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Added more detailed docs to the QR decompositions classes.

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Hauke Heibel 2010-08-05 08:56:19 +02:00
parent 976d7c19e8
commit 3dd8225862
3 changed files with 21 additions and 4 deletions
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8
Eigen/src/QR/ColPivHouseholderQR.h
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@ -34,7 +34,13 @@
*
* \param MatrixType the type of the matrix of which we are computing the QR decomposition
*
* This class performs a rank-revealing QR decomposition using Householder transformations.
* This class performs a rank-revealing QR decomposition of a matrix \b A into matrices \b P, \b Q and \b R
* such that
* \f[
* \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \mathbf{R}
* \f]
* by using Householder transformations. Here, \b P is a permutation matrix, \b Q a unitary matrix and \b R an
* upper triangular matrix.
*
* This decomposition performs column pivoting in order to be rank-revealing and improve
* numerical stability. It is slower than HouseholderQR, and faster than FullPivHouseholderQR.

8
Eigen/src/QR/FullPivHouseholderQR.h
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@ -34,7 +34,13 @@
*
* \param MatrixType the type of the matrix of which we are computing the QR decomposition
*
* This class performs a rank-revealing QR decomposition using Householder transformations.
* This class performs a rank-revealing QR decomposition of a matrix \b A into matrices \b P, \b Q and \b R
* such that
* \f[
* \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \mathbf{R}
* \f]
* by using Householder transformations. Here, \b P is a permutation matrix, \b Q a unitary matrix and \b R an
* upper triangular matrix.
*
* This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal
* numerical stability. The trade-off is that it is slower than HouseholderQR and ColPivHouseholderQR.

9
Eigen/src/QR/HouseholderQR.h
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@ -36,8 +36,13 @@
*
* \param MatrixType the type of the matrix of which we are computing the QR decomposition
*
* This class performs a QR decomposition using Householder transformations. The result is
* stored in a compact way compatible with LAPACK.
* This class performs a QR decomposition of a matrix \b A into matrices \b Q and \b R
* such that
* \f[
* \mathbf{A} = \mathbf{Q} \, \mathbf{R}
* \f]
* by using Householder transformations. Here, \b Q a unitary matrix and \b R an upper triangular matrix.
* The result is stored in a compact way compatible with LAPACK.
*
* Note that no pivoting is performed. This is \b not a rank-revealing decomposition.
* If you want that feature, use FullPivHouseholderQR or ColPivHouseholderQR instead.