---
name: "cgeqp3.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/cgeqp3.f"
---

# cgeqp3.f(3)

## NAME

SRC/cgeqp3.f

## SYNOPSIS

### Functions/Subroutines

subroutine **cgeqp3** (m, n, a, lda, jpvt, tau, work, lwork, rwork, info)\
 **CGEQP3**

## Function/Subroutine Documentation

### subroutine cgeqp3 (integer m, integer n, complex, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) jpvt, complex, dimension( \* ) tau, complex, dimension( \* ) work, integer lwork, real, dimension( \* ) rwork, integer info)

**CGEQP3**

**Purpose:**

```
!>
!> CGEQP3 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 COMPLEX 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
!>          unitary 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 COMPLEX array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors.
!>
```

*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 >= N+1.
!>          For optimal performance LWORK >= ( 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.
!>
```

*RWORK*

```
!>          RWORK is REAL array, dimension (2*N)
!>
```

*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

Univ. of Colorado Denver

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 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 **157** of file **cgeqp3.f**.

## Author

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