I create my own class for the square layout:
public class SquareLayout extends LinearLayout{
    public SquareLayout(Context context) {
        super(context);
    }
    public SquareLayout(Context context, AttributeSet attrs, int defStyle) {
        super(context, attrs, defStyle);
    }
    public SquareLayout(Context context, AttributeSet attrs) {
        super(context, attrs);
    }
    @Override public void onMeasure(int widthMeasureSpec, int heightMeasureSpec) {
        int width = MeasureSpec.getSize(widthMeasureSpec);
        int height = MeasureSpec.getSize(heightMeasureSpec);
        int size = width > height ? height : width;
        setMeasuredDimension(size, size);
    }
Then, in my xml:
...
        <com.myApp.SquareLayout
            android:layout_width="fill_parent"
            android:layout_height="fill_parent"
            android:layout_gravity="center_horizontal"
            android:orientation="horizontal" >
            <ImageView
                android:id="@+id/cellImageView"
                android:adjustViewBounds="true"
                android:layout_width="fill_parent"
                android:layout_height="wrap_content"
                android:layout_marginTop="2dp"
                android:padding="2dp"
                android:scaleType="centerCrop"
                android:src="@drawable/image" />
        </com.myApp.SquareLayout>
...
Nothing written more in my java code. But instead if my layout and my Image, I see only a white rectangle...
What am I wrong?
// you forget to call super.onMeasure(widthMeasureSpec, widthMeasureSpec);
@Override
public void onMeasure(int widthMeasureSpec, int heightMeasureSpec) {
    super.onMeasure(widthMeasureSpec, widthMeasureSpec);
    int width = MeasureSpec.getSize(widthMeasureSpec);
    int height = MeasureSpec.getSize(heightMeasureSpec);
    int size = width > height ? height : width;
    setMeasuredDimension(size, size);
}
// xml file
<com.example.testapplication.SquareLayout
    android:id="@+id/layout"
    android:layout_width="fill_parent"
    android:layout_height="fill_parent"
    android:layout_gravity="center_horizontal"
    android:orientation="horizontal" >
    <ImageView
        android:id="@+id/cellImageView"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_marginTop="2dp"
        android:adjustViewBounds="true"
        android:padding="2dp"
        android:scaleType="centerCrop"
        android:src="@drawable/ic_launcher" />
  </com.example.testapplication.SquareLayout> 
                        I had problems calling setMeasuredDimension directly when applying the same technique to a RelativeLayout. I was unable to correctly align against the bottom edge. Changing to instead call up to super.onMeasure() with a new measure spec worked better.
  @Override
  protected void onMeasure(int widthMeasureSpec, int heightMeasureSpec) {
    int width = MeasureSpec.getSize(widthMeasureSpec);
    int height = MeasureSpec.getSize(heightMeasureSpec);
    int size = Math.min(width, height);
    super.onMeasure(MeasureSpec.makeMeasureSpec(size, MeasureSpec.EXACTLY),
        MeasureSpec.makeMeasureSpec(size, MeasureSpec.EXACTLY));
  }
                        Edit:
The solution below has now been deprecated, as ConstraintLayout has become the new standard and provides this functionality.
Original Answer:
Turns out the Android team gave us the solution, but nobody knows about it! Check out these two classes from the Percent Support Library:
If you want to impose the ratio of a view, you have to place it within one of these layouts. So in this case, you have to place a standard LinearLayout, not your subclass, within one of these layouts with the right aspect ratio. Example if you want to use a PercentFrameLayout:
<android.support.percent.PercentFrameLayout
         xmlns:android="http://schemas.android.com/apk/res/android"
         xmlns:app="http://schemas.android.com/apk/res-auto"
         android:layout_width="match_parent"
         android:layout_height="match_parent">
     <LinearLayout
         android:layout_width="match_parent"
         android:layout_height="match_parent"
         app:layout_aspectRatio="100%">
         <!-- Whatever subviews you want here -->
     </LinearLayout>
 </android.support.percent.PercentFrameLayout>
And there you go, all your views will be contained within a square linear layout!
don't forget to add the gradle dependency compile 'com.android.support:percent:23.3.0'  Adjust the version number as required
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