sample-diagonal-distribution.md

The sample_diagonal_distribution executable

Synopsis

Synopsis: sample_diagonal_distribution \
   [ -delta-bound <delta-bound> ] [ -eta-bound <eta-bound> ] \
      <distribution> [ <n> ]

Samples a diagonal distribution.

The samples are written to the console.

Mandatory command line arguments

An argument <distribution> where

• <distribution> is the path to the distribution

Optional command line arguments

An optional argument specifying the number of samples (defaults to 1000):

• <n> sets the number of samples to <n>

Flag specifying the search bound $B_\Delta$ in $\Delta$ (defaults to DELTA_BOUND):

• -delta-bound <eta-bound> sets $B_\Delta$ to <eta-bound>

  The bound $B_\Delta$ controls how large an offset from $k_{\eta, 0}(j)$ is considered when sampling $k = k_{\eta, 0}(j) + \Delta$ from the distribution given $j$ and $\eta$: More specifically, all offsets $\Delta \in [-B_\Delta, B_\Delta] \cap \mathbb Z$ are considered. For further details, see [E19p].

Flag specifying the search bound $B_\eta$ in $\eta$ (defaults to same as for the distribution):

• -eta-bound <eta-bound> sets $B_\eta$ to <eta-bound>

  The bound $B_\eta$ controls how many peak indices $\eta$ are considered when sampling $(\alpha_r, \eta)$ from the distribution: More specifically, the peaks with peak indices $\eta \in [-B_\eta, B_\eta] \cap \mathbb Z$ are considered. For further details, see [E19p].

Interpreting the output

The console output contains samples on the format

$ ./sample_diagonal_distribution distributions/diagonal-distribution-det-dim-2048-m-2048-sigma-12-s-30.txt
Importing the distribution from "distributions/diagonal-distribution-det-dim-2048-m-2048-sigma-12-s-30.txt"...
sample: 1 / 1000
alpha_d: -35935825122891931833729655096486168792909163231305841470249344837021947587308045765076385318496915475277737582203874198462546225870436994380377675669387310860366691753536674524576826913585403531486838031867949207265817601955728129395134022648764999202313667450223458713974240563228793173889505234392577276894678082560754503608606508034187029181280487066047211394673679842681430790585212427102162128988167354964281487241659849773162759397934337190091070463341257006548070888721147623053024467363017071762302817279194486698367207024568491034211964893697144497916106505798081261589977701101935802905955868746084949330036
alpha_r: -36524337458574239265628208067896842506950326527017259394730180489542756732680357389881218357076938075192295258411090398918184660492852191584152986278505394204601716219309586003426913958842532059465023984393734705508972204045662420718481156344455970029163456386050542779611257311689312202047260840833739770686467536601049794750711541184745471580915382450614435009184294534422161360377609344335407194261827711389776974773732143560606868889997224964631515267260868029148380293053851598201224756805836349624148610715314860934760138139510380369135588446221239622495355624638261020831078107665093370053208281117884125449232
j: 117230176424540293862944053032138388243432696641335594043065703595042649164565862966079387760043623026080279243567547024157901262056698174254532194079373155205985610434226113182507393376750855001196470177077136714076332520510559413166717769044043432836718936436912478691595400736453067575743514787948303226345212981324224129831753056330365257944030208127111712252852508691028172244505242927813361686452460370850262096301388425862299228885248786095781139462469768546628263916167117164779950039716325779890600345059873262716669169883110494242352509462703122640535469031898325637359081022748518316436920519130524080079797476
k: 144901767494676867523
eta: 0

(..)

where

• $(\alpha_r, \eta)$ are first sampled from the distribution,
• $j$ is then sampled from all values of $j$ yielding $\alpha_r$, and
• $k$ is finally sampled given $j$ and $\eta$,

for further details see [E19p]. In summary

• $(\alpha_d, \alpha_r)$ is the admissible argument pair sampled, and
• $(j, k)$ is the integer pair sampled.