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<h1>eigh
<small>Interface</small>
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<h3>Contents</h3>
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<h4 class="card-header bg-primary text-white">Subroutines</h4>
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<a class="list-group-item" href="../interface/eigh.html#proc-stdlib_linalg_eigh_c">stdlib_linalg_eigh_c</a>
<a class="list-group-item" href="../interface/eigh.html#proc-stdlib_linalg_eigh_d">stdlib_linalg_eigh_d</a>
<a class="list-group-item" href="../interface/eigh.html#proc-stdlib_linalg_eigh_s">stdlib_linalg_eigh_s</a>
<a class="list-group-item" href="../interface/eigh.html#proc-stdlib_linalg_eigh_z">stdlib_linalg_eigh_z</a>
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<h2>public interface eigh</h2>
<p>Solves the eigendecomposition <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#eigh-eigenvalues-and-eigenvectors-of-a-real-symmetric-or-complex-hermitian-square-matrix">Specification</a>)</p>
<h3 id="summary">Summary</h3>
<p>Subroutine interface for computing eigenvalues and eigenvectors of a real symmetric or complex Hermitian square matrix.</p>
<h3 id="description">Description</h3>
<p>This interface provides methods for computing the eigenvalues, and optionally eigenvectors,
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). The vectors are orthogonal, and may be returned as columns of an optional
matrix <code>vectors</code> with the same kind and size as <code>A</code>.
Preallocated space for both eigenvalues <code>lambda</code> and the eigenvector matrix must be user-provided. </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>Subroutines</h2>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigh_c"></span> <h3>private module subroutine stdlib_linalg_eigh_c(a, lambda, vectors, upper_a, overwrite_a, err)
</h3></div>
<div class="card-body">
<p>Eigendecomposition of a real symmetric or complex Hermitian matrix A returning an array <code>lambda</code>
of eigenvalues, and optionally right or left eigenvectors. </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~198"></span>
complex(kind=sp),
</td>
<td>intent(inout),</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-lambda~35"></span>
real(kind=sp),
</td>
<td>intent(out)</td>
<td></td> <td>
</td>
<td>::</td>
<td><strong>lambda</strong>(:)</td>
<td>
<p>Array of eigenvalues</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-vectors~3"></span>
complex(kind=sp),
</td>
<td>intent(out),</td>
<td>optional,</td> <td>
target
</td>
<td>::</td>
<td><strong>vectors</strong>(:,:)</td>
<td>
<p>The columns of vectors contain the orthonormal eigenvectors of A</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-upper_a~3"></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-overwrite_a~67"></span>
logical(kind=lk),
</td>
<td>intent(in),</td>
<td>optional</td> <td>
</td>
<td>::</td>
<td><strong>overwrite_a</strong></td>
<td>
<p>[optional] Can A data be overwritten and destroyed?</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~111"></span>
type(<a href='../type/linalg_state_type.html'>linalg_state_type</a>),
</td>
<td>intent(out),</td>
<td>optional</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>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigh_d"></span> <h3>private module subroutine stdlib_linalg_eigh_d(a, lambda, vectors, upper_a, overwrite_a, err)
</h3></div>
<div class="card-body">
<p>Eigendecomposition of a real symmetric or complex Hermitian matrix A returning an array <code>lambda</code>
of eigenvalues, and optionally right or left eigenvectors. </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~197"></span>
real(kind=dp),
</td>
<td>intent(inout),</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-lambda~34"></span>
real(kind=dp),
</td>
<td>intent(out)</td>
<td></td> <td>
</td>
<td>::</td>
<td><strong>lambda</strong>(:)</td>
<td>
<p>Array of eigenvalues</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-vectors~2"></span>
real(kind=dp),
</td>
<td>intent(out),</td>
<td>optional,</td> <td>
target
</td>
<td>::</td>
<td><strong>vectors</strong>(:,:)</td>
<td>
<p>The columns of vectors contain the orthonormal eigenvectors of A</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-upper_a~2"></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-overwrite_a~66"></span>
logical(kind=lk),
</td>
<td>intent(in),</td>
<td>optional</td> <td>
</td>
<td>::</td>
<td><strong>overwrite_a</strong></td>
<td>
<p>[optional] Can A data be overwritten and destroyed?</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~110"></span>
type(<a href='../type/linalg_state_type.html'>linalg_state_type</a>),
</td>
<td>intent(out),</td>
<td>optional</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>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigh_s"></span> <h3>private module subroutine stdlib_linalg_eigh_s(a, lambda, vectors, upper_a, overwrite_a, err)
</h3></div>
<div class="card-body">
<p>Eigendecomposition of a real symmetric or complex Hermitian matrix A returning an array <code>lambda</code>
of eigenvalues, and optionally right or left eigenvectors. </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~196"></span>
real(kind=sp),
</td>
<td>intent(inout),</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-lambda~33"></span>
real(kind=sp),
</td>
<td>intent(out)</td>
<td></td> <td>
</td>
<td>::</td>
<td><strong>lambda</strong>(:)</td>
<td>
<p>Array of eigenvalues</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-vectors"></span>
real(kind=sp),
</td>
<td>intent(out),</td>
<td>optional,</td> <td>
target
</td>
<td>::</td>
<td><strong>vectors</strong>(:,:)</td>
<td>
<p>The columns of vectors contain the orthonormal eigenvectors of A</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-upper_a"></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-overwrite_a~65"></span>
logical(kind=lk),
</td>
<td>intent(in),</td>
<td>optional</td> <td>
</td>
<td>::</td>
<td><strong>overwrite_a</strong></td>
<td>
<p>[optional] Can A data be overwritten and destroyed?</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~109"></span>
type(<a href='../type/linalg_state_type.html'>linalg_state_type</a>),
</td>
<td>intent(out),</td>
<td>optional</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>
</div>
</div>
<div class="card">
<div class="card-header codesum"><span class="anchor" id="proc-stdlib_linalg_eigh_z"></span> <h3>private module subroutine stdlib_linalg_eigh_z(a, lambda, vectors, upper_a, overwrite_a, err)
</h3></div>
<div class="card-body">
<p>Eigendecomposition of a real symmetric or complex Hermitian matrix A returning an array <code>lambda</code>
of eigenvalues, and optionally right or left eigenvectors. </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~199"></span>
complex(kind=dp),
</td>
<td>intent(inout),</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-lambda~36"></span>
real(kind=dp),
</td>
<td>intent(out)</td>
<td></td> <td>
</td>
<td>::</td>
<td><strong>lambda</strong>(:)</td>
<td>
<p>Array of eigenvalues</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-vectors~4"></span>
complex(kind=dp),
</td>
<td>intent(out),</td>
<td>optional,</td> <td>
target
</td>
<td>::</td>
<td><strong>vectors</strong>(:,:)</td>
<td>
<p>The columns of vectors contain the orthonormal eigenvectors of A</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-upper_a~4"></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-overwrite_a~68"></span>
logical(kind=lk),
</td>
<td>intent(in),</td>
<td>optional</td> <td>
</td>
<td>::</td>
<td><strong>overwrite_a</strong></td>
<td>
<p>[optional] Can A data be overwritten and destroyed?</p>
</td>
</tr>
<tr>
<td>
<span class="anchor" id="variable-err~112"></span>
type(<a href='../type/linalg_state_type.html'>linalg_state_type</a>),
</td>
<td>intent(out),</td>
<td>optional</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>
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