# geqrt - Man Page

geqrt: QR factor, with T

## Synopsis

### Functions

subroutine cgeqrt (m, n, nb, a, lda, t, ldt, work, info)
CGEQRT
subroutine dgeqrt (m, n, nb, a, lda, t, ldt, work, info)
DGEQRT
subroutine sgeqrt (m, n, nb, a, lda, t, ldt, work, info)
SGEQRT
subroutine zgeqrt (m, n, nb, a, lda, t, ldt, work, info)
ZGEQRT

## Function 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

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.

### subroutine dgeqrt (integer m, integer n, integer nb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer info)

DGEQRT

Purpose:

``` DGEQRT computes a blocked QR factorization of a real 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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

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 dgeqrt.f.

### subroutine sgeqrt (integer m, integer n, integer nb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer info)

SGEQRT

Purpose:

``` SGEQRT computes a blocked QR factorization of a real 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 REAL 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 REAL 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 REAL 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

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 sgeqrt.f.

### subroutine zgeqrt (integer m, integer n, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer info)

ZGEQRT

Purpose:

``` ZGEQRT 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*16 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*16 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*16 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

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 zgeqrt.f.

## Author

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## Info

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