---
name: "cgeqrt.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/cgeqrt.f"
---

# cgeqrt.f(3)

## NAME

SRC/cgeqrt.f

## SYNOPSIS

### Functions/Subroutines

subroutine **cgeqrt** (m, n, nb, a, lda, t, ldt, work, info)\
 **CGEQRT**

## Function/Subroutine Documentation

### subroutine cgeqrt (integer m, integer n, integer nb, complex, dimension( lda, \* ) a, integer lda, complex, dimension( ldt, \* ) t, integer ldt, complex, dimension( \* ) work, integer info)

**CGEQRT**

**Purpose:**

```
!>
!> CGEQRT computes a blocked QR factorization of a complex M-by-N matrix A
!> using the compact WY representation of Q.
!>
```

**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.
!>
```

*NB*

```
!>          NB is INTEGER
!>          The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1.
!>
```

*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 elements below the diagonal
!>          are the columns of V.
!>
```

*LDA*

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

*T*

```
!>          T is COMPLEX array, dimension (LDT,MIN(M,N))
!>          The upper triangular block reflectors stored in compact form
!>          as a sequence of upper triangular blocks.  See below
!>          for further details.
!>
```

*LDT*

```
!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB.
!>
```

*WORK*

```
!>          WORK is COMPLEX array, dimension (NB*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 V stores the elementary reflectors H(i) in the i-th column
!>  below the diagonal. For example, if M=5 and N=3, the matrix V is
!>
!>               V = (  1       )
!>                   ( v1  1    )
!>                   ( v1 v2  1 )
!>                   ( v1 v2 v3 )
!>                   ( v1 v2 v3 )
!>
!>  where the vi's represent the vectors which define H(i), which are returned
!>  in the matrix A.  The 1's along the diagonal of V are not stored in A.
!>
!>  Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each
!>  block is of order NB except for the last block, which is of order
!>  IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
!>  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
!>  for the last block) T's are stored in the NB-by-K matrix T as
!>
!>               T = (T1 T2 ... TB).
!>
```

Definition at line **140** of file **cgeqrt.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.