From 95f12ce6f3b414046f37513fe9312a3d9bcecb97 Mon Sep 17 00:00:00 2001 From: Claude Date: Thu, 23 Jul 2026 22:06:30 +0000 Subject: [PATCH] Mark the -1 and +1 null-space steps with orange triangles Adds a down triangle at the -1 step and an up triangle at the +1 step along the taste-20.9 null-space line (the two moves shown in the book text). Both predict the same taste as the direct-inversion solution. Co-Authored-By: Claude Opus 4.8 Claude-Session: https://claude.ai/code/session_01DsTypY4FcRbrXRxorb9raz --- pls/pls-model-inversion-null-space.png | Bin 87917 -> 94101 bytes pls/pls-model-inversion-null-space.py | 17 ++++++++++++++++- 2 files changed, 16 insertions(+), 1 deletion(-) diff --git a/pls/pls-model-inversion-null-space.png b/pls/pls-model-inversion-null-space.png index f29a19f422557b6b931f01c353d7925c7a97db1c..de05898c610d0a0002a957e9b24577aebac793dc 100644 GIT binary patch delta 58389 zcmY&=1yGe;wDzI9LmCOC8|m`U-Hmj2H@tv!qaa-Z0)m93f^;_`-3Jhq?uP%x@7}rd z&oIO=!`^%KdY-k|uR=;&MXJ$A0H(=Njt)mxmfu6?4KG$`)goEvVJjizL{h;YQBfID z2MAFZ$wT44qJL!}A9{y{G{m?pzgSFq`S4Jt9Po!--uY)+{`NZ8<>uz^gi!iJ(d|}- zM?M_pZ}_JxSHzuSp<}*i;kYnDJHsYgyFq;8>`xvxh>7=l1<}!TYVdNXGyv7}=SvuP zF6qvnmB-3f!u7K;mhhn^sb&jv4@CZF95+ARSeK4js=ojg#=hs7cxA+?!awa5<0S9K zQ%t!90}RPnI&~ur1~$Jo1u!xmBZNRWfV->TO=Zt?7SXChaG^Qfz89=ifm|uGFRQf) z3hUZX=!l=4Fv8Fn;poGY-2q35q?f**g5F5U^gjQ4^kQd9dBToxXR?qA`OH?MQ1$_` 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tau[0], tau[1], color=BLACK, marker="s", s=70, zorder=5, label="Direct-inversion solution" ) + # The two null-space moves from the text: a -1 and a +1 step along the + # null-space direction from the direct-inversion solution. Both sit on the + # orange (taste 20.9) line and predict the same taste. + step_minus = tau + (-1.0) * g_ns + step_plus = tau + (1.0) * g_ns + step_down = ax.scatter( + step_minus[0], step_minus[1], color=ORANGE, marker="v", s=120, + edgecolors=BLACK, linewidths=0.8, zorder=6, label="Null-space step (-1)", + ) + step_up = ax.scatter( + step_plus[0], step_plus[1], color=ORANGE, marker="^", s=120, + edgecolors=BLACK, linewidths=0.8, zorder=6, label="Null-space step (+1)", + ) ax.axhline(0, color="0.7", lw=0.8) ax.axvline(0, color="0.7", lw=0.8) ax.set_xlabel("$t_1$") @@ -138,7 +151,9 @@ def build_figure(out_dir: Path) -> None: handles=[line3, line1, line2], loc="upper left", framealpha=0.9, fontsize=9, title="Null spaces" ) ax.add_artist(lines_legend) - ax.legend(handles=[cal, os_circles, di], loc="lower right", framealpha=0.9, fontsize=9) + ax.legend( + handles=[cal, os_circles, di, step_down, step_up], loc="lower right", framealpha=0.9, fontsize=9 + ) fig.tight_layout() fig.savefig(out_dir / "pls-model-inversion-null-space.png") plt.close(fig)