掩盖的Numpy阵列比普通的numpy阵列慢很多

Question

我有一个函数可以计算numpy数组中所有行对之间的成对相关性。它工作正常，但后来我记得，我经常需要处理缺失的数据。我用掩码数组来尝试解决这个问题，但它会使计算速度减慢很多。任何有关使用蒙版功能的想法。我认为真正的瓶颈将在np.ma.dot函数中。但我添加了一些配置文件，我很快就用iPython进行了嘲弄。根据这些阵列所具有的行数，我应该说5000就在频谱的低端。有些可能超过300,000。带有掩码数组的代码看起来比没有代码慢20倍，但显然缺少数据，没有掩码数组的代码每隔一段时间就会产生一个NaN。

首先一个快速和肮脏的方式来产生一些示例数据

genotypes = np.empty((5000,200)) 
for i in xrange(5000): 
    genotypes[i] = np.random.binomial(3,.333, size=200) 

pValues = np.random.uniform(0,1,5000) 

然后功能测试

def testMask(pValsArray, genotypeArray): 
    nSNPs = len(pValsArray)-1 
    genotypeArray = np.ma.masked_array(genotypeArray, np.isnan(genotypeArray)) 
    chisq = np.sum(-2 * np.log(pValsArray)) 
    ms = genotypeArray.mean(axis=1)[(slice(None,None,None),None)] 
    datam = genotypeArray - ms 
    datass = np.ma.sqrt(np.ma.sum(datam**2, axis=1)) 
    runningSum = 0 
    for i in xrange(nSNPs): 
     temp = np.ma.dot(datam[i:],datam[i].T) 
     d = (datass[i:]*datass[i]) 
     rs = temp/d 
     rs = np.absolute(rs)[1:] 
     runningSum += 3.25 * np.sum(rs) + .75 * np.dot(rs, rs) 
    sigmaSq = 4*nSNPs+2*runningSum 
    E = 2*nSNPs 
    df = (2*(E*E))/sigmaSq 
    runningSum = sigmaSq/(2*E) 
    d = chisq/runningSum 
    brownsP = stats.chi2.sf(d, df) 
    return brownsP 

def testNotMask(pValsArray, genotypeArray): 
    nSNPs = len(pValsArray)-1 
    chisq = np.sum(-2 * np.log(pValsArray)) 
    ms = genotypeArray.mean(axis=1)[(slice(None,None,None),None)] 
    datam = genotypeArray - ms 
    datass = np.sqrt(stats.ss(datam, axis=1)) 
    runningSum = 0 
    for i in xrange(nSNPs): 
     temp = np.dot(datam[i:],datam[i].T) 
     d = (datass[i:]*datass[i]) 
     rs = temp/d 
     rs = np.absolute(rs)[1:] 
     runningSum += 3.25 * np.sum(rs) + .75 * np.dot(rs, rs) 
    sigmaSq = 4*nSNPs+2*runningSum 
    E = 2*nSNPs 
    df = (2*(E*E))/sigmaSq 
    runningSum = sigmaSq/(2*E) 
    d = chisq/runningSum 
    brownsP = stats.chi2.sf(d, df) 
    return brownsP 

还有一些时间

%timeit testMask(pValues, genotypes) 
1 loops, best of 3: 14.3 s per loop 

%timeit testNotMask(pValues, genotypes) 
1 loops, best of 3: 678 ms per loop 

添加一些丢失的数据，去再次：

randis = np.random.randint(0,5000, 10) 
randjs = np.random.randint(0,200, 10) 

for i,j in zip(randis, randjs): 
    genotypes[i,j] = None 



%timeit testMask(pValues, genotypes) 
1 loops, best of 3: 14.2 s per loop 

%timeit testNotMask(pValues, genotypes) 
1 loops, best of 3: 654 ms per loop 

和一些剖析：

%prun 

     2559677 function calls in 15.045 seconds 

    Ordered by: internal time 

    ncalls tottime percall cumtime percall filename:lineno(function) 
    9791 5.259 0.001 5.259 0.001 {method 'copy' of 'numpy.ndarray' objects} 
    4999 2.877 0.001 11.888 0.002 extras.py:949(dot) 
    9794 1.566 0.000 1.566 0.000 {numpy.core.multiarray.copyto} 
    14997 1.497 0.000 1.564 0.000 {numpy.core._dotblas.dot} 
    30007 0.559 0.000 0.559 0.000 {method 'reduce' of 'numpy.ufunc' objects} 
    94996 0.450 0.000 0.875 0.000 core.py:2751(_update_from) 
    864970 0.347 0.000 0.347 0.000 {getattr} 
    5000 0.346 0.000 0.802 0.000 core.py:1065(__call__) 
     1 0.240 0.240 15.045 15.045 <ipython-input-115-2aab1c8ea4c5>:1(testMask) 
    5000 0.196 0.000 0.196 0.000 core.py:771(__call__) 
    5001 0.147 0.000 0.551 0.000 core.py:917(__call__) 
    24996 0.143 0.000 0.609 0.000 core.py:2930(__getitem__) 
    54998 0.140 0.000 0.775 0.000 core.py:2776(__array_finalize__) 
    419985 0.126 0.000 0.126 0.000 {method 'update' of 'dict' objects} 
     1 0.093 0.093 0.111 0.111 core.py:5990(power) 
    339994 0.077 0.000 0.077 0.000 {isinstance} 
    50015 0.072 0.000 0.072 0.000 {numpy.core.multiarray.array} 
    60002 0.060 0.000 0.568 0.000 {method 'view' of 'numpy.ndarray' objects} 
    5000 0.060 0.000 0.199 0.000 core.py:2626(__new__) 
    14999 0.058 0.000 7.412 0.000 core.py:3341(filled) 
    25005 0.055 0.000 0.092 0.000 core.py:609(getdata) 

编辑：

我试图perimosocordiae的答案，但我仍然得到nan秒。它看起来像mean,stats.ss和np.sqrt函数都关心nan值。

def fastNotMask(pValsArray, genotypeArray): 
    nSNPs = len(pValsArray)-1 
    chisq = np.sum(-2 * np.log(pValsArray)) 
    ms = genotypeArray.mean(axis=1)[(slice(None,None,None),None)] 
    print ms 
    datam = genotypeArray - ms 
    print datam 
    datass = np.sqrt(stats.ss(datam, axis=1)) 
    print datass 
    runningSum = 0 
    for i in xrange(nSNPs): 
     temp = np.dot(datam[i:],datam[i].T) 
     d = (datass[i:]*datass[i]) 
     rs = temp/d 
     rs = np.absolute(rs)[1:] 
     runningSum += 3.25 * np.nansum(rs) + .75 * np.nansum(rs * rs) 
    print runningSum 
    sigmaSq = 4*nSNPs+2*runningSum 
    E = 2*nSNPs 
    df = (2*(E*E))/sigmaSq 
    runningSum = sigmaSq/(2*E) 
    d = chisq/runningSum 
    brownsP = stats.chi2.sf(d, df) 
    return brownsP 

用少量输出测试这个结果表明nan没有得到正确的处理。

pValues = np.random.uniform(0,1,10) 

genotypes = np.empty((10,10)) 
for i in xrange(10): 
    genotypes[i] = np.random.binomial(2,.5, size=10) 

randis = np.random.randint(0,10, 2) 
randjs = np.random.randint(0,10, 2) 

for i,j in zip(randis, randjs): 
    genotypes[i,j] = None 

print testfastMask(pValues, genotypes) 



[[ 1.5] 
[ 1.2] 
[ 0.9] 
[ 1.2] 
[ 1.1] 
[ 0.6] 
[ nan] 
[ 1.1] 
[ nan] 
[ 0.8]] 
[[-0.5 -0.5 0.5 0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5] 
[-0.2 0.8 -0.2 -0.2 -0.2 -0.2 -0.2 0.8 -0.2 -0.2] 
[-0.9 0.1 -0.9 1.1 0.1 -0.9 1.1 0.1 0.1 0.1] 
[-0.2 -0.2 -0.2 -0.2 0.8 -0.2 -0.2 -1.2 0.8 0.8] 
[-0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0.9 -0.1 0.9 -1.1] 
[-0.6 1.4 0.4 -0.6 -0.6 0.4 -0.6 -0.6 0.4 0.4] 
[ nan nan nan nan nan nan nan nan nan nan] 
[-0.1 0.9 -1.1 -1.1 0.9 -0.1 0.9 -1.1 0.9 -0.1] 
[ nan nan nan nan nan nan nan nan nan nan] 
[ 1.2 -0.8 -0.8 0.2 -0.8 0.2 1.2 0.2 0.2 -0.8]] 
[ 1.58113883 1.26491106 2.21359436 1.8973666 1.70293864 2.0976177 
     nan 2.62678511   nan 2.36643191] 
nan 
nan 

我在这里错过了什么吗？这可能是一个版本问题。我使用python 2.7和numpy 1.7.1？

干杯的帮助。

Answer 1

编辑：原来的答案不为numpy的版本< = 1.8工作，其中np.nansum([NaN, NaN]) == 0.0（note the FutureWarning）。对于早期版本，您必须手动检查情况：

tmp = 3.25 * np.nansum(rs) + .75 * np.nansum(rs * rs) 
if not np.isnan(tmp): 
    runningSum += tmp 

或者，你可以建立tmp值的列表/阵列，并呼吁对np.nansum。

---

原来的答案：

所有你需要改变的是这一行testNotMask：

runningSum += 3.25 * np.sum(rs) + .75 * np.dot(rs, rs) 

这样：

runningSum += 3.25 * np.nansum(rs) + .75 * np.nansum(rs * rs) 

其他所有操作都正常工作与NaN值，所以你可以得到所有的演讲d的非屏蔽数组，同时仍然得到正确的结果。

这是证明。功能fastNotMask只是testNotMask与应用上述更改。

In [63]: genotypes = np.random.binomial(3, .333, size=(5000, 200)).astype(float) 

In [64]: pValues = np.random.uniform(0,1,5000) 

In [65]: %timeit testMask(pValues, genotypes) 
1 loops, best of 3: 11.3 s per loop 

In [66]: %timeit testNotMask(pValues, genotypes) 
1 loops, best of 3: 3.53 s per loop 

In [67]: %timeit fastNotMask(pValues, genotypes) 
1 loops, best of 3: 3.96 s per loop 

In [68]: randjs = np.random.randint(0,200, 10) 

In [69]: randis = np.random.randint(0,5000,10) 

In [70]: genotypes[randis,randjs] = None 

In [71]: %timeit testMask(pValues, genotypes) 
1 loops, best of 3: 33 s per loop 

In [72]: %timeit testNotMask(pValues, genotypes) 
1 loops, best of 3: 3.6 s per loop 

In [73]: %timeit fastNotMask(pValues, genotypes) 
1 loops, best of 3: 3.98 s per loop 

In [74]: testMask(pValues, genotypes) 
Out[74]: 0.47606794747438386 

In [75]: testNotMask(pValues, genotypes) 
Out[75]: nan 

In [76]: fastNotMask(pValues, genotypes) 
Out[76]: 0.47613597091679449 

注意，有精密testMask和fastNotMask之间略有差别。我其实不确定这是从哪里来的，但我会认为这并不重要。