Dave Keenan & Douglas Blumeyer's guide to RTT/Conventions for names, variables, units, and notations: Difference between revisions

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β†’Objects: add coinciding-damage method tie-breaking objects
Dave Keenan (talk | contribs)
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Replaced πΆβ‚š with 𝑋 for complexity pretransformer. Deleted rows for simplicity pretransformer. Replaced unreduced 𝐢⁻¹ with 1/𝐢. Deleted unreduced 𝑆⁻¹.
Line 407: Line 407:
! colspan="17" |damage
! colspan="17" |damage
|-
|-
|<math>s^{-1}</math>
|
|<math>c</math>
|<math>c</math>
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity|complexity]]
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity|complexity]]
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|
|
|-
|-
|<math>c^{-1}</math>
|<math>\dfrac1c</math>
|<math>s</math>
|<math>s</math>
|[[simplicity]]
|[[simplicity]]
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|
|
|-
|-
|<math>S^{-1}</math>
|
|<math>C</math>
|<math>C</math>
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval complexity weight matrix]]
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval complexity weight matrix]]
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|
|
|-
|-
|<math>C^{-1}</math>
|<math>\dfrac1C</math>
|<math>S</math>
|<math>S</math>
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval simplicity weight matrix]]
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval simplicity weight matrix]]
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! colspan="17" |damage
! colspan="17" |damage
|-
|-
|<math>s^{-1}</math>
|
|<math>c</math>
|<math>c</math>
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity|complexity]]
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity|complexity]]
Line 1,338: Line 1,338:
|
|
|-
|-
|<math>c^{-1}</math>
|<math>\dfrac1c</math>
|<math>s</math>
|<math>s</math>
|[[simplicity]]
|[[simplicity]]
Line 1,536: Line 1,536:
|
|
|-
|-
|<math>S^{-1}</math>
|
|<math>C</math>
|<math>C</math>
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval complexity weight matrix]]
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval complexity weight matrix]]
Line 1,552: Line 1,552:
|
|
|-
|-
|<math>C^{-1}</math>
|<math>\dfrac1C</math>
|<math>S</math>
|<math>S</math>
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval simplicity weight matrix]]
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval simplicity weight matrix]]
Line 1,718: Line 1,718:
|
|
|-
|-
|<math>S_{\text{p}}^{-1}</math>
|
|<math>C_{\text{p}}</math>
|<math>X</math>
|[[complexity prescaler]]
|[[complexity prescaler]]
|<math>\small\mathsf{πŸ™}\scriptsize\mathsf{(C)}</math>
|<math>\small\mathsf{πŸ™}\scriptsize\mathsf{(C)}</math>
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|<math>𝒄_{\text{p}}</math>
|<math>𝒄_{\text{p}}</math>
|<math>c_{\text{p}i}</math>
|<math>c_{\text{p}i}</math>
|
|-
|<math>C_{\text{p}}^{-1}</math>
|<math>S_{\text{p}}</math>
|[[simplicity prescaler]]
|<math>\small\mathsf{πŸ™}\scriptsize\mathsf{(S)}</math>
|<math>\small\mathsf{(S)}</math>
|simplicity weight
|
|<math>\scriptsize (d, d)</math>
|real
|matrix
|
|⟨[...⟩ ...]
|
|
|<math>𝒔_{\text{p}}</math>
|<math>s_{\text{p}i}</math>
|
|
|-
|-
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|
|
|<math>β€– Β· β€–_q</math>
|<math>β€– Β· β€–_q</math>
|[[power norm]] (<math>q</math>-norm)
|[[power norm]] (<math>p</math>-norm)
|
|
|
|
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! colspan="17" |damage
! colspan="17" |damage
|-
|-
|<math>s^{-1}</math>
|
|<math>c</math>
|<math>c</math>
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity|complexity]]
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity|complexity]]
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|
|
|-
|-
|<math>c^{-1}</math>
|<math>\dfrac1c</math>
|<math>s</math>
|<math>s</math>
|[[simplicity]]
|[[simplicity]]
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|
|
|-
|-
|<math>S^{-1}</math>
|
|<math>C</math>
|<math>C</math>
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval complexity weight matrix]]
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval complexity weight matrix]]
Line 2,771: Line 2,753:
|
|
|-
|-
|<math>C^{-1}</math>
|<math>\dfrac1C</math>
|<math>S</math>
|<math>S</math>
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval simplicity weight matrix]]
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval simplicity weight matrix]]
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|-
|-
|
|
|<math>C_{\text{p}}</math>
|<math>X</math>
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Prescaling_vs_pretransforming|complexity pretransformer]]
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Prescaling_vs_pretransforming|complexity pretransformer]]
|<math>\small\mathsf{πŸ™}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{πŸ™}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{C)}</math><ref>In these tables, "alternative" means any complexity other than the default of log-product complexity, and "alt" stands for its abbreviation.</ref>
|<math>\small\mathsf{πŸ™}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{πŸ™}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{C)}</math><ref>In these tables, "alternative" means any complexity other than the default of log-product complexity, and "alt" stands for its abbreviation.</ref>
Line 2,954: Line 2,936:
|<math>𝒄_{\text{p}}</math>
|<math>𝒄_{\text{p}}</math>
|<math>c_{\text{p}i}</math> or [math]c_{\text{p}ij}[/math]
|<math>c_{\text{p}i}</math> or [math]c_{\text{p}ij}[/math]
|
|-
|
|<math>S_{\text{p}}</math>
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Prescaling_vs_pretransforming|simplicity pretransformer]]
|<math>\small\mathsf{πŸ™}\scriptsize\mathsf{(S)}</math> or <math>\small\mathsf{πŸ™}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{S)}</math>
|<math>\small\mathsf{(S)}</math> or <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math>
|simplicity weight or <alternative>-simplicity weight
|
|<math>\scriptsize (d, d)</math> or <math>\scriptsize (d+1, d+1)</math>
|real
|matrix
|
|⟨[...⟩ ...]
|<math>𝒔_{\text{p}i}</math>
|
|<math>𝒔_{\text{p}}</math>
|<math>s_{\text{p}i}</math> or [math]s_{\text{p}ij}[/math]
|
|
|-
|-
Line 3,012: Line 2,976:
|
|
|<math>β€– Β· β€–_q</math>
|<math>β€– Β· β€–_q</math>
|[[power norm]] (<math>q</math>-norm)
|[[power norm]] (<math>p</math>-norm)
|
|
|
|
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