Mujoco_WASM/python/mujoco/sysid/report/templates/covariance.html

<style>
  .cov-and-corr {
    display: flex;
    flex-direction: row;
    flex-wrap: wrap;
    gap: 2rem;
    justify-content: flex-start;
    margin-bottom: 1rem;
  }

  /* Container for a single matrix (covariance or correlation) */
  .cov-matrix-container {
    border: 1px solid var(--border-color);
    padding: 1rem;
    border-radius: 5px;
    background-color: var(--card-bg);
    box-shadow: 2px 2px 5px rgba(0, 0, 0, 0.05);
    max-width: 100%;
    overflow-x: auto;
  }

  .cov-matrix-container h4 {
    margin-top: 0;
    margin-bottom: 0.8rem;
    text-align: left;
    color: var(--heading-color);
    font-weight: 600;
    font-size: 1.1rem;
  }

  .cov-matrix-container p.explanation {
    font-size: 0.85rem;
    color: var(--text-muted);
    margin-top: 1rem;
    max-width: 600px;
    line-height: 1.4;
    text-align: left;
  }

  .cov-matrix-container p.explanation strong {
    color: var(--text-color);
  }

  table.cov {
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Helvetica Neue", Arial, sans-serif;
    font-size: 0.9rem;
    color: var(--text-color);
    text-wrap: nowrap;
    margin-left: 0;
  }

  table.cov tbody tr td {
    padding: 0 4px;
    text-align: left;
    border-top: 1px solid var(--border-color);
    vertical-align: middle;
    /* Ensure text is readable on colored backgrounds - might need text shadow or specific color logic in python generation */
  }

  table.cov thead,
  table.cov thead th {
    background-color: var(--bg-color);
    /* Very light grey header background */
    color: var(--heading-color);
    font-weight: 600;
    border-top: none;
    border-bottom: 2px solid var(--border-color);
    /* Keep a stronger bottom border for header */
    text-align: right;
  }

  /* Body row styles */
  table.cov tbody tr {
    background-color: var(--card-bg);
  }

  table.cov {
    border-collapse: collapse;
    margin: auto;
    margin-bottom: 1rem;
  }

  table.cov th,
  table.cov td {
    border: 1px solid var(--border-color);
    padding: 0 4px;
    /* Very compact */
    text-align: center;
    font-size: 0.9em;
  }

  /* Row Headers (first cell in each body row) */
  table.cov tbody th {
    background-color: var(--bg-color);
    font-weight: bold;
    text-align: left;
    padding-left: 10px;
    position: sticky;
    /* Keep row headers visible */
    left: 0;
    z-index: 1;
    color: var(--heading-color);
  }

  /* Top-left corner cell */
  table.cov thead th:first-child {
    background-color: var(--border-color);
    /* Slightly darker than bg-color */
    z-index: 3;
    /* Ensure it's above row/col headers */
    position: sticky;
    left: 0;
    /* Also sticky */
  }

  table.cov td span {
    display: inline-block;
    min-width: 100%;
  }

  table.cov td.blank {
    border: 0;
    background-color: var(--card-bg);
  }
</style>
<div class="cov-and-corr">
  {% if message %}
  <div class="cov-matrix-container" style="width: 100%;">
    <h4>Covariance & Correlation</h4>
    <p class="explanation" style="color: var(--text-color);">
      {{ message }}
    </p>
  </div>
  {% else %}
  <div class="cov-matrix-container">
    <h4>Covariance Matrix</h4>
    <table class="cov">
      <tbody>
        {% for row in covariance_data %}
        {% set outer_loop = loop %}
        <tr>
          <th>{{dim_names[outer_loop.index0] }}</th>
          {% for cell in row %}
          {%if loop.index0 <= outer_loop.index0 %} <td
            style="background-color: {{ cell.bgcolor }}; color: {{ cell.textcolor }};" title="{{ cell.value }}" {%if
            outer_loop.index0==loop.index0 %}class="diag" {% endif %}>
            <span>
              {{ "%.1e" | format(cell.value) }}
            </span>
            </td>
            {% else %}
            <td class="blank" />
            {% endif %}
            {% endfor %}
        </tr>
        {% endfor %}
      </tbody>
    </table>
    <p class="explanation">
      The covariance matrix shows how pairs of parameters vary together.
      The diagonal elements (Variance) show the variance of each parameter (how much it varies on its own).
      Larger positive values indicate the parameter estimate is less certain.
      The off-diagonal elements (Covariance) show the covariance between pairs of parameters, better viewed in the
      normalized correlation matrix.
    </p>
  </div> {# End cov-matrix-container for covariance #}

  <div class="cov-matrix-container">
    <h4>Correlation Matrix</h4>
    <table class="cov">
      <tbody>
        {% for row in correlation_data %}
        {% set outer_loop = loop %}
        <tr>
          <th>{{ dim_names[outer_loop.index0] }}</th>
          {% for cell in row %}
          {%if loop.index0 <= outer_loop.index0 %} <td
            style="background-color: {{ cell.bgcolor }}; color: {{ cell.textcolor }};" title="{{ cell.value }}" {%if
            outer_loop.index0==loop.index0 %}class="diag" {% endif %}>
            <span>
              {{ "%.2f" | format(cell.value) }}
            </span>
            </td>
            {% else %}
            <td class="blank" />
            {% endif %}
            {% endfor %}
        </tr>
        {% endfor %}
      </tbody>
    </table>
    <p class="explanation">
      The correlation matrix is a normalized version of the covariance matrix.
      Values range from -1 to +1.
      The diagonal elements are always 1, representing perfect correlation of a parameter with itself.
      Off-diagonal elements (Correlation Coefficient) show the linear correlation between pairs of parameters.
      +1 indicates perfect positive correlation, -1 indicates perfect negative correlation, and 0 indicates no linear
      correlation.
      Values close to +1 or -1 suggests that the parameters are highly dependent. Thus, if their variance is also high,
      their confidence intervals will be large.
    </p>
  </div>
  {% endif %}
</div>