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<h1>eigvalsh
<small>Interface</small>
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<a class="list-group-item" href="../interface/eigvalsh.html#proc-stdlib_linalg_eigvalsh_c">stdlib_linalg_eigvalsh_c</a>
<a class="list-group-item" href="../interface/eigvalsh.html#proc-stdlib_linalg_eigvalsh_d">stdlib_linalg_eigvalsh_d</a>
<a class="list-group-item" href="../interface/eigvalsh.html#proc-stdlib_linalg_eigvalsh_noerr_c">stdlib_linalg_eigvalsh_noerr_c</a>
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<h2>public interface eigvalsh</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 a real
symmetric <script type="math/tex"> A = A^T </script> or complex Hermitian <script type="math/tex"> A = A^H </script> square matrix.
(<a href="../page/specs/stdlib_linalg.html#eigvalsh-eigenvalues-of-a-real-symmetric-or-complex-hermitian-square-matrix">Specification</a>)</p>
<h3 id="summary">Summary</h3>
<p>Function interface for computing the eigenvalues of a real symmetric or complex hermitian square matrix.</p>
<h3 id="description">Description</h3>
<p>This interface provides functions for returning the eigenvalues of a real symmetric or complex Hermitian
square matrix. Supported data types include <code>real</code> and <code>complex</code>. The matrix must be symmetric
(if <code>real</code>) or Hermitian (if <code>complex</code>). Only the lower or upper half of the matrix is accessed,
and the user can select which using the optional <code>upper_a</code> flag (default: use lower half).
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 eigenproblem solvers <code>*SYEV</code>/<code>*HEEV</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_eigvalsh_c"></span> <h3>private module function stdlib_linalg_eigvalsh_c(a, upper_a, err) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of real symmetric / complex hermitian 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~247"></span>
complex(kind=sp),
</td>
<td>intent(in),</td>
<td></td> <td>
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-upper_a~9"></span>
logical(kind=lk),
</td>
<td>intent(in),</td>
<td>optional</td> <td>
</td>
<td>::</td>
<td><strong>upper_a</strong></td>
<td>
<p>[optional] Should the upper/lower half of A be used? Default: lower</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~124"></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>real(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_eigvalsh_d"></span> <h3>private module function stdlib_linalg_eigvalsh_d(a, upper_a, err) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of real symmetric / complex hermitian 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~245"></span>
real(kind=dp),
</td>
<td>intent(in),</td>
<td></td> <td>
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-upper_a~7"></span>
logical(kind=lk),
</td>
<td>intent(in),</td>
<td>optional</td> <td>
</td>
<td>::</td>
<td><strong>upper_a</strong></td>
<td>
<p>[optional] Should the upper/lower half of A be used? Default: lower</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~123"></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>real(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_eigvalsh_noerr_c"></span> <h3>private module function stdlib_linalg_eigvalsh_noerr_c(a, upper_a) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of real symmetric / complex hermitian 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~248"></span>
complex(kind=sp),
</td>
<td>intent(in),</td>
<td></td> <td>
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-upper_a~10"></span>
logical(kind=lk),
</td>
<td>intent(in),</td>
<td>optional</td> <td>
</td>
<td>::</td>
<td><strong>upper_a</strong></td>
<td>
<p>[optional] Should the upper/lower half of A be used? Default: lower</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>real(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_eigvalsh_noerr_d"></span> <h3>private module function stdlib_linalg_eigvalsh_noerr_d(a, upper_a) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of real symmetric / complex hermitian 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~246"></span>
real(kind=dp),
</td>
<td>intent(in),</td>
<td></td> <td>
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-upper_a~8"></span>
logical(kind=lk),
</td>
<td>intent(in),</td>
<td>optional</td> <td>
</td>
<td>::</td>
<td><strong>upper_a</strong></td>
<td>
<p>[optional] Should the upper/lower half of A be used? Default: lower</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>real(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_eigvalsh_noerr_s"></span> <h3>private module function stdlib_linalg_eigvalsh_noerr_s(a, upper_a) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of real symmetric / complex hermitian 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~244"></span>
real(kind=sp),
</td>
<td>intent(in),</td>
<td></td> <td>
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-upper_a~6"></span>
logical(kind=lk),
</td>
<td>intent(in),</td>
<td>optional</td> <td>
</td>
<td>::</td>
<td><strong>upper_a</strong></td>
<td>
<p>[optional] Should the upper/lower half of A be used? Default: lower</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>real(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_eigvalsh_noerr_z"></span> <h3>private module function stdlib_linalg_eigvalsh_noerr_z(a, upper_a) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of real symmetric / complex hermitian 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~250"></span>
complex(kind=dp),
</td>
<td>intent(in),</td>
<td></td> <td>
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-upper_a~12"></span>
logical(kind=lk),
</td>
<td>intent(in),</td>
<td>optional</td> <td>
</td>
<td>::</td>
<td><strong>upper_a</strong></td>
<td>
<p>[optional] Should the upper/lower half of A be used? Default: lower</p>
</td>
</tr>
</tbody>
</table>
<h4>
Return Value
<small>real(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_eigvalsh_s"></span> <h3>private module function stdlib_linalg_eigvalsh_s(a, upper_a, err) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of real symmetric / complex hermitian 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~243"></span>
real(kind=sp),
</td>
<td>intent(in),</td>
<td></td> <td>
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-upper_a~5"></span>
logical(kind=lk),
</td>
<td>intent(in),</td>
<td>optional</td> <td>
</td>
<td>::</td>
<td><strong>upper_a</strong></td>
<td>
<p>[optional] Should the upper/lower half of A be used? Default: lower</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~122"></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>real(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_eigvalsh_z"></span> <h3>private module function stdlib_linalg_eigvalsh_z(a, upper_a, err) result(lambda)
</h3></div>
<div class="card-body">
<p>Return an array of eigenvalues of real symmetric / complex hermitian 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~249"></span>
complex(kind=dp),
</td>
<td>intent(in),</td>
<td></td> <td>
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-upper_a~11"></span>
logical(kind=lk),
</td>
<td>intent(in),</td>
<td>optional</td> <td>
</td>
<td>::</td>
<td><strong>upper_a</strong></td>
<td>
<p>[optional] Should the upper/lower half of A be used? Default: lower</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~125"></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>real(kind=dp), allocatable, (:)</small>
</h4>
<p>Array of singular values</p>
</div>
</div>
</div>
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