I am using the amsmath package and fonts, but would like to import a few delimiters from stix. Following the instructions here: How to use only selected math symbols of the STIX fonts?
I can import the desired delimiters. However, I would like to automatically scale those delimiters according to the size of the interior math expression (the commands \left{ and \right} come to mind). I know I can manually change their size with commands like \bigl\lBrace, but it is important that it can happen automatically (as done with the \left and \right commands).
MWE:
\documentclass{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\DeclareFontEncoding{LS2}{}{\noaccents@}
\DeclareFontSubstitution{LS2}{stix}{m}{n}
\DeclareSymbolFont{largesymbolstix}{LS2}{stixex}{m} {n}
\DeclareMathDelimiter{\lBrace}{\mathopen}{largesymbolstix}{"E8}{largesymbols}{"0E}
\DeclareMathDelimiter{\rBrace}{\mathclose}{largesymbolstix}{"E9}{largesymbols}{"0F}
\DeclareMathDelimiter{\lbrbrak}{\mathopen}{largesymbolstix}{"EE}{largesymbols}{"14}
\DeclareMathDelimiter{\rbrbrak}{\mathclose}{largesymbolstix}{"EF}{largesymbols}{"15}
\DeclareMathDelimiter{\lParen}{\mathopen}{largesymbolstix}{"DE}{largesymbols}{"02}
\DeclareMathDelimiter{\rParen}{\mathclose}{largesymbolstix}{"DF}{largesymbols}{"03}
\begin{document}
$\left\lBrace \begin{array}{cc}x & y\\y& z\end{array} \right\rBrace$
\end{document}
If I remove the \left and \right commands, my output has the correct braces, but not appropriately sized. Any ideas?

{}icon above the question box. – barbara beeton Jul 27 '19 at 20:54largesymbolstixin both places of every line. – egreg Jul 27 '19 at 21:11