## linear_algebra Class QR_j

```java.lang.Object
|
+--linear_algebra.QR_j
```

public class QR_j
extends java.lang.Object

This class contains the LINPACK DQRDC (QR decomposition) and DQRSL (QR solve) routines.

IMPORTANT: The "_j" suffixes indicate that these routines use Java/C style indexing. For example, you will see

```   for (i = 0; i < n; i++)
```
rather than
```   for (i = 1; i <= n; i++)
```
To use the "_j" routines you will have to fill elements 0 through n - 1 rather than elements 1 through n. Versions of these programs that use FORTYRAN style indexing are also available. They end with the suffix "_f77".

This class was translated by a statistician from FORTRAN versions of the LINPACK routines. It is NOT an official translation. When public domain Java numerical analysis routines become available from the people who produce LAPACK, then THE CODE PRODUCED BY THE NUMERICAL ANALYSTS SHOULD BE USED.

 Constructor Summary `QR_j()`

 Method Summary `static void` ```dqrdc_j(double[][] x, int n, int p, double[] qraux, int[] jpvt, double[] work, int job)```            This method decomposes an n by p matrix X into a product, QR, of an orthogonal n by n matrix Q and an upper triangular n by p matrix R. `static int` ```dqrsl_j(double[][] x, int n, int k, double[] qraux, double[] y, double[] qy, double[] qty, double[] b, double[] rsd, double[] xb, int job)```            This method "applies the output of DQRDC to compute coordinate transformations, projections, and least squares solutions." For details, see the comments in the code.

 Methods inherited from class java.lang.Object `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

 Constructor Detail

### QR_j

`public QR_j()`
 Method Detail

### dqrdc_j

```public static void dqrdc_j(double[][] x,
int n,
int p,
double[] qraux,
int[] jpvt,
double[] work,
int job)```

This method decomposes an n by p matrix X into a product, QR, of an orthogonal n by n matrix Q and an upper triangular n by p matrix R. For details, see the comments in the code. This method is a translation from FORTRAN to Java of the LINPACK subroutine DQRDC. In the LINPACK listing DQRDC is attributed to G.W. Stewart with a date of 8/14/78. Translated by Steve Verrill, February 25, 1997.

Parameters:
`n` - The number of rows of the matrix X
`p` - The number of columns of the matrix X
`qraux` - This vector "contains further information required to recover the orthogonal part of the decomposition."
`jpvt` - This output vector contains pivoting information.
`work` - This vector is used as temporary space
`job` - This value indicates whether column pivoting should be performed

### dqrsl_j

```public static int dqrsl_j(double[][] x,
int n,
int k,
double[] qraux,
double[] y,
double[] qy,
double[] qty,
double[] b,
double[] rsd,
double[] xb,
int job)```

This method "applies the output of DQRDC to compute coordinate transformations, projections, and least squares solutions." For details, see the comments in the code. This method is a translation from FORTRAN to Java of the LINPACK subroutine DQRSL. In the LINPACK listing DQRSL is attributed to G.W. Stewart with a date of 8/14/78. Translated by Steve Verrill, February 27, 1997.

Parameters:
`n` - The number of rows of X
`k` - k <= min(n,p) where p is the number of columns of X
`qraux` - This vector "contains further information required to recover the orthogonal part of the decomposition"
`y` - This n by 1 vector will be manipulated by DQRSL
`qy` - On output, this vector contains Qy if it has been requested
`qty` - On output, this vector contains transpose(Q)y if it has been requested
`b` - Parameter estimates
`rsd` - Residuals
`xb` - Predicted values
`job` - Specifies what is to be computed (see the code for details)