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<h1>eigvals
<small>Interface</small>
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<h3>Contents</h3>
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<h4 class="card-header bg-primary text-white">Functions</h4>
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<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_generalized_c">stdlib_linalg_eigvals_generalized_c</a>
<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_generalized_d">stdlib_linalg_eigvals_generalized_d</a>
<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_generalized_s">stdlib_linalg_eigvals_generalized_s</a>
<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_generalized_z">stdlib_linalg_eigvals_generalized_z</a>
<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_noerr_generalized_c">stdlib_linalg_eigvals_noerr_generalized_c</a>
<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_noerr_generalized_d">stdlib_linalg_eigvals_noerr_generalized_d</a>
<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_noerr_generalized_s">stdlib_linalg_eigvals_noerr_generalized_s</a>
<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_noerr_generalized_z">stdlib_linalg_eigvals_noerr_generalized_z</a>
<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_noerr_standard_c">stdlib_linalg_eigvals_noerr_standard_c</a>
<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_noerr_standard_d">stdlib_linalg_eigvals_noerr_standard_d</a>
<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_noerr_standard_s">stdlib_linalg_eigvals_noerr_standard_s</a>
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<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_standard_s">stdlib_linalg_eigvals_standard_s</a>
<a class="list-group-item" href="../interface/eigvals.html#proc-stdlib_linalg_eigvals_standard_z">stdlib_linalg_eigvals_standard_z</a>
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<h2>public interface eigvals</h2>
<p>Returns the eigenvalues <script type="math/tex"> lambda </script>, <script type="math/tex"> A \cdot \bar{v} - \lambda \cdot \bar{v} </script>, for square matrix <script type="math/tex"> A </script>.
(<a href="../page/specs/stdlib_linalg.html#eigvals-eigenvalues-of-a-square-matrix">Specification</a>)</p>
<h3 id="summary">Summary</h3>
<p>Function interface for computing the eigenvalues of a square matrix.</p>
<h3 id="description">Description</h3>
<p>This interface provides functions for returning the eigenvalues of a general square matrix.
Supported data types include <code>real</code> and <code>complex</code>, and no assumption is made on the matrix structure.
An <code>error stop</code> is thrown in case of failure; otherwise, error information can be returned
as an optional <code>type(linalg_state_type)</code> output flag. </p>
<div class="alert alert-info">
<p class="alert-title h4">Note</p>
<p>The solution is based on LAPACK's general eigenproblem solvers <code>*GEEV</code>.</p>
<div class="alert alert-info">
<p class="alert-title h4">Note</p>
</div>
<p>BLAS/LAPACK backends do not currently support extended precision (<code>xdp</code>).</p>
</div>
<br>
<h2>Functions</h2>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_generalized_c"></span> <h3>private module function stdlib_linalg_eigvals_generalized_c(a, b, err) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~190"></span>
complex(kind=sp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-b~75"></span>
complex(kind=sp),
</td>
<td>intent(inout),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>b</strong></td>
<td>
<p>Generalized problem matrix B[n,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~106"></span>
type(<a href='../type/linalg_state_type.html'>linalg_state_type</a>),
</td>
<td>intent(out)</td>
<td></td> <td>
</td>
<td>::</td>
<td><strong>err</strong></td>
<td>
<p>[optional] state return flag. On error if not requested, the code will stop</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=sp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_generalized_d"></span> <h3>private module function stdlib_linalg_eigvals_generalized_d(a, b, err) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~186"></span>
real(kind=dp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-b~73"></span>
real(kind=dp),
</td>
<td>intent(inout),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>b</strong></td>
<td>
<p>Generalized problem matrix B[n,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~104"></span>
type(<a href='../type/linalg_state_type.html'>linalg_state_type</a>),
</td>
<td>intent(out)</td>
<td></td> <td>
</td>
<td>::</td>
<td><strong>err</strong></td>
<td>
<p>[optional] state return flag. On error if not requested, the code will stop</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=dp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_generalized_s"></span> <h3>private module function stdlib_linalg_eigvals_generalized_s(a, b, err) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~182"></span>
real(kind=sp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-b~71"></span>
real(kind=sp),
</td>
<td>intent(inout),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>b</strong></td>
<td>
<p>Generalized problem matrix B[n,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~102"></span>
type(<a href='../type/linalg_state_type.html'>linalg_state_type</a>),
</td>
<td>intent(out)</td>
<td></td> <td>
</td>
<td>::</td>
<td><strong>err</strong></td>
<td>
<p>[optional] state return flag. On error if not requested, the code will stop</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=sp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_generalized_z"></span> <h3>private module function stdlib_linalg_eigvals_generalized_z(a, b, err) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~194"></span>
complex(kind=dp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-b~77"></span>
complex(kind=dp),
</td>
<td>intent(inout),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>b</strong></td>
<td>
<p>Generalized problem matrix B[n,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~108"></span>
type(<a href='../type/linalg_state_type.html'>linalg_state_type</a>),
</td>
<td>intent(out)</td>
<td></td> <td>
</td>
<td>::</td>
<td><strong>err</strong></td>
<td>
<p>[optional] state return flag. On error if not requested, the code will stop</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=dp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_noerr_generalized_c"></span> <h3>private module function stdlib_linalg_eigvals_noerr_generalized_c(a, b) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~191"></span>
complex(kind=sp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-b~76"></span>
complex(kind=sp),
</td>
<td>intent(inout),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>b</strong></td>
<td>
<p>Generalized problem matrix B[n,n]</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=sp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_noerr_generalized_d"></span> <h3>private module function stdlib_linalg_eigvals_noerr_generalized_d(a, b) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~187"></span>
real(kind=dp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-b~74"></span>
real(kind=dp),
</td>
<td>intent(inout),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>b</strong></td>
<td>
<p>Generalized problem matrix B[n,n]</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=dp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_noerr_generalized_s"></span> <h3>private module function stdlib_linalg_eigvals_noerr_generalized_s(a, b) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~183"></span>
real(kind=sp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-b~72"></span>
real(kind=sp),
</td>
<td>intent(inout),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>b</strong></td>
<td>
<p>Generalized problem matrix B[n,n]</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=sp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_noerr_generalized_z"></span> <h3>private module function stdlib_linalg_eigvals_noerr_generalized_z(a, b) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~195"></span>
complex(kind=dp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-b~78"></span>
complex(kind=dp),
</td>
<td>intent(inout),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>b</strong></td>
<td>
<p>Generalized problem matrix B[n,n]</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=dp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_noerr_standard_c"></span> <h3>private module function stdlib_linalg_eigvals_noerr_standard_c(a) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~189"></span>
complex(kind=sp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=sp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_noerr_standard_d"></span> <h3>private module function stdlib_linalg_eigvals_noerr_standard_d(a) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~185"></span>
real(kind=dp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=dp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_noerr_standard_s"></span> <h3>private module function stdlib_linalg_eigvals_noerr_standard_s(a) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~181"></span>
real(kind=sp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=sp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_noerr_standard_z"></span> <h3>private module function stdlib_linalg_eigvals_noerr_standard_z(a) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~193"></span>
complex(kind=dp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=dp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_standard_c"></span> <h3>private module function stdlib_linalg_eigvals_standard_c(a, err) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~188"></span>
complex(kind=sp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~105"></span>
type(<a href='../type/linalg_state_type.html'>linalg_state_type</a>),
</td>
<td>intent(out)</td>
<td></td> <td>
</td>
<td>::</td>
<td><strong>err</strong></td>
<td>
<p>[optional] state return flag. On error if not requested, the code will stop</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>complex(kind=sp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigvals_standard_d"></span> <h3>private module function stdlib_linalg_eigvals_standard_d(a, err) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of matrix A.</p>
<h4>Arguments</h4>
<table class="table table-striped varlist">
<thead>
<tr>
<th scope="col">Type</th>
<th scope="col">Intent</th><th scope="col">Optional</th> <th scope="col">Attributes</th>
<th scope="col"></th>
<th scope="col">Name</th>
<th scope="col"></th>
</thead>
<tbody>
<tr>
<td>
<span class="anchor" id="variable-a~184"></span>
real(kind=dp),
</td>
<td>intent(in),</td>
<td></td> <td>
dimension(:,:), target
</td>
<td>::</td>
<td><strong>a</strong></td>
<td>
<p>Input matrix A[m,n]</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~103"></span>
type(<a href='../type/linalg_state_type.html'>linalg_state_type</a>),
</td>
<td>intent(out)</td>
<td></td> <td>
</td>
<td>::</td>
<td><strong>err</strong></td>
<td>
<p>[optional] state return flag. On error if not requested, the code will stop</p>
</td>