# cgeqrfp.f - Man Page

SRC/cgeqrfp.f

## Synopsis

### Functions/Subroutines

subroutine cgeqrfp (m, n, a, lda, tau, work, lwork, info)
CGEQRFP

## Function/Subroutine Documentation

### subroutine cgeqrfp (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)

CGEQRFP

Purpose:

``` CGEQR2P computes a QR factorization of a complex M-by-N matrix A:

A = Q * ( R ),
( 0 )

where:

Q is a M-by-M orthogonal matrix;
R is an upper-triangular N-by-N matrix with nonnegative diagonal
entries;
0 is a (M-N)-by-N zero matrix, if M > N.```
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 COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n). The diagonal entries of R
are real and nonnegative; the elements below the diagonal,
with the array TAU, represent the unitary matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).```

LDA

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

TAU

```          TAU is COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).```

WORK

```          WORK is COMPLEX 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 >= max(1,N).
For optimum performance LWORK >= N*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.

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**H

where tau is a complex scalar, and v is a 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).

See Lapack Working Note 203 for details```

Definition at line 148 of file cgeqrfp.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cgeqrfp(3) is an alias of cgeqrfp.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK