# dgeqp3.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dgeqp3.f

## SYNOPSIS

### Functions/Subroutines

subroutine dgeqp3 (M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)
DGEQP3

## Function/Subroutine Documentation

### subroutine dgeqp3 (integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, integer, dimension( * ) JPVT, double precision, dimension( * ) TAU, double precision, dimension( * ) WORK, integer LWORK, integer INFO)

DGEQP3

Purpose:

``` DGEQP3 computes a QR factorization with column pivoting of a
matrix A:  A*P = Q*R  using Level 3 BLAS.
```

Parameters:

M

```          M is INTEGER
The number of rows of the matrix A. M >= 0.
```

N

```          N is INTEGER
The number of columns of the matrix A.  N >= 0.
```

A

```          A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the upper triangle of the array contains the
min(M,N)-by-N upper trapezoidal matrix R; the elements below
the diagonal, together with the array TAU, represent the
orthogonal matrix Q as a product of min(M,N) elementary
reflectors.
```

LDA

```          LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
```

JPVT

```          JPVT is INTEGER array, dimension (N)
On entry, if JPVT(J).ne.0, the J-th column of A is permuted
to the front of A*P (a leading column); if JPVT(J)=0,
the J-th column of A is a free column.
On exit, if JPVT(J)=K, then the J-th column of A*P was the
the K-th column of A.
```

TAU

```          TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors.
```

WORK

```          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO=0, WORK(1) returns the optimal LWORK.
```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK. LWORK >= 3*N+1.
For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB
is the optimal blocksize.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
```

INFO

```          INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

Further Details:

```  The matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) . . . H(k), where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v**T

where tau is a real scalar, and v is a real/complex vector
with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
A(i+1:m,i), and tau in TAU(i).
```

Contributors:

G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA

Definition at line 153 of file dgeqp3.f.

## Author

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