RFC: add support for computing the variance of complex array #1007

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1. rgommers commented on Jun 23, 2026

   

   rgommers

   on Jun 23, 2026

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   The tracking issue for adding complex number support to all relevant APIs was gh-373, and for both std and var it says only:

   • No complex number support.
   • Change to only real number data types.

   No reason for it given unfortunately. Probably was because of the correction keyword and/or the inf/nan special cases. correction does seem well-defined as total variance; there's also pseudo/relational variance and generalized variance, in case numbers aren't simply uncorrelated points in the complex plane (hard to find a single concise reference, https://en.wikipedia.org/wiki/Variance#For_complex_variables has the latter).

   If all libraries implement total variance though, I don't see a reason yet not to do the same in the standard.

   @kgryte do you remember why you excluded std/var?
2. kgryte

   changed the title [-]Variance of complex array[/-] [+]RFC: add support for computing the variance of complex array[/+] on Jun 25, 2026
3. kgryte

   added

   RFCRequest for comments. Feature requests and proposed changes.Request for comments. Feature requests and proposed changes.

   topic: Complex Data TypesComplex number data types.Complex number data types.

   topic: StatisticsStatistics.Statistics.

   on Jun 25, 2026
4. kgryte commented on Jun 25, 2026

   

   kgryte

   on Jun 25, 2026

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   Complex support was originally added in the v2022 revision, and, in that revision, complex number support in mean, std, and var were considered lower priority. In the v2024 revision, we added support for complex numbers in mean (ref: #850).

   So, I think the answer is that we have added complex support to statistical APIs on an as requested basis since adding initial support in 2022.
5. rgommers commented on Jun 25, 2026

   

   rgommers

   on Jun 25, 2026

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   Then I think we should check all the statistical functions for whether they have universal complex dtype support; std is well-defined as well, so should be treated the same as `var.
6. ev-br commented on Jun 25, 2026

   

   ev-br

   on Jun 25, 2026

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   numpy, torch, jax and cupy seem to be in agreement:

   In [1]: import numpy as np
   
   In [2]: x = np.asarray([1 + 2j, 3 + 4j, 5 + 6j])
   
   In [3]: np.var(x)
   Out[3]: np.float64(5.333333333333333)
   
   In [4]: np.var(x.real) + np.var(x.imag)
   Out[4]: np.float64(5.333333333333333)
   
   In [6]: import torch
   
   In [7]: xt = torch.as_tensor(x)
   
   In [8]: torch.var(xt, correction=0)
   Out[8]: tensor(5.3333, dtype=torch.float64)
   
   In [10]: torch.var(xt.real, correction=0) + torch.var(xt.imag, correction=0)
   Out[10]: tensor(5.3333, dtype=torch.float64)
   
   In [12]: torch.std(xt, correction=0)**2
   Out[12]: tensor(5.3333, dtype=torch.float64)
   
   In [13]: import jax.numpy as jnp
   
   In [14]: xj = jnp.asarray(x)
   An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.
   
   In [15]: jnp.var(xj)
   Out[15]: Array(5.3333335, dtype=float32)
   
   In [16]: jnp.var(xj.real), jnp.var(xj.imag)
   Out[16]: (Array(2.6666667, dtype=float32), Array(2.6666667, dtype=float32))
   
   In [17]: jnp.std(xj)**2
   Out[17]: Array(5.333333, dtype=float32)
   
   In [18]: import cupy
   
   In [19]: xc = cupy.asarray(x)
   
   In [20]: cupy.var(xc)
   Out[20]: array(5.33333333)
   
   In [21]: cupy.var(xc.real), cupy.var(xc.imag)
   Out[21]: (array(2.66666667), array(2.66666667))
   
   In [22]: cupy.std(xc)**2
   Out[22]: array(5.33333333)
   
7. rgommers commented on Jun 25, 2026

   

   rgommers

   on Jun 25, 2026

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   Discussed in today's meeting, everyone was happy to move forward with this.