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Merge pull request oneapi-src#2543 from spencerpatty/dev/spatty/update_pcg_usm
[oneMKL][Sparse BLAS] Add preconditioned conjugate gradient in USM with two examples
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‎Libraries/oneMKL/sparse_conjugate_gradient/GNUmakefile

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all: run
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run: sparse_cg
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run: sparse_cg sparse_cg2
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./sparse_cg
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./sparse_cg2
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MKL_COPTS = -DMKL_ILP64 -qmkl -qmkl-sycl-impl="blas,sparse"
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sparse_cg: sparse_cg.cpp
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icpx $< -fsycl -o $@ $(DPCPP_OPTS)
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sparse_cg2: sparse_cg2.cpp
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icpx $< -fsycl -o $@ $(DPCPP_OPTS)
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clean:
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-rm -f sparse_cg genxir
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-rm -f sparse_cg sparse_cg2 genxir
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.PHONY: clean run all

‎Libraries/oneMKL/sparse_conjugate_gradient/README.md

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@@ -17,7 +17,7 @@ Sparse Conjugate Gradient uses oneMKL sparse linear algebra routines to solve a
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This sample performs its computations on the default SYCL* device. You can set the `SYCL_DEVICE_TYPE` environment variable to `cpu` or `gpu` to select the device to use.
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## Key Implementation Details
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oneMKL sparse routines use a two-stage method where the sparse matrix is analyzed to prepare subsequent calculations (the _optimize_ step). Sparse matrix-vector multiplication and triangular solves (`gemv` and `trsv`) are used to implement the main loop, along with vector routines from BLAS.
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oneMKL sparse routines use a two-stage method where the sparse matrix is analyzed to prepare subsequent calculations (the _optimize_ step). Sparse matrix-vector multiplication and triangular solves (`gemv` and `trsv`) are used to implement the main loop, along with vector routines from BLAS. Two implementations are provided: The first implementation, in `sparse_cg.cpp`, has several places where a device to host copy and wait are initiated to allow the alpha and beta coefficients to be initiated in the BLAS vector routines as host scalars. The second implementation, in `sparse_cg2.cpp`, keeps the coefficients for alpha and beta on the device, which require that custom axpby2 and axpy3 functions are written to handle the construction of alpha and beta coefficients on-the-fly from the device. This removes some of the synchronization points that are seen in the first implementation.
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## Using Visual Studio Code* (Optional)
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You can use Visual Studio Code (VS Code) extensions to set your environment, create launch configurations,
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## Running the Sparse Conjugate Gradient Sample
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### Example of Output
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If everything is working correctly, the example program will rapidly converge to a solution and display the solution vector's first few entries. The test will run in both single and double precision (if available on the selected device).
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If everything is working correctly, the example programs will rapidly converge to a solution. Each test will run in both single and double precision (if available on the selected device).
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The first PCG implementation with host side coefficients:
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```
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./sparse_cg
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########################################################################
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# Sparse Conjugate Gradient Solver
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# Sparse Preconditioned Conjugate Gradient Solver with USM
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#
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# Uses the preconditioned conjugate gradient algorithm to
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# iteratively solve the symmetric linear system
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#
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# Uses the symmetric Gauss-Seidel preconditioner.
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#
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# alpha and beta constants in PCG algorithm are host side.
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#
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########################################################################
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Running tests on Intel(R) Gen9 HD Graphics NEO.
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Running tests on Intel(R) Data Center GPU Max 1550.
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Running with single precision real data type:
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relative norm of residual on 1 iteration: 0.0856119
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relative norm of residual on 2 iteration: 0.00204826
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relative norm of residual on 3 iterations: 6.68015e-05
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Preconditioned CG process has successfully converged, and
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the following solution has been obtained:
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x[0] = 0.0666633
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x[1] = 0.0835483
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x[2] = 0.0835491
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x[3] = 0.0666627
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...
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sparse PCG parameters:
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A size: (4096, 4096)
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Preconditioner = Symmetric Gauss-Seidel
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max iterations = 500
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relative tolerance limit = 1e-05
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absolute tolerance limit = 0.0005
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relative norm of residual on 1 iteration: 0.178532
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relative norm of residual on 2 iteration: 0.0280123
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relative norm of residual on 3 iteration: 0.0048948
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relative norm of residual on 4 iteration: 0.000796108
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relative norm of residual on 5 iteration: 0.000119025
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relative norm of residual on 6 iteration: 1.86945e-05
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absolute norm of residual on 6 iteration: 0.000149556
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Preconditioned CG process has successfully converged in absolute error in 6 steps with
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relative error ||r||_2 / ||r_0||_2 = 1.86945e-05 > 1e-05
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absolute error ||r||_2 = 0.000149556 < 0.0005
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Running with double precision real data type:
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relative norm of residual on 1 iteration: 0.0856119
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relative norm of residual on 2 iteration: 0.00204827
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relative norm of residual on 3 iteration: 6.68017e-05
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Preconditioned CG process has successfully converged, and
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the following solution has been obtained:
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x[0] = 0.0666633
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x[1] = 0.0835483
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x[2] = 0.0835491
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x[3] = 0.0666627
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...
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sparse PCG parameters:
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A size: (4096, 4096)
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Preconditioner = Symmetric Gauss-Seidel
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max iterations = 500
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relative tolerance limit = 1e-05
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absolute tolerance limit = 0.0005
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relative norm of residual on 1 iteration: 0.178532
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relative norm of residual on 2 iteration: 0.0280123
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relative norm of residual on 3 iteration: 0.0048948
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relative norm of residual on 4 iteration: 0.000796108
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relative norm of residual on 5 iteration: 0.000119025
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relative norm of residual on 6 iteration: 1.86945e-05
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absolute norm of residual on 6 iteration: 0.000149556
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Preconditioned CG process has successfully converged in absolute error in 6 steps with
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relative error ||r||_2 / ||r_0||_2 = 1.86945e-05 > 1e-05
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absolute error ||r||_2 = 0.000149556 < 0.0005
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```
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and the second PCG implementation with device side coefficients:
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```
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./sparse_cg2
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########################################################################
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# Sparse Preconditioned Conjugate Gradient Solver with USM 2
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#
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# Uses the preconditioned conjugate gradient algorithm to
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# iteratively solve the symmetric linear system
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#
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# A * x = b
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#
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# where A is a symmetric sparse matrix in CSR format, and
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# x and b are dense vectors.
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#
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# Uses the symmetric Gauss-Seidel preconditioner.
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#
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# alpha and beta constants in PCG algorithm are kept
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# device side.
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#
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########################################################################
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Running tests on Intel(R) Data Center GPU Max 1550.
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Running with single precision real data type:
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sparse PCG parameters:
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A size: (4096, 4096)
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Preconditioner = Symmetric Gauss-Seidel
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max iterations = 500
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relative tolerance limit = 1e-05
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absolute tolerance limit = 0.0005
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relative norm of residual on 1 iteration: 0.178532
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relative norm of residual on 2 iteration: 0.0280123
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relative norm of residual on 3 iteration: 0.0048948
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relative norm of residual on 4 iteration: 0.000796109
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relative norm of residual on 5 iteration: 0.000119025
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relative norm of residual on 6 iteration: 1.86945e-05
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absolute norm of residual on 6 iteration: 0.000149556
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Preconditioned CG process has successfully converged in absolute error in 6 steps with
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relative error ||r||_2 / ||r_0||_2 = 1.86945e-05 > 1e-05
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absolute error ||r||_2 = 0.000149556 < 0.0005
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Running with double precision real data type:
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sparse PCG parameters:
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A size: (4096, 4096)
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Preconditioner = Symmetric Gauss-Seidel
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max iterations = 500
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relative tolerance limit = 1e-05
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absolute tolerance limit = 0.0005
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relative norm of residual on 1 iteration: 0.178532
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relative norm of residual on 2 iteration: 0.0280123
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relative norm of residual on 3 iteration: 0.0048948
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relative norm of residual on 4 iteration: 0.000796108
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relative norm of residual on 5 iteration: 0.000119025
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relative norm of residual on 6 iteration: 1.86945e-05
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absolute norm of residual on 6 iteration: 0.000149556
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Preconditioned CG process has successfully converged in absolute error in 6 steps with
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relative error ||r||_2 / ||r_0||_2 = 1.86945e-05 > 1e-05
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absolute error ||r||_2 = 0.000149556 < 0.0005
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```
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### Troubleshooting
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If an error occurs, troubleshoot the problem using the Diagnostics Utility for Intel® oneAPI Toolkits.

‎Libraries/oneMKL/sparse_conjugate_gradient/makefile

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all: run
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run: sparse_cg.exe
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run: sparse_cg.exe sparse_cg2.exe
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.\sparse_cg
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.\sparse_cg2
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DPCPP_OPTS=/I"$(MKLROOT)\include" /Qmkl /Qmkl-sycl-impl="blas,sparse" /EHsc -fsycl-device-code-split=per_kernel OpenCL.lib
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SYCL_OPTS=/I"$(MKLROOT)\include" /Qmkl /Qmkl-sycl-impl="blas,sparse" /EHsc -fsycl-device-code-split=per_kernel OpenCL.lib
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sparse_cg.exe: sparse_cg.cpp
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icx-cl -fsycl sparse_cg.cpp /Fesparse_cg.exe $(DPCPP_OPTS)
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icx-cl -fsycl sparse_cg.cpp /Fesparse_cg.exe $(SYCL_OPTS)
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sparse_cg2.exe: sparse_cg2.cpp
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icx-cl -fsycl sparse_cg2.cpp /Fesparse_cg2.exe $(SYCL_OPTS)
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clean:
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del /q sparse_cg.exe sparse_cg.exp sparse_cg.lib
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del /q sparse_cg2.exe sparse_cg2.exp sparse_cg2.lib
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pseudo: clean run all

‎Libraries/oneMKL/sparse_conjugate_gradient/sample.json

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"guid": "3814C3C8-6CD1-40C9-A94B-CB4D4F58E2B9",
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"name": "Sparse Conjugate Gradient",
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"categories": ["Toolkit/oneAPI Libraries/oneMKL"],
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"description": "Solve Sparse linear systems with the Conjugate Gradient method using Intel® oneMKL sparse BLAS",
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"description": "Solve Sparse linear systems with the Conjugate Gradient method using Intel® oneMKL Sparse BLAS",
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"toolchain": [ "dpcpp" ],
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"dependencies": [ "mkl" ],
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"languages": [ { "cpp": { "properties": { "projectOptions": [ { "projectType": "makefile" } ] } } } ],

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