# gelqt3 - Man Page

gelqt3: LQ factor, with T, recursive

## Synopsis

### Functions

recursive subroutine cgelqt3 (m, n, a, lda, t, ldt, info)
CGELQT3
recursive subroutine dgelqt3 (m, n, a, lda, t, ldt, info)
DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.
recursive subroutine sgelqt3 (m, n, a, lda, t, ldt, info)
SGELQT3
recursive subroutine zgelqt3 (m, n, a, lda, t, ldt, info)
ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

## Function Documentation

### recursive subroutine cgelqt3 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)

CGELQT3

Purpose:

``` CGELQT3 recursively computes a LQ factorization of a complex M-by-N
matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson,
IBM J. Res. Develop. Vol 44 No. 4 July 2000.```
Parameters

M

```          M is INTEGER
The number of rows of the matrix A.  M =< N.```

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 complex M-by-N matrix A.  On exit, the elements on and
below the diagonal contain the N-by-N lower triangular matrix L; the
elements above the diagonal are the rows of V.  See below for
further details.```

LDA

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

T

```          T is COMPLEX array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.```

LDT

```          LDT is INTEGER
The leading dimension of the array T.  LDT >= max(1,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

NAG Ltd.

Further Details:

```  The matrix V stores the elementary reflectors H(i) in the i-th row
above the diagonal. For example, if M=5 and N=3, the matrix V is

V = (  1  v1 v1 v1 v1 )
(     1  v2 v2 v2 )
(     1  v3 v3 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.  The
block reflector H is then given by

H = I - V * T * V**T

where V**T is the transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).```

Definition at line 115 of file cgelqt3.f.

### recursive subroutine dgelqt3 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)

DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

``` DGELQT3 recursively computes a LQ factorization of a real M-by-N
matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson,
IBM J. Res. Develop. Vol 44 No. 4 July 2000.```
Parameters

M

```          M is INTEGER
The number of rows of the matrix A.  M =< N.```

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 real M-by-N matrix A.  On exit, the elements on and
below the diagonal contain the N-by-N lower triangular matrix L; the
elements above the diagonal are the rows of V.  See below for
further details.```

LDA

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

T

```          T is DOUBLE PRECISION array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.```

LDT

```          LDT is INTEGER
The leading dimension of the array T.  LDT >= max(1,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

NAG Ltd.

Further Details:

```  The matrix V stores the elementary reflectors H(i) in the i-th row
above the diagonal. For example, if M=5 and N=3, the matrix V is

V = (  1  v1 v1 v1 v1 )
(     1  v2 v2 v2 )
(     1  v3 v3 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.  The
block reflector H is then given by

H = I - V * T * V**T

where V**T is the transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).```

Definition at line 130 of file dgelqt3.f.

### recursive subroutine sgelqt3 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)

SGELQT3

Purpose:

``` SGELQT3 recursively computes a LQ factorization of a real M-by-N
matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson,
IBM J. Res. Develop. Vol 44 No. 4 July 2000.```
Parameters

M

```          M is INTEGER
The number of rows of the matrix A.  M =< N.```

N

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

A

```          A is REAL array, dimension (LDA,N)
On entry, the real M-by-N matrix A.  On exit, the elements on and
below the diagonal contain the N-by-N lower triangular matrix L; the
elements above the diagonal are the rows of V.  See below for
further details.```

LDA

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

T

```          T is REAL array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.```

LDT

```          LDT is INTEGER
The leading dimension of the array T.  LDT >= max(1,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

NAG Ltd.

Further Details:

```  The matrix V stores the elementary reflectors H(i) in the i-th row
above the diagonal. For example, if M=5 and N=3, the matrix V is

V = (  1  v1 v1 v1 v1 )
(     1  v2 v2 v2 )
(     1  v3 v3 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.  The
block reflector H is then given by

H = I - V * T * V**T

where V**T is the transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).```

Definition at line 115 of file sgelqt3.f.

### recursive subroutine zgelqt3 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

``` ZGELQT3 recursively computes a LQ factorization of a complex M-by-N
matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson,
IBM J. Res. Develop. Vol 44 No. 4 July 2000.```
Parameters

M

```          M is INTEGER
The number of rows of the matrix A.  M =< N.```

N

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

A

```          A is COMPLEX*16 array, dimension (LDA,N)
On entry, the complex M-by-N matrix A.  On exit, the elements on and
below the diagonal contain the N-by-N lower triangular matrix L; the
elements above the diagonal are the rows of V.  See below for
further details.```

LDA

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

T

```          T is COMPLEX*16 array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.```

LDT

```          LDT is INTEGER
The leading dimension of the array T.  LDT >= max(1,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

NAG Ltd.

Further Details:

```  The matrix V stores the elementary reflectors H(i) in the i-th row
above the diagonal. For example, if M=5 and N=3, the matrix V is

V = (  1  v1 v1 v1 v1 )
(     1  v2 v2 v2 )
(     1  v3 v3 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.  The
block reflector H is then given by

H = I - V * T * V**T

where V**T is the transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).```

Definition at line 130 of file zgelqt3.f.

## Author

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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK