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update lattice orderings
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@alegresor
alegresor committed Aug 4, 2023
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2 changes: 1 addition & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
name = "QMCGenerators"
uuid = "fcae8fc2-2969-4f4b-b6c9-a95746d81969"
authors = ["alegresor agsorokin3@gmail.com"]
version = "1.3.0"
version = "1.3.1"

[deps]
CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
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170 changes: 84 additions & 86 deletions docs/src/tutorial.md
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Expand Up @@ -159,9 +159,9 @@ Next(ls,4)
Next(ls,4)
# output
4×5 Matrix{Float64}:
0.375 0.875 0.375 0.875 0.875
0.875 0.375 0.875 0.375 0.375
0.625 0.125 0.625 0.125 0.125
0.375 0.875 0.375 0.875 0.875
0.125 0.625 0.125 0.625 0.625
```
```jldoctest tut_ls; output = false
Expand Down Expand Up @@ -423,13 +423,12 @@ Next(ls,4)

### Linear Ordering

By default, digital sequences are generated in Gray code order. One may generate the first $2^m$ points in linear order via
By default, digital sequences are generated in Gray code order. One may generate the first 8 points in linear order via

```jldoctest tut_ds_order
m = 3
n = 2^m
n = 8
ds = DigitalSeqB2G(4)
FirstLinear(ds,m)
FirstLinear(ds,n)
# output
8×4 Matrix{Float64}:
0.0 0.0 0.0 0.0
Expand Down Expand Up @@ -461,19 +460,18 @@ Next(ds,n)
Similarly, Lattices are by default generated in extensible ordering. A linear ordering is also available

```jldoctest tut_ls_order
m = 3
n = 2^m
n = 8
ls = LatticeSeqB2(4)
FirstLinear(ls,m)
FirstLinear(ls,n)
# output
8×4 Matrix{Float64}:
0.0 0.0 0.0 0.0
0.125 0.625 0.125 0.625
0.25 0.25 0.25 0.25
0.375 0.875 0.375 0.875
0.5 0.5 0.5 0.5
0.625 0.125 0.625 0.125
0.25 0.25 0.25 0.25
0.75 0.75 0.75 0.75
0.125 0.625 0.125 0.625
0.625 0.125 0.625 0.125
0.375 0.875 0.375 0.875
0.875 0.375 0.875 0.375
```

Expand All @@ -487,9 +485,9 @@ Next(ls,n)
0.5 0.5 0.5 0.5
0.75 0.75 0.75 0.75
0.25 0.25 0.25 0.25
0.375 0.875 0.375 0.875
0.875 0.375 0.875 0.375
0.625 0.125 0.625 0.125
0.375 0.875 0.375 0.875
0.125 0.625 0.125 0.625
```

Expand All @@ -498,7 +496,7 @@ Linear order for randomized sequences has expected syntax
```jldoctest tut_ds_order_rand
ds = DigitalSeqB2G(LinearMatrixScramble(4,11))
rds = RandomDigitalShift(ds,1,17)
FirstLinear(rds,2)
FirstLinear(rds,4)
# output
4×4 Matrix{Float64}:
0.844967 0.66901 0.686087 0.362606
Expand All @@ -509,7 +507,7 @@ FirstLinear(rds,2)

```jldoctest tut_ds_order_rand
rds = RandomDigitalShift(ds,2,17)
xs = FirstRLinear(rds,2)
xs = FirstRLinear(rds,4)
xs[1]
# output
4×4 Matrix{Float64}:
Expand All @@ -531,7 +529,7 @@ xs[2]

```jldoctest tut_ds_order_rand
rds = RandomOwenScramble(ds,2,17)
xs = FirstRLinear(rds,2)
xs = FirstRLinear(rds,4)
xs[1]
# output
4×4 Matrix{Float64}:
Expand All @@ -555,13 +553,13 @@ For lattices a similar API holds

```jldoctest tut_ds_order_rand
rls = RandomShift(LatticeSeqB2(4),2,17)
xs = FirstRLinear(rls,2)
xs = FirstRLinear(rls,4)
xs[1]
# output
4×4 Matrix{Float64}:
0.447971 0.593933 0.190141 0.331784
0.697971 0.843933 0.440141 0.581784
0.947971 0.0939328 0.690141 0.831784
0.697971 0.843933 0.440141 0.581784
0.197971 0.343933 0.940141 0.081784
```

Expand All @@ -570,8 +568,8 @@ xs[2]
# output
4×4 Matrix{Float64}:
0.868892 0.697591 0.828991 0.475479
0.118892 0.947591 0.0789912 0.725479
0.368892 0.197591 0.328991 0.975479
0.118892 0.947591 0.0789912 0.725479
0.618892 0.447591 0.578991 0.225479
```

Expand All @@ -580,23 +578,23 @@ xs[2]
For digital sequences, we sometimes want the binary representation of points. We can get the binary representations as integers and then convert them to their floating point values as follows

```jldoctest tut_ds_binary
ds = DigitalSeqB2G(4)
ds = DigitalSeqB2G(3)
xb = NextBinary(ds,4)
# output
4×4 Matrix{UInt64}:
0x0000000000000000 0x0000000000000000 … 0x0000000000000000
0x0000000080000000 0x0000000080000000 0x0000000080000000
0x00000000c0000000 0x0000000040000000 0x0000000040000000
0x0000000040000000 0x00000000c0000000 0x00000000c0000000
4×3 Matrix{UInt64}:
0x0000000000000000 0x0000000000000000 0x0000000000000000
0x0000000080000000 0x0000000080000000 0x0000000080000000
0x00000000c0000000 0x0000000040000000 0x0000000040000000
0x0000000040000000 0x00000000c0000000 0x00000000c0000000
```
```jldoctest tut_ds_binary
BinaryToFloat64(xb,ds)
# output
4×4 Matrix{Float64}:
0.0 0.0 0.0 0.0
0.5 0.5 0.5 0.5
0.75 0.25 0.25 0.25
0.25 0.75 0.75 0.75
4×3 Matrix{Float64}:
0.0 0.0 0.0
0.5 0.5 0.5
0.75 0.25 0.25
0.25 0.75 0.75
```

This is also compatible with randomized digital sequences
Expand All @@ -606,109 +604,109 @@ Reset!(ds)
rds_single = RandomDigitalShift(ds,1,11)
xb = NextBinary(rds_single,4)
# output
4×4 Matrix{UInt64}:
0x001293891708f524 0x0016da39893c2ad5 … 0x00167b863bac2dff
0x000293891708f524 0x0006da39893c2ad5 0x00067b863bac2dff
0x000a93891708f524 0x001eda39893c2ad5 0x001e7b863bac2dff
0x001a93891708f524 0x000eda39893c2ad5 0x000e7b863bac2dff
4×3 Matrix{UInt64}:
0x001293891708f524 0x0016da39893c2ad5 0x001b9c72840fa196
0x000293891708f524 0x0006da39893c2ad5 0x000b9c72840fa196
0x000a93891708f524 0x001eda39893c2ad5 0x00139c72840fa196
0x001a93891708f524 0x000eda39893c2ad5 0x00039c72840fa196
```
```jldoctest tut_ds_binary
BinaryToFloat64(xb,rds_single)
# output
4×4 Matrix{Float64}:
0.58051 0.714139 0.862848 0.702579
0.0805097 0.214139 0.362848 0.202579
0.33051 0.964139 0.612848 0.952579
0.83051 0.464139 0.112848 0.452579
4×3 Matrix{Float64}:
0.58051 0.714139 0.862848
0.0805097 0.214139 0.362848
0.33051 0.964139 0.612848
0.83051 0.464139 0.112848
```
```jldoctest tut_ds_binary
Reset!(ds)
rds_multiple = RandomDigitalShift(ds,2,11)
xbs = NextRBinary(rds_multiple,4)
xbs[1]
# output
4×4 Matrix{UInt64}:
0x001293891708f524 0x001b9c72840fa196 … 0x001d6f2b8e3bf612
0x000293891708f524 0x000b9c72840fa196 0x000d6f2b8e3bf612
0x000a93891708f524 0x00139c72840fa196 0x00156f2b8e3bf612
0x001a93891708f524 0x00039c72840fa196 0x00056f2b8e3bf612
4×3 Matrix{UInt64}:
0x001293891708f524 0x001b9c72840fa196 0x001b92b4f3a3bb3f
0x000293891708f524 0x000b9c72840fa196 0x000b92b4f3a3bb3f
0x000a93891708f524 0x00139c72840fa196 0x001392b4f3a3bb3f
0x001a93891708f524 0x00039c72840fa196 0x000392b4f3a3bb3f
```
```jldoctest tut_ds_binary
xbs[2]
# output
4×4 Matrix{UInt64}:
0x0016da39893c2ad5 0x00167b863bac2dff … 0x001cd7a908e348e1
0x0006da39893c2ad5 0x00067b863bac2dff 0x000cd7a908e348e1
0x000eda39893c2ad5 0x001e7b863bac2dff 0x0014d7a908e348e1
0x001eda39893c2ad5 0x000e7b863bac2dff 0x0004d7a908e348e1
4×3 Matrix{UInt64}:
0x0016da39893c2ad5 0x00167b863bac2dff 0x00006a9dbda72567
0x0006da39893c2ad5 0x00067b863bac2dff 0x00106a9dbda72567
0x000eda39893c2ad5 0x001e7b863bac2dff 0x00086a9dbda72567
0x001eda39893c2ad5 0x000e7b863bac2dff 0x00186a9dbda72567
```
```jldoctest tut_ds_binary; output = false
BinaryToFloat64(xbs,rds_multiple)
# output
2-element Vector{Matrix{Float64}}:
[0.5805097055341872 0.8628475741689268 0.8616585501275508 0.9198205736171892; 0.08050970553418724 0.36284757416892677 0.36165855012755077 0.41982057361718916; 0.33050970553418724 0.6128475741689268 0.6116585501275508 0.6698205736171892; 0.8305097055341872 0.11284757416892677 0.11165855012755077 0.16982057361718916]
[0.7141387634631778 0.702578655765535 0.013014669814919055 0.9013257192221112; 0.21413876346317784 0.20257865576553502 0.513014669814919 0.40132571922211124; 0.46413876346317784 0.952578655765535 0.26301466981491906 0.6513257192221112; 0.9641387634631778 0.452578655765535 0.763014669814919 0.15132571922211124]
[0.5805097055341872 0.8628475741689268 0.8616585501275508; 0.08050970553418724 0.36284757416892677 0.36165855012755077; 0.33050970553418724 0.6128475741689268 0.6116585501275508; 0.8305097055341872 0.11284757416892677 0.11165855012755077]
[0.7141387634631778 0.702578655765535 0.013014669814919055; 0.21413876346317784 0.20257865576553502 0.513014669814919; 0.46413876346317784 0.952578655765535 0.26301466981491906; 0.9641387634631778 0.452578655765535 0.763014669814919]
```
```jldoctest tut_ds_binary
Reset!(ds)
NextBinary(RandomOwenScramble(ds,1,11),4)
# output
4×4 Matrix{UInt64}:
0x001a5eef4cd370c6 0x00028467570b42be … 0x0001a6384b638476
0x000ff20fe5ead1ba 0x001cf89a1a9a2567 0x00151c3bba0d1d72
0x000691102ee5e771 0x0009fddc7fb98782 0x000b360939d54a00
0x001689e7a7bc5106 0x0014908fa8a77dff 0x001a7c08956e0175
4×3 Matrix{UInt64}:
0x001a5eef4cd370c6 0x00028467570b42be 0x0003828fa0349158
0x000ff20fe5ead1ba 0x001cf89a1a9a2567 0x001e02e9de330269
0x000691102ee5e771 0x0009fddc7fb98782 0x000bb5aca8044288
0x001689e7a7bc5106 0x0014908fa8a77dff 0x00158be9ceaeef56
```

Getting binary points with linear ordering is also supported.

```jldoctest tut_ds_binary
Reset!(ds) # resets rds_single and rds_multiple as well
FirstLinearBinary(ds,2)
FirstLinearBinary(ds,4)
# output
4×4 Matrix{UInt64}:
0x0000000000000000 0x0000000000000000 … 0x0000000000000000
0x0000000080000000 0x0000000080000000 0x0000000080000000
0x0000000040000000 0x00000000c0000000 0x00000000c0000000
0x00000000c0000000 0x0000000040000000 0x0000000040000000
4×3 Matrix{UInt64}:
0x0000000000000000 0x0000000000000000 0x0000000000000000
0x0000000080000000 0x0000000080000000 0x0000000080000000
0x0000000040000000 0x00000000c0000000 0x00000000c0000000
0x00000000c0000000 0x0000000040000000 0x0000000040000000
```
```jldoctest tut_ds_binary
FirstLinearBinary(rds_single,2)
FirstLinearBinary(rds_single,4)
# output
4×4 Matrix{UInt64}:
0x001293891708f524 0x0016da39893c2ad5 … 0x00167b863bac2dff
0x000293891708f524 0x0006da39893c2ad5 0x00067b863bac2dff
0x001a93891708f524 0x000eda39893c2ad5 0x000e7b863bac2dff
0x000a93891708f524 0x001eda39893c2ad5 0x001e7b863bac2dff
4×3 Matrix{UInt64}:
0x001293891708f524 0x0016da39893c2ad5 0x001b9c72840fa196
0x000293891708f524 0x0006da39893c2ad5 0x000b9c72840fa196
0x001a93891708f524 0x000eda39893c2ad5 0x00039c72840fa196
0x000a93891708f524 0x001eda39893c2ad5 0x00139c72840fa196
```
```jldoctest tut_ds_binary
xbs = FirstRLinearBinary(rds_multiple,2)
xbs = FirstRLinearBinary(rds_multiple,4)
xbs[1]
# output
4×4 Matrix{UInt64}:
0x001293891708f524 0x001b9c72840fa196 … 0x001d6f2b8e3bf612
0x000293891708f524 0x000b9c72840fa196 0x000d6f2b8e3bf612
0x001a93891708f524 0x00039c72840fa196 0x00056f2b8e3bf612
0x000a93891708f524 0x00139c72840fa196 0x00156f2b8e3bf612
4×3 Matrix{UInt64}:
0x001293891708f524 0x001b9c72840fa196 0x001b92b4f3a3bb3f
0x000293891708f524 0x000b9c72840fa196 0x000b92b4f3a3bb3f
0x001a93891708f524 0x00039c72840fa196 0x000392b4f3a3bb3f
0x000a93891708f524 0x00139c72840fa196 0x001392b4f3a3bb3f
```
```jldoctest tut_ds_binary
xbs[2]
# output
4×4 Matrix{UInt64}:
0x0016da39893c2ad5 0x00167b863bac2dff … 0x001cd7a908e348e1
0x0006da39893c2ad5 0x00067b863bac2dff 0x000cd7a908e348e1
0x001eda39893c2ad5 0x000e7b863bac2dff 0x0004d7a908e348e1
0x000eda39893c2ad5 0x001e7b863bac2dff 0x0014d7a908e348e1
4×3 Matrix{UInt64}:
0x0016da39893c2ad5 0x00167b863bac2dff 0x00006a9dbda72567
0x0006da39893c2ad5 0x00067b863bac2dff 0x00106a9dbda72567
0x001eda39893c2ad5 0x000e7b863bac2dff 0x00186a9dbda72567
0x000eda39893c2ad5 0x001e7b863bac2dff 0x00086a9dbda72567
```
```jldoctest tut_ds_binary
Reset!(ds)
FirstLinearBinary(RandomOwenScramble(ds,1,11),2)
FirstLinearBinary(RandomOwenScramble(ds,1,11),4)
# output
4×4 Matrix{UInt64}:
0x001a5eef4cd370c6 0x00028467570b42be … 0x0001a6384b638476
0x000ff20fe5ead1ba 0x001cf89a1a9a2567 0x00151c3bba0d1d72
0x001691102ee5e771 0x0011fddc7fb98782 0x001b360939d54a00
0x000689e7a7bc5106 0x000c908fa8a77dff 0x000a7c08956e0175
4×3 Matrix{UInt64}:
0x001a5eef4cd370c6 0x00028467570b42be 0x0003828fa0349158
0x000ff20fe5ead1ba 0x001cf89a1a9a2567 0x001e02e9de330269
0x001691102ee5e771 0x0011fddc7fb98782 0x0013b5aca8044288
0x000689e7a7bc5106 0x000c908fa8a77dff 0x000d8be9ceaeef56
```

These may be converted to floats as before.
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