scipy.odr.ODR传入sy(y_err)时出现「解处秩不足」错误

我计划用ODR处理实验室数据，先通过模拟数据学习scipy.odr的用法。测试发现，只要向odr.RealData类传入y误差(sy)，就会出现StopReason提示“Problem is not full rank at solution”，且拟合参数和初始猜测值完全一致，没有更新。尝试添加setup参数fit_type=2（强制使用类似numpy.polyfit的线性回归），结果没有变化。该问题疑似和Stack Overflow帖子78522990相关，但目前该帖无解决方案，仅讨论numpy和scipy版本问题。

复现代码 #

if __name__ == "__main__":

    import scipy
    import numpy as np
    import pandas as pd
    
    print(f"scipy version: {scipy.__version__}")
    print(f"numpy version: {np.__version__}")
    print(f"pandas version: {pd.__version__}")
    print("")
    
    np.random.seed(10)
    pd.options.display.float_format = '{:,.4f}'.format
    
    
    def fit_func(beta, x):
        y = beta[0] + beta[1]*np.exp(-1 * beta[2] * x)
        return y
    
    
    # initial guess of parameters
    beta0 = (1.00, 85.0, 0.02)
    
    # actual parameters unknown to us but close to beta0
    beta = (np.abs(np.random.normal(beta0[0], 2.000)),
            np.abs(np.random.normal(beta0[1], 5.000)),
            np.abs(np.random.normal(beta0[2], 0.004)),
            )
    
    # noiseless data
    x = np.linspace(10, 90, 81)
    y = fit_func(beta, x)
    
    # simulate discrepancy
    dx = np.random.normal(0, 0.2, len(x))
    dy = np.random.normal(0, 1.0, len(y))
    
    # add discrepancy
    x += dx
    y += dy
    
    # estimate uncertainty
    sx = 0.5 + np.abs(dx)
    sy = 1.4 + np.abs(dy)
    
    # ODR with 'sy'
    odr_noisy = scipy.odr.ODR(
        data=scipy.odr.RealData(x, y, sx, sy),
        model=scipy.odr.Model(fit_func),
        beta0=beta0,
        )
    output_noisy = odr_noisy.run()
    print(f"ODR_NOISY: {output_noisy.stopreason}")
    
    # ODR without 'sy'
    odr_clean = scipy.odr.ODR(
        data=scipy.odr.RealData(x, y, sx, None),
        model=scipy.odr.Model(fit_func),
        beta0=beta0,
        )
    output_clean = odr_clean.run()
    print(f"ODR_CLEAN: {output_clean.stopreason}")
    
    # compare results
    results = {"initial": beta0,
               "ODR noisy": output_noisy.beta,
               "ODR clean": output_clean.beta,
               "actual": beta,
               }
    table = pd.DataFrame(results).transpose()
    table.columns = ["beta[0]", "beta[1]", "beta[2]"]
    print(f"\n{table}")

输出结果 #

scipy version: 1.16.2
numpy version: 2.3.3
pandas version: 2.3.3

ODR_NOISY: ['Problem is not full rank at solution', 'Sum of squares convergence']
ODR_CLEAN: ['Sum of squares convergence']

           beta[0]  beta[1]  beta[2]
initial     1.0000  85.0000   0.0200
ODR noisy   1.0000  85.0000   0.0200
ODR clean   0.7697  90.5035   0.0129
actual      3.6632  88.5764   0.0138

可视化图表 #

更新补充信息 #

• 系统：Windows 11 Pro for Workstations，OS版本26200.6899
• scipy通过miniforge/mamba安装
• 详细构建信息：

1.16.2 2.3.3 sys.version_info(major=3, minor=13, micro=0, releaselevel='final', serial=0)
Build Dependencies:
  blas:
    detection method: pkgconfig
    found: true
    include directory: C:/Users/nukamoi/AppData/Local/miniforge3/envs/pyvt/Library/include
    lib directory: C:/Users/nukamoi/AppData/Local/miniforge3/envs/pyvt/Library/lib
    name: mkl-sdl
    openblas configuration: unknown
    pc file directory: C:\miniconda3\conda-bld\scipy_1759489068917\_h_env\Library\lib\pkgconfig
    version: '2025'
  lapack:
    detection method: pkgconfig
    found: true
    include directory: C:/Users/nukamoi/AppData/Local/miniforge3/envs/pyvt/Library/include
    lib directory: C:/Users/nukamoi/AppData/Local/miniforge3/envs/pyvt/Library/lib
    name: mkl-sdl
    openblas configuration: unknown
    pc file directory: C:\miniconda3\conda-bld\scipy_1759489068917\_h_env\Library\lib\pkgconfig
    version: '2025'
  pybind11:
    detection method: pkgconfig
    include directory: C:/Users/nukamoi/AppData/Local/miniforge3/envs/pyvt/Library/include
    name: pybind11
    version: 2.13.6
Compilers:
  c:
    args: -IC:\miniconda3\conda-bld\scipy_1759489068917\work\scipy\linalg, -IC:\miniconda3\conda-bld\scipy_1759489068917\work\scipy\_lib
    commands: clang-cl.exe
    linker: lld-link
    name: clang-cl
    version: 20.1.8
  c++:
    commands: clang-cl.exe
    linker: lld-link
    name: clang-cl
    version: 20.1.8
  cython:
    commands: cython
    linker: cython
    name: cython
    version: 3.1.4
  fortran:
    commands: ifort
    linker: xilink
    name: intel-cl
    version: 2021.6.0
  pythran:
    include directory: ..\..\_h_env\Lib\site-packages\pythran
    version: 0.18.0
Machine Information:
  build:
    cpu: x86_64
    endian: little
    family: x86_64
    system: windows
  cross-compiled: false
  host:
    cpu: x86_64
    endian: little
    family: x86_64
    system: windows
Python Information:
  path: C:\miniconda3\conda-bld\scipy_1759489068917\_h_env\python.exe
  version: '3.13'

Build Dependencies:
  blas:
    detection method: pkgconfig
    found: true
    include directory: C:/Users/nukamoi/AppData/Local/miniforge3/envs/pyvt/Library/include
    lib directory: C:/Users/nukamoi/AppData/Local/miniforge3/envs/pyvt/Library/lib
    name: mkl-sdl
    openblas configuration: unknown
    pc file directory: C:\miniconda3\conda-bld\numpy_and_numpy_base_1757670256083\_h_env\Library\lib\pkgconfig
    version: '2025'
  lapack:
    detection method: pkgconfig
    found: true
    include directory: C:/Users/nukamoi/AppData/Local/miniforge3/envs/pyvt/Library/include
    lib directory: C:/Users/nukamoi/AppData/Local/miniforge3/envs/pyvt/Library/lib
    name: mkl-sdl
    openblas configuration: unknown
    pc file directory: C:\miniconda3\conda-bld\numpy_and_numpy_base_1757670256083\_h_env\Library\lib\pkgconfig
    version: '2025'
Compilers:
  c:
    commands: cl.exe
    linker: link
    name: msvc
    version: 19.29.30159
  c++:
    commands: cl.exe
    linker: link
    name: msvc
    version: 19.29.30159
  cython:
    commands: cython
    linker: cython
    name: cython
    version: 3.1.3
Machine Information:
  build:
    cpu: x86_64
    endian: little
    family: x86_64
    system: windows
  host:
    cpu: x86_64
    endian: little
    family: x86_64
    system: windows
Python Information:
  path: C:\miniconda3\conda-bld\numpy_and_numpy_base_1757670256083\_h_env\python.exe
  version: '3.13'
SIMD Extensions:
  baseline:
  - SSE
  - SSE2
  - SSE3
  found:
  - SSSE3
  - SSE41
  - POPCNT
  - SSE42
  - AVX
  - F16C

内容的提问来源于stack exchange，提问作者nukamoi