spark-instrumented-optimizer/docs/ml-linalg-guide.md
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

5.8 KiB

layout title displayTitle license
global MLlib Linear Algebra Acceleration Guide MLlib Linear Algebra Acceleration Guide 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.

Introduction

This guide provides necessary information to enable accelerated linear algebra processing for Spark MLlib.

Spark MLlib defines Vector and Matrix as basic data types for machine learning algorithms. On top of them, BLAS and LAPACK operations are implemented and supported by netlib-java (the algorithms may call Breeze and it will in turn call netlib-java). netlib-java can use optimized native linear algebra libraries (refered to as "native libraries" or "BLAS libraries" hereafter) for faster numerical processing. Intel MKL and OpenBLAS are two popular ones.

However due to license differences, the official released Spark binaries by default don't contain native libraries support for netlib-java.

The following sections describe how to enable netlib-java with native libraries support for Spark MLlib and how to install native libraries and configure them properly.

Enable netlib-java with native library proxies

netlib-java depends on libgfortran. It requires GFORTRAN 1.4 or above. This can be obtained by installing libgfortran package. After installation, the following command can be used to verify if it is installed properly.

strings /path/to/libgfortran.so.3.0.0 | grep GFORTRAN_1.4

To build Spark with netlib-java native library proxies, you need to add -Pnetlib-lgpl to Maven build command line. For example:

$SPARK_SOURCE_HOME/build/mvn -Pnetlib-lgpl -DskipTests -Pyarn -Phadoop-2.7 clean package

If you only want to enable it in your project, include com.github.fommil.netlib:all:1.1.2 as a dependency of your project.

Install native linear algebra libraries

Intel MKL and OpenBLAS are two popular native linear algebra libraries. You can choose one of them based on your preference. We provide basic instructions as below. You can refer to netlib-java documentation for more advanced installation instructions.

Intel MKL

  • Download and install Intel MKL. The installation should be done on all nodes of the cluster. We assume the installation location is $MKLROOT (e.g. /opt/intel/mkl).
  • Create soft links to libmkl_rt.so with specific names in system library search paths. For instance, make sure /usr/local/lib is in system library search paths and run the following commands:
$ ln -sf $MKLROOT/lib/intel64/libmkl_rt.so /usr/local/lib/libblas.so.3
$ ln -sf $MKLROOT/lib/intel64/libmkl_rt.so /usr/local/lib/liblapack.so.3

OpenBLAS

The installation should be done on all nodes of the cluster. Generic version of OpenBLAS are available with most distributions. You can install it with a distribution package manager like apt or yum.

For Debian / Ubuntu:

sudo apt-get install libopenblas-base
sudo update-alternatives --config libblas.so.3

For CentOS / RHEL:

sudo yum install openblas

Check if native libraries are enabled for MLlib

To verify native libraries are properly loaded, start spark-shell and run the following code:

scala> import com.github.fommil.netlib.BLAS;
scala> System.out.println(BLAS.getInstance().getClass().getName());

If they are correctly loaded, it should print com.github.fommil.netlib.NativeSystemBLAS. Otherwise the warnings should be printed:

WARN BLAS: Failed to load implementation from:com.github.fommil.netlib.NativeSystemBLAS
WARN BLAS: Failed to load implementation from:com.github.fommil.netlib.NativeRefBLAS

If native libraries are not properly configured in the system, the Java implementation (javaBLAS) will be used as fallback option.

Spark Configuration

The default behavior of multi-threading in either Intel MKL or OpenBLAS may not be optimal with Spark's execution model 1.

Therefore configuring these native libraries to use a single thread for operations may actually improve performance (see SPARK-21305). It is usually optimal to match this to the number of spark.task.cpus, which is 1 by default and typically left at 1.

You can use the options in config/spark-env.sh to set thread number for Intel MKL or OpenBLAS:

  • For Intel MKL:
MKL_NUM_THREADS=1
  • For OpenBLAS:
OPENBLAS_NUM_THREADS=1

  1. Please refer to the following resources to understand how to configure the number of threads for these BLAS implementations: Intel MKL or Intel oneMKL and OpenBLAS. ↩︎