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{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"DirectSolver yields incorrect result for random and close to random matrices","articleBody":"\nI was considering swapping cupy sparse solvers for nvmath Python/cuDSS DirectSolver, but I am unable to obtain correct results even for small problem instances. \n\n### Minimal example\n\nIn `example01_cupy.py` replace\n\n```\nn = 8\n...\na += sp.diags([2.0] * n, format=\"csr\", dtype=\"float64\")\n```\nwith\n```\nn = 100\n...\n# a += sp.diags([2.0] * n, format=\"csr\", dtype=\"float64\")\n```\n\nThe same remains true, if I used small, but not tiny values for the diagonal like `0.01`.\n\n### Example observation 1\n\n```\n||A||: \t40.65133430135082\n||b||: \t14.142135623730951\n\ndet(A): 7.262125991606542e+28\n\n02-10 17:35:07 userlogger   INFO     = SPECIFICATION PHASE =\n02-10 17:35:07 userlogger   INFO     The LHS package is cupyx.\n02-10 17:35:07 userlogger   INFO     The RHS package is cupy.\n02-10 17:35:07 userlogger   INFO     The device_id=0, dtype = float64, index type = int32.\n02-10 17:35:07 userlogger   INFO     The number of equations = 100.\n02-10 17:35:07 userlogger   INFO     The operands' memory space is cuda, and the execution space is on device 0.\n02-10 17:35:07 userlogger   INFO     The specified stream for the DirectSolver ctor is \u003ccuda.core.experimental._stream.Stream object at 0x14b6709b87c0\u003e.\n02-10 17:35:07 userlogger   INFO     The library handle has been created: 94793135484384.\n02-10 17:35:07 userlogger   INFO     The sparse direct solver operation has been created.\n02-10 17:35:07 userlogger   INFO     Starting solver phase ANALYSIS...\n02-10 17:35:07 userlogger   INFO     This call is non-blocking and will return immediately after the operation is launched on the device.\n02-10 17:35:07 userlogger   INFO     Starting solver phase FACTORIZATION...\n02-10 17:35:07 userlogger   INFO     This call is non-blocking and will return immediately after the operation is launched on the device.\n02-10 17:35:07 userlogger   INFO     Starting solver phase SOLVE...\n02-10 17:35:07 userlogger   INFO     This call is non-blocking and will return immediately after the operation is launched on the device.\n02-10 17:35:07 userlogger   INFO     The DirectSolver object's resources have been released.\n\n CuDSS:\n||x||: \t\t29391823863.993862\n||Ax - b||: \t92575181911.9934\n\nCuPy:\n||x||: \t\t10.647411227999223\n||Ax - b||: \t4.289313285599112e-14\n\nNumPy:\n||x||: \t\t10.647411227999223\n||Ax - b||: \t4.29904389535207e-14\n```\n\n**Note that I computed the determinant to check whether A is invertible.** \n\n### Example observation 2\n\nVice versa I made the observation that DirectSolver sometimes returns not `nan` even though the determinant is 0. Note that here `b = cp.ones((n, 1), order=\"F\")` was only a vector\n\n```\n||A||: \t5.6922584694712395\n||b||: \t10.0\n\ndet(A): 0.0\n\n02-10 17:30:48 userlogger   INFO     = SPECIFICATION PHASE =\n02-10 17:30:48 userlogger   INFO     The LHS package is cupyx.\n02-10 17:30:48 userlogger   INFO     The RHS package is cupy.\n02-10 17:30:48 userlogger   INFO     The device_id=0, dtype = float64, index type = int32.\n02-10 17:30:48 userlogger   INFO     The number of equations = 100.\n02-10 17:30:48 userlogger   INFO     The operands' memory space is cuda, and the execution space is on device 0.\n02-10 17:30:48 userlogger   INFO     The specified stream for the DirectSolver ctor is \u003ccuda.core.experimental._stream.Stream object at 0x14c6b6504580\u003e.\n02-10 17:30:48 userlogger   INFO     The library handle has been created: 94064601263200.\n02-10 17:30:48 userlogger   INFO     The sparse direct solver operation has been created.\n02-10 17:30:48 userlogger   INFO     Starting solver phase ANALYSIS...\n02-10 17:30:48 userlogger   INFO     This call is non-blocking and will return immediately after the operation is launched on the device.\n02-10 17:30:48 userlogger   INFO     Starting solver phase FACTORIZATION...\n02-10 17:30:48 userlogger   INFO     This call is non-blocking and will return immediately after the operation is launched on the device.\n02-10 17:30:48 userlogger   INFO     Starting solver phase SOLVE...\n02-10 17:30:48 userlogger   INFO     This call is non-blocking and will return immediately after the operation is launched on the device.\n02-10 17:30:48 userlogger   INFO     The DirectSolver object's resources have been released.\n\n CuDSS:\n||x||: \t\t1.5379474527090538e+102\n||Ax - b||: \t1.5379474527090537e+89\n\nCuPy:\n||x||: \t\tnan\n||Ax - b||: \tnan\n\nNumPy:\n||x||: \t\tnan\n||Ax - b||: \tnan\n```\n\n","author":{"url":"https://github.com/TimoEckstein","@type":"Person","name":"TimoEckstein"},"datePublished":"2026-02-10T16:54:53.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":3},"url":"https://github.com/56/nvmath-python/issues/56"}