spark-instrumented-optimizer/python/pyspark/ml/recommendation.py
Ludovic Henry 5b77ebb57b [SPARK-35150][ML] Accelerate fallback BLAS with dev.ludovic.netlib
### What changes were proposed in this pull request?

Following https://github.com/apache/spark/pull/30810, I've continued looking for ways to accelerate the usage of BLAS in Spark. With this PR, I integrate work done in the [`dev.ludovic.netlib`](https://github.com/luhenry/netlib/) Maven package.

The `dev.ludovic.netlib` library wraps the original `com.github.fommil.netlib` library and focus on accelerating the linear algebra routines in use in Spark. When running the `org.apache.spark.ml.linalg.BLASBenchmark` benchmarking suite, I get the results at [1] on an Intel machine. Moreover, this library is thoroughly tested to return the exact same results as the reference implementation.

Under the hood, it reimplements the necessary algorithms in pure autovectorization-friendly Java 8, as well as takes advantage of the Vector API and Foreign Linker API introduced in JDK 16 when available.

A table summarising which version gets loaded in which case:

```
|                       | BLAS.nativeBLAS                                    | BLAS.javaBLAS                                      |
| --------------------- | -------------------------------------------------- | -------------------------------------------------- |
| with -Pnetlib-lgpl    | 1. dev.ludovic.netlib.blas.NetlibNativeBLAS, a     | 1. dev.ludovic.netlib.blas.VectorizedBLAS          |
|                       |     wrapper for com.github.fommil:all              |    (JDK16+, relies on the Vector API, requires     |
|                       | 2. dev.ludovic.netlib.blas.ForeignBLAS (JDK16+,    |     `--add-modules=jdk.incubator.vector` on JDK16) |
|                       |    relies on the Foreign Linker API, requires      | 2. dev.ludovic.netlib.blas.Java11BLAS (JDK11+)     |
|                       |    `--add-modules=jdk.incubator.foreign            | 3. dev.ludovic.netlib.blas.JavaBLAS                |
|                       |     -Dforeign.restricted=warn`)                    | 4. dev.ludovic.netlib.blas.NetlibF2jBLAS, a        |
|                       | 3. fails to load, falls back to BLAS.javaBLAS in   |     wrapper for com.github.fommil:core             |
|                       |     org.apache.spark.ml.linalg.BLAS                |                                                    |
| --------------------- | -------------------------------------------------- | -------------------------------------------------- |
| without -Pnetlib-lgpl | 1. dev.ludovic.netlib.blas.ForeignBLAS (JDK16+,    | 1. dev.ludovic.netlib.blas.VectorizedBLAS          |
|                       |    relies on the Foreign Linker API, requires      |    (JDK16+, relies on the Vector API, requires     |
|                       |    `--add-modules=jdk.incubator.foreign            |     `--add-modules=jdk.incubator.vector` on JDK16) |
|                       |     -Dforeign.restricted=warn`)                    | 2. dev.ludovic.netlib.blas.Java11BLAS (JDK11+)     |
|                       | 2. fails to load, falls back to BLAS.javaBLAS in   | 3. dev.ludovic.netlib.blas.JavaBLAS                |
|                       |     org.apache.spark.ml.linalg.BLAS                | 4. dev.ludovic.netlib.blas.NetlibF2jBLAS, a        |
|                       |                                                    |     wrapper for com.github.fommil:core             |
| --------------------- | -------------------------------------------------- | -------------------------------------------------- |
```

### Why are the changes needed?

Accelerates linear algebra operations when the pure-java fallback method is in use. Transparently falls back to native implementation (OpenBLAS, MKL) when available.

### Does this PR introduce _any_ user-facing change?

No, all changes are transparent to the user.

### How was this patch tested?

The `dev.ludovic.netlib` library has its own test suite [2]. It has also been validated by running the Spark test suite and benchmarking suite.

[1] Results for `org.apache.spark.ml.linalg.BLASBenchmark`:
#### JDK8:
```
[info] OpenJDK 64-Bit Server VM 1.8.0_292-b10 on Linux 5.8.0-50-generic
[info] Intel(R) Xeon(R) E-2276G CPU  3.80GHz
[info]
[info] f2jBLAS    = dev.ludovic.netlib.blas.NetlibF2jBLAS
[info] javaBLAS   = dev.ludovic.netlib.blas.Java8BLAS
[info] nativeBLAS = dev.ludovic.netlib.blas.Java8BLAS
[info]
[info] daxpy:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 223            232           8        448.0           2.2       1.0X
[info] java                                                221            228           7        453.0           2.2       1.0X
[info]
[info] saxpy:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 122            128           4        821.2           1.2       1.0X
[info] java                                                122            128           4        822.3           1.2       1.0X
[info]
[info] ddot:                                     Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 109            112           2        921.4           1.1       1.0X
[info] java                                                 70             74           3       1423.5           0.7       1.5X
[info]
[info] sdot:                                     Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                  96             98           2       1046.1           1.0       1.0X
[info] java                                                 47             49           2       2121.7           0.5       2.0X
[info]
[info] dscal:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 184            195           8        544.3           1.8       1.0X
[info] java                                                185            196           7        539.5           1.9       1.0X
[info]
[info] sscal:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                  99            104           4       1011.9           1.0       1.0X
[info] java                                                 99            104           4       1010.4           1.0       1.0X
[info]
[info] dspmv[U]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        947.2           1.1       1.0X
[info] java                                                  0              0           0       1584.8           0.6       1.7X
[info]
[info] dspr[U]:                                  Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        867.4           1.2       1.0X
[info] java                                                  1              1           0        865.0           1.2       1.0X
[info]
[info] dsyr[U]:                                  Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        485.9           2.1       1.0X
[info] java                                                  1              1           0        486.8           2.1       1.0X
[info]
[info] dgemv[N]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1843.0           0.5       1.0X
[info] java                                                  0              0           0       2690.6           0.4       1.5X
[info]
[info] dgemv[T]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1214.7           0.8       1.0X
[info] java                                                  0              0           0       2536.8           0.4       2.1X
[info]
[info] sgemv[N]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1895.9           0.5       1.0X
[info] java                                                  0              0           0       2961.1           0.3       1.6X
[info]
[info] sgemv[T]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1223.4           0.8       1.0X
[info] java                                                  0              0           0       3091.4           0.3       2.5X
[info]
[info] dgemm[N,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 560            575          20       1787.1           0.6       1.0X
[info] java                                                226            232           5       4432.4           0.2       2.5X
[info]
[info] dgemm[N,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 570            586          23       1755.2           0.6       1.0X
[info] java                                                227            232           4       4410.1           0.2       2.5X
[info]
[info] dgemm[T,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 863            879          17       1158.4           0.9       1.0X
[info] java                                                227            231           3       4407.9           0.2       3.8X
[info]
[info] dgemm[T,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                1282           1305          23        780.0           1.3       1.0X
[info] java                                                227            232           4       4413.4           0.2       5.7X
[info]
[info] sgemm[N,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 538            548           8       1858.6           0.5       1.0X
[info] java                                                221            226           3       4521.1           0.2       2.4X
[info]
[info] sgemm[N,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 549            558          10       1819.9           0.5       1.0X
[info] java                                                222            229           7       4503.5           0.2       2.5X
[info]
[info] sgemm[T,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 838            852          12       1193.0           0.8       1.0X
[info] java                                                222            229           5       4500.5           0.2       3.8X
[info]
[info] sgemm[T,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 905            919          18       1104.8           0.9       1.0X
[info] java                                                221            228           5       4521.3           0.2       4.1X
```

#### JDK11:
```
[info] OpenJDK 64-Bit Server VM 11.0.11+9-LTS on Linux 5.8.0-50-generic
[info] Intel(R) Xeon(R) E-2276G CPU  3.80GHz
[info]
[info] f2jBLAS    = dev.ludovic.netlib.blas.NetlibF2jBLAS
[info] javaBLAS   = dev.ludovic.netlib.blas.Java11BLAS
[info] nativeBLAS = dev.ludovic.netlib.blas.Java11BLAS
[info]
[info] daxpy:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 195            204          10        512.7           2.0       1.0X
[info] java                                                195            202           7        512.4           2.0       1.0X
[info]
[info] saxpy:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 108            113           4        923.3           1.1       1.0X
[info] java                                                102            107           4        984.4           1.0       1.1X
[info]
[info] ddot:                                     Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 107            110           3        938.1           1.1       1.0X
[info] java                                                 69             72           3       1447.1           0.7       1.5X
[info]
[info] sdot:                                     Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                  96             98           2       1046.5           1.0       1.0X
[info] java                                                 43             45           2       2317.1           0.4       2.2X
[info]
[info] dscal:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 155            168           8        644.2           1.6       1.0X
[info] java                                                158            169           8        632.8           1.6       1.0X
[info]
[info] sscal:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                  85             90           4       1178.1           0.8       1.0X
[info] java                                                 86             90           4       1167.7           0.9       1.0X
[info]
[info] dspmv[U]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   0              0           0       1182.1           0.8       1.0X
[info] java                                                  0              0           0       1432.1           0.7       1.2X
[info]
[info] dspr[U]:                                  Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        898.7           1.1       1.0X
[info] java                                                  1              1           0        891.5           1.1       1.0X
[info]
[info] dsyr[U]:                                  Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        495.4           2.0       1.0X
[info] java                                                  1              1           0        495.7           2.0       1.0X
[info]
[info] dgemv[N]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   0              0           0       2271.6           0.4       1.0X
[info] java                                                  0              0           0       3648.1           0.3       1.6X
[info]
[info] dgemv[T]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1229.3           0.8       1.0X
[info] java                                                  0              0           0       2711.3           0.4       2.2X
[info]
[info] sgemv[N]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   0              0           0       2677.5           0.4       1.0X
[info] java                                                  0              0           0       3288.2           0.3       1.2X
[info]
[info] sgemv[T]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1233.0           0.8       1.0X
[info] java                                                  0              0           0       2766.3           0.4       2.2X
[info]
[info] dgemm[N,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 520            536          16       1923.6           0.5       1.0X
[info] java                                                214            221           7       4669.5           0.2       2.4X
[info]
[info] dgemm[N,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 593            612          17       1686.5           0.6       1.0X
[info] java                                                215            219           3       4643.3           0.2       2.8X
[info]
[info] dgemm[T,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 853            870          16       1172.8           0.9       1.0X
[info] java                                                215            218           3       4659.7           0.2       4.0X
[info]
[info] dgemm[T,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                1350           1370          23        740.8           1.3       1.0X
[info] java                                                215            219           4       4656.6           0.2       6.3X
[info]
[info] sgemm[N,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 460            468           6       2173.2           0.5       1.0X
[info] java                                                210            213           2       4752.7           0.2       2.2X
[info]
[info] sgemm[N,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 535            544           8       1869.3           0.5       1.0X
[info] java                                                210            215           5       4761.8           0.2       2.5X
[info]
[info] sgemm[T,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 843            853          11       1186.8           0.8       1.0X
[info] java                                                209            214           4       4793.4           0.2       4.0X
[info]
[info] sgemm[T,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 891            904          15       1122.0           0.9       1.0X
[info] java                                                209            214           4       4777.2           0.2       4.3X
```

#### JDK16:
```
[info] OpenJDK 64-Bit Server VM 16+36 on Linux 5.8.0-50-generic
[info] Intel(R) Xeon(R) E-2276G CPU  3.80GHz
[info]
[info] f2jBLAS    = dev.ludovic.netlib.blas.NetlibF2jBLAS
[info] javaBLAS   = dev.ludovic.netlib.blas.VectorizedBLAS
[info] nativeBLAS = dev.ludovic.netlib.blas.VectorizedBLAS
[info]
[info] daxpy:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 194            199           7        515.7           1.9       1.0X
[info] java                                                181            186           3        551.1           1.8       1.1X
[info]
[info] saxpy:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 109            115           4        915.0           1.1       1.0X
[info] java                                                 88             92           3       1138.8           0.9       1.2X
[info]
[info] ddot:                                     Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 108            110           2        922.6           1.1       1.0X
[info] java                                                 54             56           2       1839.2           0.5       2.0X
[info]
[info] sdot:                                     Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                  96             97           2       1046.1           1.0       1.0X
[info] java                                                 29             30           1       3393.4           0.3       3.2X
[info]
[info] dscal:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 156            165           5        643.0           1.6       1.0X
[info] java                                                150            159           5        667.1           1.5       1.0X
[info]
[info] sscal:                                    Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                  85             91           6       1171.0           0.9       1.0X
[info] java                                                 75             79           3       1340.6           0.7       1.1X
[info]
[info] dspmv[U]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        917.0           1.1       1.0X
[info] java                                                  0              0           0       8147.2           0.1       8.9X
[info]
[info] dspr[U]:                                  Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        859.3           1.2       1.0X
[info] java                                                  1              1           0        859.3           1.2       1.0X
[info]
[info] dsyr[U]:                                  Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0        482.1           2.1       1.0X
[info] java                                                  1              1           0        482.6           2.1       1.0X
[info]
[info] dgemv[N]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   0              0           0       2214.2           0.5       1.0X
[info] java                                                  0              0           0       7975.8           0.1       3.6X
[info]
[info] dgemv[T]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1231.4           0.8       1.0X
[info] java                                                  0              0           0       8680.9           0.1       7.0X
[info]
[info] sgemv[N]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   0              0           0       2684.3           0.4       1.0X
[info] java                                                  0              0           0      18527.1           0.1       6.9X
[info]
[info] sgemv[T]:                                 Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                   1              1           0       1235.4           0.8       1.0X
[info] java                                                  0              0           0      17347.9           0.1      14.0X
[info]
[info] dgemm[N,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 530            552          18       1887.5           0.5       1.0X
[info] java                                                 58             64           3      17143.9           0.1       9.1X
[info]
[info] dgemm[N,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 598            620          17       1671.1           0.6       1.0X
[info] java                                                 58             64           3      17196.6           0.1      10.3X
[info]
[info] dgemm[T,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 834            847          14       1199.4           0.8       1.0X
[info] java                                                 57             63           4      17486.9           0.1      14.6X
[info]
[info] dgemm[T,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                1338           1366          22        747.3           1.3       1.0X
[info] java                                                 58             63           3      17356.6           0.1      23.2X
[info]
[info] sgemm[N,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 489            501           9       2045.5           0.5       1.0X
[info] java                                                 36             38           2      27721.9           0.0      13.6X
[info]
[info] sgemm[N,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 478            488           9       2094.0           0.5       1.0X
[info] java                                                 36             38           2      27813.2           0.0      13.3X
[info]
[info] sgemm[T,N]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 825            837          10       1211.6           0.8       1.0X
[info] java                                                 35             38           2      28433.1           0.0      23.5X
[info]
[info] sgemm[T,T]:                               Best Time(ms)   Avg Time(ms)   Stdev(ms)    Rate(M/s)   Per Row(ns)   Relative
[info] ------------------------------------------------------------------------------------------------------------------------
[info] f2j                                                 900            918          15       1111.6           0.9       1.0X
[info] java                                                 36             38           2      28073.0           0.0      25.3X
```

[2] https://github.com/luhenry/netlib/tree/master/blas/src/test/java/dev/ludovic/netlib/blas

Closes #32253 from luhenry/master.

Authored-by: Ludovic Henry <git@ludovic.dev>
Signed-off-by: Sean Owen <srowen@gmail.com>
2021-04-27 14:00:59 -05:00

650 lines
23 KiB
Python

#
# Licensed to the Apache Software Foundation (ASF) under one or more
# contributor license agreements. See the NOTICE file distributed with
# this work for additional information regarding copyright ownership.
# The ASF licenses this file to You under the Apache License, Version 2.0
# (the "License"); you may not use this file except in compliance with
# the License. You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
import sys
from pyspark import since, keyword_only
from pyspark.ml.param.shared import HasPredictionCol, HasBlockSize, HasMaxIter, HasRegParam, \
HasCheckpointInterval, HasSeed
from pyspark.ml.wrapper import JavaEstimator, JavaModel
from pyspark.ml.common import inherit_doc
from pyspark.ml.param import Params, TypeConverters, Param
from pyspark.ml.util import JavaMLWritable, JavaMLReadable
__all__ = ['ALS', 'ALSModel']
@inherit_doc
class _ALSModelParams(HasPredictionCol, HasBlockSize):
"""
Params for :py:class:`ALS` and :py:class:`ALSModel`.
.. versionadded:: 3.0.0
"""
userCol = Param(Params._dummy(), "userCol", "column name for user ids. Ids must be within " +
"the integer value range.", typeConverter=TypeConverters.toString)
itemCol = Param(Params._dummy(), "itemCol", "column name for item ids. Ids must be within " +
"the integer value range.", typeConverter=TypeConverters.toString)
coldStartStrategy = Param(Params._dummy(), "coldStartStrategy", "strategy for dealing with " +
"unknown or new users/items at prediction time. This may be useful " +
"in cross-validation or production scenarios, for handling " +
"user/item ids the model has not seen in the training data. " +
"Supported values: 'nan', 'drop'.",
typeConverter=TypeConverters.toString)
def __init__(self, *args):
super(_ALSModelParams, self).__init__(*args)
self._setDefault(blockSize=4096)
@since("1.4.0")
def getUserCol(self):
"""
Gets the value of userCol or its default value.
"""
return self.getOrDefault(self.userCol)
@since("1.4.0")
def getItemCol(self):
"""
Gets the value of itemCol or its default value.
"""
return self.getOrDefault(self.itemCol)
@since("2.2.0")
def getColdStartStrategy(self):
"""
Gets the value of coldStartStrategy or its default value.
"""
return self.getOrDefault(self.coldStartStrategy)
@inherit_doc
class _ALSParams(_ALSModelParams, HasMaxIter, HasRegParam, HasCheckpointInterval, HasSeed):
"""
Params for :py:class:`ALS`.
.. versionadded:: 3.0.0
"""
rank = Param(Params._dummy(), "rank", "rank of the factorization",
typeConverter=TypeConverters.toInt)
numUserBlocks = Param(Params._dummy(), "numUserBlocks", "number of user blocks",
typeConverter=TypeConverters.toInt)
numItemBlocks = Param(Params._dummy(), "numItemBlocks", "number of item blocks",
typeConverter=TypeConverters.toInt)
implicitPrefs = Param(Params._dummy(), "implicitPrefs", "whether to use implicit preference",
typeConverter=TypeConverters.toBoolean)
alpha = Param(Params._dummy(), "alpha", "alpha for implicit preference",
typeConverter=TypeConverters.toFloat)
ratingCol = Param(Params._dummy(), "ratingCol", "column name for ratings",
typeConverter=TypeConverters.toString)
nonnegative = Param(Params._dummy(), "nonnegative",
"whether to use nonnegative constraint for least squares",
typeConverter=TypeConverters.toBoolean)
intermediateStorageLevel = Param(Params._dummy(), "intermediateStorageLevel",
"StorageLevel for intermediate datasets. Cannot be 'NONE'.",
typeConverter=TypeConverters.toString)
finalStorageLevel = Param(Params._dummy(), "finalStorageLevel",
"StorageLevel for ALS model factors.",
typeConverter=TypeConverters.toString)
def __init__(self, *args):
super(_ALSParams, self).__init__(*args)
self._setDefault(rank=10, maxIter=10, regParam=0.1, numUserBlocks=10, numItemBlocks=10,
implicitPrefs=False, alpha=1.0, userCol="user", itemCol="item",
ratingCol="rating", nonnegative=False, checkpointInterval=10,
intermediateStorageLevel="MEMORY_AND_DISK",
finalStorageLevel="MEMORY_AND_DISK", coldStartStrategy="nan")
@since("1.4.0")
def getRank(self):
"""
Gets the value of rank or its default value.
"""
return self.getOrDefault(self.rank)
@since("1.4.0")
def getNumUserBlocks(self):
"""
Gets the value of numUserBlocks or its default value.
"""
return self.getOrDefault(self.numUserBlocks)
@since("1.4.0")
def getNumItemBlocks(self):
"""
Gets the value of numItemBlocks or its default value.
"""
return self.getOrDefault(self.numItemBlocks)
@since("1.4.0")
def getImplicitPrefs(self):
"""
Gets the value of implicitPrefs or its default value.
"""
return self.getOrDefault(self.implicitPrefs)
@since("1.4.0")
def getAlpha(self):
"""
Gets the value of alpha or its default value.
"""
return self.getOrDefault(self.alpha)
@since("1.4.0")
def getRatingCol(self):
"""
Gets the value of ratingCol or its default value.
"""
return self.getOrDefault(self.ratingCol)
@since("1.4.0")
def getNonnegative(self):
"""
Gets the value of nonnegative or its default value.
"""
return self.getOrDefault(self.nonnegative)
@since("2.0.0")
def getIntermediateStorageLevel(self):
"""
Gets the value of intermediateStorageLevel or its default value.
"""
return self.getOrDefault(self.intermediateStorageLevel)
@since("2.0.0")
def getFinalStorageLevel(self):
"""
Gets the value of finalStorageLevel or its default value.
"""
return self.getOrDefault(self.finalStorageLevel)
@inherit_doc
class ALS(JavaEstimator, _ALSParams, JavaMLWritable, JavaMLReadable):
"""
Alternating Least Squares (ALS) matrix factorization.
ALS attempts to estimate the ratings matrix `R` as the product of
two lower-rank matrices, `X` and `Y`, i.e. `X * Yt = R`. Typically
these approximations are called 'factor' matrices. The general
approach is iterative. During each iteration, one of the factor
matrices is held constant, while the other is solved for using least
squares. The newly-solved factor matrix is then held constant while
solving for the other factor matrix.
This is a blocked implementation of the ALS factorization algorithm
that groups the two sets of factors (referred to as "users" and
"products") into blocks and reduces communication by only sending
one copy of each user vector to each product block on each
iteration, and only for the product blocks that need that user's
feature vector. This is achieved by pre-computing some information
about the ratings matrix to determine the "out-links" of each user
(which blocks of products it will contribute to) and "in-link"
information for each product (which of the feature vectors it
receives from each user block it will depend on). This allows us to
send only an array of feature vectors between each user block and
product block, and have the product block find the users' ratings
and update the products based on these messages.
For implicit preference data, the algorithm used is based on
`"Collaborative Filtering for Implicit Feedback Datasets",
<https://doi.org/10.1109/ICDM.2008.22>`_, adapted for the blocked
approach used here.
Essentially instead of finding the low-rank approximations to the
rating matrix `R`, this finds the approximations for a preference
matrix `P` where the elements of `P` are 1 if r > 0 and 0 if r <= 0.
The ratings then act as 'confidence' values related to strength of
indicated user preferences rather than explicit ratings given to
items.
.. versionadded:: 1.4.0
Notes
-----
The input rating dataframe to the ALS implementation should be deterministic.
Nondeterministic data can cause failure during fitting ALS model.
For example, an order-sensitive operation like sampling after a repartition makes
dataframe output nondeterministic, like `df.repartition(2).sample(False, 0.5, 1618)`.
Checkpointing sampled dataframe or adding a sort before sampling can help make the
dataframe deterministic.
Examples
--------
>>> df = spark.createDataFrame(
... [(0, 0, 4.0), (0, 1, 2.0), (1, 1, 3.0), (1, 2, 4.0), (2, 1, 1.0), (2, 2, 5.0)],
... ["user", "item", "rating"])
>>> als = ALS(rank=10, seed=0)
>>> als.setMaxIter(5)
ALS...
>>> als.getMaxIter()
5
>>> als.setRegParam(0.1)
ALS...
>>> als.getRegParam()
0.1
>>> als.clear(als.regParam)
>>> model = als.fit(df)
>>> model.getBlockSize()
4096
>>> model.getUserCol()
'user'
>>> model.setUserCol("user")
ALSModel...
>>> model.getItemCol()
'item'
>>> model.setPredictionCol("newPrediction")
ALS...
>>> model.rank
10
>>> model.userFactors.orderBy("id").collect()
[Row(id=0, features=[...]), Row(id=1, ...), Row(id=2, ...)]
>>> test = spark.createDataFrame([(0, 2), (1, 0), (2, 0)], ["user", "item"])
>>> predictions = sorted(model.transform(test).collect(), key=lambda r: r[0])
>>> predictions[0]
Row(user=0, item=2, newPrediction=0.69291...)
>>> predictions[1]
Row(user=1, item=0, newPrediction=3.47356...)
>>> predictions[2]
Row(user=2, item=0, newPrediction=-0.899198...)
>>> user_recs = model.recommendForAllUsers(3)
>>> user_recs.where(user_recs.user == 0)\
.select("recommendations.item", "recommendations.rating").collect()
[Row(item=[0, 1, 2], rating=[3.910..., 1.997..., 0.692...])]
>>> item_recs = model.recommendForAllItems(3)
>>> item_recs.where(item_recs.item == 2)\
.select("recommendations.user", "recommendations.rating").collect()
[Row(user=[2, 1, 0], rating=[4.892..., 3.991..., 0.692...])]
>>> user_subset = df.where(df.user == 2)
>>> user_subset_recs = model.recommendForUserSubset(user_subset, 3)
>>> user_subset_recs.select("recommendations.item", "recommendations.rating").first()
Row(item=[2, 1, 0], rating=[4.892..., 1.076..., -0.899...])
>>> item_subset = df.where(df.item == 0)
>>> item_subset_recs = model.recommendForItemSubset(item_subset, 3)
>>> item_subset_recs.select("recommendations.user", "recommendations.rating").first()
Row(user=[0, 1, 2], rating=[3.910..., 3.473..., -0.899...])
>>> als_path = temp_path + "/als"
>>> als.save(als_path)
>>> als2 = ALS.load(als_path)
>>> als.getMaxIter()
5
>>> model_path = temp_path + "/als_model"
>>> model.save(model_path)
>>> model2 = ALSModel.load(model_path)
>>> model.rank == model2.rank
True
>>> sorted(model.userFactors.collect()) == sorted(model2.userFactors.collect())
True
>>> sorted(model.itemFactors.collect()) == sorted(model2.itemFactors.collect())
True
>>> model.transform(test).take(1) == model2.transform(test).take(1)
True
"""
@keyword_only
def __init__(self, *, rank=10, maxIter=10, regParam=0.1, numUserBlocks=10,
numItemBlocks=10, implicitPrefs=False, alpha=1.0, userCol="user", itemCol="item",
seed=None, ratingCol="rating", nonnegative=False, checkpointInterval=10,
intermediateStorageLevel="MEMORY_AND_DISK",
finalStorageLevel="MEMORY_AND_DISK", coldStartStrategy="nan", blockSize=4096):
"""
__init__(self, \\*, rank=10, maxIter=10, regParam=0.1, numUserBlocks=10,
numItemBlocks=10, implicitPrefs=False, alpha=1.0, userCol="user", itemCol="item", \
seed=None, ratingCol="rating", nonnegative=False, checkpointInterval=10, \
intermediateStorageLevel="MEMORY_AND_DISK", \
finalStorageLevel="MEMORY_AND_DISK", coldStartStrategy="nan", blockSize=4096)
"""
super(ALS, self).__init__()
self._java_obj = self._new_java_obj("org.apache.spark.ml.recommendation.ALS", self.uid)
kwargs = self._input_kwargs
self.setParams(**kwargs)
@keyword_only
@since("1.4.0")
def setParams(self, *, rank=10, maxIter=10, regParam=0.1, numUserBlocks=10,
numItemBlocks=10, implicitPrefs=False, alpha=1.0, userCol="user", itemCol="item",
seed=None, ratingCol="rating", nonnegative=False, checkpointInterval=10,
intermediateStorageLevel="MEMORY_AND_DISK",
finalStorageLevel="MEMORY_AND_DISK", coldStartStrategy="nan", blockSize=4096):
"""
setParams(self, \\*, rank=10, maxIter=10, regParam=0.1, numUserBlocks=10, \
numItemBlocks=10, implicitPrefs=False, alpha=1.0, userCol="user", itemCol="item", \
seed=None, ratingCol="rating", nonnegative=False, checkpointInterval=10, \
intermediateStorageLevel="MEMORY_AND_DISK", \
finalStorageLevel="MEMORY_AND_DISK", coldStartStrategy="nan", blockSize=4096)
Sets params for ALS.
"""
kwargs = self._input_kwargs
return self._set(**kwargs)
def _create_model(self, java_model):
return ALSModel(java_model)
@since("1.4.0")
def setRank(self, value):
"""
Sets the value of :py:attr:`rank`.
"""
return self._set(rank=value)
@since("1.4.0")
def setNumUserBlocks(self, value):
"""
Sets the value of :py:attr:`numUserBlocks`.
"""
return self._set(numUserBlocks=value)
@since("1.4.0")
def setNumItemBlocks(self, value):
"""
Sets the value of :py:attr:`numItemBlocks`.
"""
return self._set(numItemBlocks=value)
@since("1.4.0")
def setNumBlocks(self, value):
"""
Sets both :py:attr:`numUserBlocks` and :py:attr:`numItemBlocks` to the specific value.
"""
self._set(numUserBlocks=value)
return self._set(numItemBlocks=value)
@since("1.4.0")
def setImplicitPrefs(self, value):
"""
Sets the value of :py:attr:`implicitPrefs`.
"""
return self._set(implicitPrefs=value)
@since("1.4.0")
def setAlpha(self, value):
"""
Sets the value of :py:attr:`alpha`.
"""
return self._set(alpha=value)
@since("1.4.0")
def setUserCol(self, value):
"""
Sets the value of :py:attr:`userCol`.
"""
return self._set(userCol=value)
@since("1.4.0")
def setItemCol(self, value):
"""
Sets the value of :py:attr:`itemCol`.
"""
return self._set(itemCol=value)
@since("1.4.0")
def setRatingCol(self, value):
"""
Sets the value of :py:attr:`ratingCol`.
"""
return self._set(ratingCol=value)
@since("1.4.0")
def setNonnegative(self, value):
"""
Sets the value of :py:attr:`nonnegative`.
"""
return self._set(nonnegative=value)
@since("2.0.0")
def setIntermediateStorageLevel(self, value):
"""
Sets the value of :py:attr:`intermediateStorageLevel`.
"""
return self._set(intermediateStorageLevel=value)
@since("2.0.0")
def setFinalStorageLevel(self, value):
"""
Sets the value of :py:attr:`finalStorageLevel`.
"""
return self._set(finalStorageLevel=value)
@since("2.2.0")
def setColdStartStrategy(self, value):
"""
Sets the value of :py:attr:`coldStartStrategy`.
"""
return self._set(coldStartStrategy=value)
def setMaxIter(self, value):
"""
Sets the value of :py:attr:`maxIter`.
"""
return self._set(maxIter=value)
def setRegParam(self, value):
"""
Sets the value of :py:attr:`regParam`.
"""
return self._set(regParam=value)
def setPredictionCol(self, value):
"""
Sets the value of :py:attr:`predictionCol`.
"""
return self._set(predictionCol=value)
def setCheckpointInterval(self, value):
"""
Sets the value of :py:attr:`checkpointInterval`.
"""
return self._set(checkpointInterval=value)
def setSeed(self, value):
"""
Sets the value of :py:attr:`seed`.
"""
return self._set(seed=value)
@since("3.0.0")
def setBlockSize(self, value):
"""
Sets the value of :py:attr:`blockSize`.
"""
return self._set(blockSize=value)
class ALSModel(JavaModel, _ALSModelParams, JavaMLWritable, JavaMLReadable):
"""
Model fitted by ALS.
.. versionadded:: 1.4.0
"""
@since("3.0.0")
def setUserCol(self, value):
"""
Sets the value of :py:attr:`userCol`.
"""
return self._set(userCol=value)
@since("3.0.0")
def setItemCol(self, value):
"""
Sets the value of :py:attr:`itemCol`.
"""
return self._set(itemCol=value)
@since("3.0.0")
def setColdStartStrategy(self, value):
"""
Sets the value of :py:attr:`coldStartStrategy`.
"""
return self._set(coldStartStrategy=value)
@since("3.0.0")
def setPredictionCol(self, value):
"""
Sets the value of :py:attr:`predictionCol`.
"""
return self._set(predictionCol=value)
@since("3.0.0")
def setBlockSize(self, value):
"""
Sets the value of :py:attr:`blockSize`.
"""
return self._set(blockSize=value)
@property
@since("1.4.0")
def rank(self):
"""rank of the matrix factorization model"""
return self._call_java("rank")
@property
@since("1.4.0")
def userFactors(self):
"""
a DataFrame that stores user factors in two columns: `id` and
`features`
"""
return self._call_java("userFactors")
@property
@since("1.4.0")
def itemFactors(self):
"""
a DataFrame that stores item factors in two columns: `id` and
`features`
"""
return self._call_java("itemFactors")
def recommendForAllUsers(self, numItems):
"""
Returns top `numItems` items recommended for each user, for all users.
.. versionadded:: 2.2.0
Parameters
----------
numItems : int
max number of recommendations for each user
Returns
-------
:py:class:`pyspark.sql.DataFrame`
a DataFrame of (userCol, recommendations), where recommendations are
stored as an array of (itemCol, rating) Rows.
"""
return self._call_java("recommendForAllUsers", numItems)
def recommendForAllItems(self, numUsers):
"""
Returns top `numUsers` users recommended for each item, for all items.
.. versionadded:: 2.2.0
Parameters
----------
numUsers : int
max number of recommendations for each item
Returns
-------
:py:class:`pyspark.sql.DataFrame`
a DataFrame of (itemCol, recommendations), where recommendations are
stored as an array of (userCol, rating) Rows.
"""
return self._call_java("recommendForAllItems", numUsers)
def recommendForUserSubset(self, dataset, numItems):
"""
Returns top `numItems` items recommended for each user id in the input data set. Note that
if there are duplicate ids in the input dataset, only one set of recommendations per unique
id will be returned.
.. versionadded:: 2.3.0
Parameters
----------
dataset : :py:class:`pyspark.sql.DataFrame`
a DataFrame containing a column of user ids. The column name must match `userCol`.
numItems : int
max number of recommendations for each user
Returns
-------
:py:class:`pyspark.sql.DataFrame`
a DataFrame of (userCol, recommendations), where recommendations are
stored as an array of (itemCol, rating) Rows.
"""
return self._call_java("recommendForUserSubset", dataset, numItems)
def recommendForItemSubset(self, dataset, numUsers):
"""
Returns top `numUsers` users recommended for each item id in the input data set. Note that
if there are duplicate ids in the input dataset, only one set of recommendations per unique
id will be returned.
.. versionadded:: 2.3.0
Parameters
----------
dataset : :py:class:`pyspark.sql.DataFrame`
a DataFrame containing a column of item ids. The column name must match `itemCol`.
numUsers : int
max number of recommendations for each item
Returns
-------
:py:class:`pyspark.sql.DataFrame`
a DataFrame of (itemCol, recommendations), where recommendations are
stored as an array of (userCol, rating) Rows.
"""
return self._call_java("recommendForItemSubset", dataset, numUsers)
if __name__ == "__main__":
import doctest
import pyspark.ml.recommendation
from pyspark.sql import SparkSession
globs = pyspark.ml.recommendation.__dict__.copy()
# The small batch size here ensures that we see multiple batches,
# even in these small test examples:
spark = SparkSession.builder\
.master("local[2]")\
.appName("ml.recommendation tests")\
.getOrCreate()
sc = spark.sparkContext
globs['sc'] = sc
globs['spark'] = spark
import tempfile
temp_path = tempfile.mkdtemp()
globs['temp_path'] = temp_path
try:
(failure_count, test_count) = doctest.testmod(globs=globs, optionflags=doctest.ELLIPSIS)
spark.stop()
finally:
from shutil import rmtree
try:
rmtree(temp_path)
except OSError:
pass
if failure_count:
sys.exit(-1)