MatrixSingularException when column is 0 all at pinv

[y-shimizu]

Hi,

I wanted to compute the Moore-Penrose pseudo inverse of a Matrix.
But I am troubled by the exception:

val m = DenseMatrix((0d,3d,6d), (0d,4d,7d), (0d,5d,9d))
val mi = pinv(m)


>Exception in thread "main" breeze.linalg.MatrixSingularException: 
>   at breeze.linalg.operators.DenseMatrixMultiplyStuff$implOpSolveMatrixBy_DMD_DMD_eq_DMD$.LUSolve(DenseMatrixOps.scala:145)
>   at breeze.linalg.operators.DenseMatrixMultiplyStuff$implOpSolveMatrixBy_DMD_DMD_eq_DMD$.apply(DenseMatrixOps.scala:119)
>   at breeze.linalg.operators.DenseMatrixMultiplyStuff$implOpSolveMatrixBy_DMD_DMD_eq_DMD$.apply(DenseMatrixOps.scala:107)
>   at breeze.linalg.NumericOps$class.$bslash(NumericOps.scala:270)
>   at breeze.linalg.DenseMatrix.$bslash(DenseMatrix.scala:54)
>   at breeze.linalg.pinv$$anon$2.apply(inv.scala:79)
>   at breeze.generic.UFunc$class.apply(UFunc.scala:48)
>   at breeze.linalg.pinv$.apply(inv.scala:54)
>   at Test$.delayedEndpoint$Test$1(Test.scala:11)
>   at Test$delayedInit$body.apply(Test.scala:3)
>   at scala.Function0$class.apply$mcV$sp(Function0.scala:40)
>   at scala.runtime.AbstractFunction0.apply$mcV$sp(AbstractFunction0.scala:12)
>   at scala.App$$anonfun$main$1.apply(App.scala:76)
>   at scala.App$$anonfun$main$1.apply(App.scala:76)
>   at scala.collection.immutable.List.foreach(List.scala:381)
>   at scala.collection.generic.TraversableForwarder$class.foreach(TraversableForwarder.scala:35)
>   at scala.App$class.main(App.scala:76)
>   at Test$.main(Test.scala:3)
>   at Test.main(Test.scala)
>   at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
>   at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:39)
>   at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:25)
>   at java.lang.reflect.Method.invoke(Method.java:597)
>   at com.intellij.rt.execution.application.AppMain.main(AppMain.java:134)

I wanted to get matrix [(0, 0, 0) (-2.526316,1.4210526,0.5789474), (1.421053, -0.7368421, -0.2631579)]
like R:

> m <- rbind(c(0,3,6), c(0,4,7), c(0,5,9))
> ginv(m)
          [,1]       [,2]       [,3]
[1,]  0.000000  0.0000000  0.0000000
[2,] -2.526316  1.4210526  0.5789474
[3,]  1.421053 -0.7368421 -0.2631579

Please tell me why is the implementation different from pinv and R:ginv .

[dlwh]

looks like the correct way to implement pinv is not with the usual
mathematical formula (as we currently do), but with an svd:
http://the-lost-beauty.blogspot.com/2009/04/moore-penrose-pseudoinverse-in-jama.html

We should fix this.

On Sun, Aug 31, 2014 at 5:07 AM, y-shimizu notifications@github.com wrote:

Hi,

I wanted to compute the Moore-Penrose pseudo inverse of a Matrix.
But I am troubled by the exception:

val m = DenseMatrix((0d,3d,6d), (0d,4d,7d), (0d,5d,9d))
val mi = pinv(m)

Exception in thread "main" breeze.linalg.MatrixSingularException:
at breeze.linalg.operators.DenseMatrixMultiplyStuff$implOpSolveMatrixBy_DMD_DMD_eq_DMD$.LUSolve(DenseMatrixOps.scala:145)
at breeze.linalg.operators.DenseMatrixMultiplyStuff$implOpSolveMatrixBy_DMD_DMD_eq_DMD$.apply(DenseMatrixOps.scala:119)
at breeze.linalg.operators.DenseMatrixMultiplyStuff$implOpSolveMatrixBy_DMD_DMD_eq_DMD$.apply(DenseMatrixOps.scala:107)
at breeze.linalg.NumericOps$class.$bslash(NumericOps.scala:270)
at breeze.linalg.DenseMatrix.$bslash(DenseMatrix.scala:54)
at breeze.linalg.pinv$$anon$2.apply(inv.scala:79)
at breeze.generic.UFunc$class.apply(UFunc.scala:48)
at breeze.linalg.pinv$.apply(inv.scala:54)
at Test$.delayedEndpoint$Test$1(Test.scala:11)
at Test$delayedInit$body.apply(Test.scala:3)
at scala.Function0$class.apply$mcV$sp(Function0.scala:40)
at scala.runtime.AbstractFunction0.apply$mcV$sp(AbstractFunction0.scala:12)
at scala.App$$anonfun$main$1.apply(App.scala:76)
at scala.App$$anonfun$main$1.apply(App.scala:76)
at scala.collection.immutable.List.foreach(List.scala:381)
at scala.collection.generic.TraversableForwarder$class.foreach(TraversableForwarder.scala:35)
at scala.App$class.main(App.scala:76)
at Test$.main(Test.scala:3)
at Test.main(Test.scala)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:39)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:25)
at java.lang.reflect.Method.invoke(Method.java:597)
at com.intellij.rt.execution.application.AppMain.main(AppMain.java:134)

I wanted to get matrix [(0, 0, 0) (-2.526316,1.4210526,0.5789474),
(1.421053, -0.7368421, -0.2631579)]
like R:

m <- rbind(c(0,3,6), c(0,4,7), c(0,5,9))
ginv(m)
[,1] [,2] [,3]
[1,] 0.000000 0.0000000 0.0000000
[2,] -2.526316 1.4210526 0.5789474
[3,] 1.421053 -0.7368421 -0.2631579

Please tell me why is the implementation different from pinv and R:ginv .

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[y-shimizu]

@dlwh
Thank you for comment.
I will try this.