                Severity: Major
                Found in mpnum/linalg.py and 1 other location - About 3 hrs to fix
                mpnum/linalg.py on lines 473..477

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 63.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Identical blocks of code found in 2 locations. Consider refactoring.
                Open

                    assert not any(rank12 == (1, 1) for rank12 in
                                   zip((1,) + startvec.ranks, startvec.ranks + (1,))), \
                        ('startvec must not contain two consecutive ranks 1, '
                         'ranks including dummy values = (1,) + {!r} + (1,)'
                         .format(startvec.ranks))
                Severity: Major
                Found in mpnum/linalg.py and 1 other location - About 3 hrs to fix
                mpnum/linalg.py on lines 596..600

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 63.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Similar blocks of code found in 2 locations. Consider refactoring.
                Open

                def _eig_leftvec_add_mps(lv, lt1, lt2):
                    """Add one column to the left vector (MPS version)"""
                    # MPS 1: Interpreted as |psiXpsi| part of the operator
                    # MPS 2: The current eigvectector candidate
                    # NB: It would be more efficient to store lt1.conj() instead of lt1.
                Severity: Major
                Found in mpnum/linalg.py and 1 other location - About 3 hrs to fix
                mpnum/linalg.py on lines 144..151

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 62.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Similar blocks of code found in 2 locations. Consider refactoring.
                Open

                def _eig_rightvec_add_mps(rv, lt1, lt2):
                    """Add one column to the right vector (MPS version)"""
                    # rv axes: 0: mps1 bond, 1: mps2 bond
                    rv = np.tensordot(rv, lt1.conj(), axes=(0, 2))
                    # rv axes: 0: mps2 bond, 1: mps1 bond, 2: physical leg
                Severity: Major
                Found in mpnum/linalg.py and 1 other location - About 3 hrs to fix
                mpnum/linalg.py on lines 131..141

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 62.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Identical blocks of code found in 2 locations. Consider refactoring.
                Open

                            eigval, eigvec_lten = _eig_minimize_locally(
                                leftvecs[pos], mpo.lt[pos:pos_end], rightvecs[pos],
                                eigvec.lt[pos:pos_end], eigs)
                Severity: Major
                Found in mpnum/linalg.py and 1 other location - About 1 hr to fix
                mpnum/linalg.py on lines 520..522

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 48.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Identical blocks of code found in 2 locations. Consider refactoring.
                Open

                            eigval, eigvec_lten = _eig_minimize_locally(
                                leftvecs[pos], mpo.lt[pos:pos_end], rightvecs[pos],
                                eigvec.lt[pos:pos_end], eigs)
                Severity: Major
                Found in mpnum/linalg.py and 1 other location - About 1 hr to fix
                mpnum/linalg.py on lines 534..536

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 48.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Identical blocks of code found in 2 locations. Consider refactoring.
                Open

                            eigval, eigvec_lten = _eig_sum_minimize_locally(
                                mpas, ndims, leftvecs[pos], slice(pos, pos_end), rightvecs[pos],
                                eigvec.lt[pos:pos_end], eigs)
                Severity: Major
                Found in mpnum/linalg.py and 1 other location - About 1 hr to fix
                mpnum/linalg.py on lines 661..663

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 45.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Identical blocks of code found in 2 locations. Consider refactoring.
                Open

                            eigval, eigvec_lten = _eig_sum_minimize_locally(
                                mpas, ndims, leftvecs[pos], slice(pos, pos_end), rightvecs[pos],
                                eigvec.lt[pos:pos_end], eigs)
                Severity: Major
                Found in mpnum/linalg.py and 1 other location - About 1 hr to fix
                mpnum/linalg.py on lines 646..648

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 45.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Similar blocks of code found in 2 locations. Consider refactoring.
                Open

                    leftvecs = [np.array(1, ndmin=3)] + [None] * (nr_sites - var_sites)
                Severity: Minor
                Found in mpnum/linalg.py and 1 other location - About 55 mins to fix
                mpnum/mparray.py on lines 1058..1058

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 37.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

                Similar blocks of code found in 2 locations. Consider refactoring.
                Open

                    rightvecs = [None] * (nr_sites - var_sites) + [np.array(1, ndmin=3)]
                Severity: Minor
                Found in mpnum/linalg.py and 1 other location - About 55 mins to fix
                mpnum/mparray.py on lines 1059..1059

                Duplicated Code

                Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                Tuning

                This issue has a mass of 37.

                We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                Refactorings

                Further Reading

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