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csrqr

README.md

cuSOLVER batched sparse QR example 1

Description

This chapter demonstrates a usage of cuSOLVER csrqr function two examples to perform batched sparse QR solver.

The example 1 performs batched sparse QR to solver a set of linear systems.

The example 2 performs batched sparse QR to solver a set of linear systems, but we assume device memory is not enough, so we need to cut 17 matrices into several chunks and compute each chunk by batched sparse QR.

Aixi = bi

All matrices Ai are small perturbations of

A = | 1.0 | 0.0 | 0.0 | 0.0 |
    | 0.0 | 2.0 | 0.0 | 0.0 |
    | 0.0 | 0.0 | 3.0 | 0.0 |
    | 0.1 | 0.1 | 0.1 | 4.0 |

All right-hand side vectors bi are small pertubation of the Matlab vector ones(4,1). We assume device memory is big enough to compute all matrices in one pass.

Supported SM Architectures

All GPUs supported by CUDA Toolkit (https://developer.nvidia.com/cuda-gpus)

Supported OSes

Linux
Windows

Supported CPU Architecture

x86_64
ppc64le
arm64-sbsa

CUDA APIs involved

Building (make)

Prerequisites

  • A Linux/Windows system with recent NVIDIA drivers.
  • CMake version 3.18 minimum

Build command on Linux

$ mkdir build
$ cd build
$ cmake ..
$ make

Make sure that CMake finds expected CUDA Toolkit. If that is not the case you can add argument -DCMAKE_CUDA_COMPILER=/path/to/cuda/bin/nvcc to cmake command.

Build command on Windows

$ mkdir build
$ cd build
$ cmake -DCMAKE_GENERATOR_PLATFORM=x64 ..
$ Open cusolver_examples.sln project in Visual Studio and build

Usage 1

$  ./cusolver_csrqr_example1

Sample example output:

numerical factorization needs working space 209664 bytes
batchId 0: sup|bj - Aj*xj| = 6.661338E-16
batchId 1: sup|bj - Aj*xj| = 1.110223E-15
batchId 2: sup|bj - Aj*xj| = 4.440892E-16
batchId 3: sup|bj - Aj*xj| = 4.440892E-16
batchId 4: sup|bj - Aj*xj| = 6.661338E-16
batchId 5: sup|bj - Aj*xj| = 6.661338E-16
batchId 6: sup|bj - Aj*xj| = 8.881784E-16
batchId 7: sup|bj - Aj*xj| = 4.440892E-16
batchId 8: sup|bj - Aj*xj| = 1.110223E-15
batchId 9: sup|bj - Aj*xj| = 4.440892E-16
batchId 10: sup|bj - Aj*xj| = 2.220446E-16
batchId 11: sup|bj - Aj*xj| = 1.332268E-15
batchId 12: sup|bj - Aj*xj| = 6.661338E-16
batchId 13: sup|bj - Aj*xj| = 6.661338E-16
batchId 14: sup|bj - Aj*xj| = 2.220446E-16
batchId 15: sup|bj - Aj*xj| = 6.661338E-16
batchId 16: sup|bj - Aj*xj| = 4.440892E-16
x0[0] = 9.936533E-01
x0[1] = 4.996754E-01
x0[2] = 3.333555E-01
x0[3] = 2.032261E-01

x1[0] = 9.954397E-01
x1[1] = 5.023664E-01
x1[2] = 3.332114E-01
x1[3] = 2.011510E-01

x2[0] = 9.952372E-01
x2[1] = 5.000749E-01
x2[2] = 3.338207E-01
x2[3] = 2.033641E-01

x3[0] = 1.001597E+00
x3[1] = 5.009494E-01
x3[2] = 3.342649E-01
x3[3] = 2.024054E-01

x4[0] = 9.924708E-01
x4[1] = 4.997259E-01
x4[2] = 3.349327E-01
x4[3] = 2.012184E-01

x5[0] = 1.006178E+00
x5[1] = 5.018936E-01
x5[2] = 3.335885E-01
x5[3] = 2.038061E-01

x6[0] = 9.985129E-01
x6[1] = 5.008987E-01
x6[2] = 3.348651E-01
x6[3] = 2.022812E-01

x7[0] = 9.989101E-01
x7[1] = 4.994274E-01
x7[2] = 3.351732E-01
x7[3] = 2.014273E-01

x8[0] = 1.002587E+00
x8[1] = 4.994259E-01
x8[2] = 3.360536E-01
x8[3] = 2.022084E-01

x9[0] = 9.988026E-01
x9[1] = 4.994268E-01
x9[2] = 3.352765E-01
x9[3] = 2.035007E-01

x10[0] = 9.965219E-01
x10[1] = 5.029465E-01
x10[2] = 3.333555E-01
x10[3] = 2.036849E-01

x11[0] = 1.003989E+00
x11[1] = 5.017441E-01
x11[2] = 3.343099E-01
x11[3] = 2.018912E-01

x12[0] = 9.966307E-01
x12[1] = 4.995508E-01
x12[2] = 3.339314E-01
x12[3] = 2.022344E-01

x13[0] = 1.003777E+00
x13[1] = 5.000499E-01
x13[2] = 3.361865E-01
x13[3] = 2.026724E-01

x14[0] = 9.990064E-01
x14[1] = 5.019747E-01
x14[2] = 3.331890E-01
x14[3] = 2.042594E-01

x15[0] = 1.005984E+00
x15[1] = 5.019228E-01
x15[2] = 3.337102E-01
x15[3] = 2.007337E-01

x16[0] = 1.002490E+00
x16[1] = 5.033651E-01
x16[2] = 3.353435E-01
x16[3] = 2.031494E-01

Usage 2

$  ./cusolver_csrqr_example2

Sample example output:

batchSizeMax = 2
batchSizeMax = 4
batchSizeMax = 8
batchSizeMax = 16
batchSizeMax = 17
numerical factorization needs internal data 272 bytes
numerical factorization needs working space 201984 bytes
current batchSize = 2
current batchSize = 2
current batchSize = 2
current batchSize = 2
current batchSize = 2
current batchSize = 2
current batchSize = 2
current batchSize = 2
current batchSize = 1
batchId 0: sup|bj - Aj*xj| = 6.661338E-16
batchId 1: sup|bj - Aj*xj| = 1.110223E-15
batchId 2: sup|bj - Aj*xj| = 4.440892E-16
batchId 3: sup|bj - Aj*xj| = 4.440892E-16
batchId 4: sup|bj - Aj*xj| = 6.661338E-16
batchId 5: sup|bj - Aj*xj| = 6.661338E-16
batchId 6: sup|bj - Aj*xj| = 8.881784E-16
batchId 7: sup|bj - Aj*xj| = 4.440892E-16
batchId 8: sup|bj - Aj*xj| = 1.110223E-15
batchId 9: sup|bj - Aj*xj| = 4.440892E-16
batchId 10: sup|bj - Aj*xj| = 2.220446E-16
batchId 11: sup|bj - Aj*xj| = 1.332268E-15
batchId 12: sup|bj - Aj*xj| = 6.661338E-16
batchId 13: sup|bj - Aj*xj| = 6.661338E-16
batchId 14: sup|bj - Aj*xj| = 2.220446E-16
batchId 15: sup|bj - Aj*xj| = 6.661338E-16
batchId 16: sup|bj - Aj*xj| = 4.440892E-16
x0[0] = 9.936533E-01
x0[1] = 4.996754E-01
x0[2] = 3.333555E-01
x0[3] = 2.032261E-01

x1[0] = 9.954397E-01
x1[1] = 5.023664E-01
x1[2] = 3.332114E-01
x1[3] = 2.011510E-01

x2[0] = 9.952372E-01
x2[1] = 5.000749E-01
x2[2] = 3.338207E-01
x2[3] = 2.033641E-01

x3[0] = 1.001597E+00
x3[1] = 5.009494E-01
x3[2] = 3.342649E-01
x3[3] = 2.024054E-01

x4[0] = 9.924708E-01
x4[1] = 4.997259E-01
x4[2] = 3.349327E-01
x4[3] = 2.012184E-01

x5[0] = 1.006178E+00
x5[1] = 5.018936E-01
x5[2] = 3.335885E-01
x5[3] = 2.038061E-01

x6[0] = 9.985129E-01
x6[1] = 5.008987E-01
x6[2] = 3.348651E-01
x6[3] = 2.022812E-01

x7[0] = 9.989101E-01
x7[1] = 4.994274E-01
x7[2] = 3.351732E-01
x7[3] = 2.014273E-01

x8[0] = 1.002587E+00
x8[1] = 4.994259E-01
x8[2] = 3.360536E-01
x8[3] = 2.022084E-01

x9[0] = 9.988026E-01
x9[1] = 4.994268E-01
x9[2] = 3.352765E-01
x9[3] = 2.035007E-01

x10[0] = 9.965219E-01
x10[1] = 5.029465E-01
x10[2] = 3.333555E-01
x10[3] = 2.036849E-01

x11[0] = 1.003989E+00
x11[1] = 5.017441E-01
x11[2] = 3.343099E-01
x11[3] = 2.018912E-01

x12[0] = 9.966307E-01
x12[1] = 4.995508E-01
x12[2] = 3.339314E-01
x12[3] = 2.022344E-01

x13[0] = 1.003777E+00
x13[1] = 5.000499E-01
x13[2] = 3.361865E-01
x13[3] = 2.026724E-01

x14[0] = 9.990064E-01
x14[1] = 5.019747E-01
x14[2] = 3.331890E-01
x14[3] = 2.042594E-01

x15[0] = 1.005984E+00
x15[1] = 5.019228E-01
x15[2] = 3.337102E-01
x15[3] = 2.007337E-01

x16[0] = 1.002490E+00
x16[1] = 5.033651E-01
x16[2] = 3.353435E-01
x16[3] = 2.031494E-01