geqrt3 - Man Page

geqrt3: QR factor, with T, recursive panel

Synopsis

Functions

recursive subroutine cgeqrt3 (m, n, a, lda, t, ldt, info)
CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
recursive subroutine dgeqrt3 (m, n, a, lda, t, ldt, info)
DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
recursive subroutine sgeqrt3 (m, n, a, lda, t, ldt, info)
SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
recursive subroutine zgeqrt3 (m, n, a, lda, t, ldt, info)
ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Function Documentation

recursive subroutine cgeqrt3 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)

CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

``` CGEQRT3 recursively computes a QR 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
above the diagonal contain the N-by-N upper triangular matrix R; the
elements below the diagonal are the columns 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 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.  The
block reflector H is then given by

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

where V**H is the conjugate transpose of V.

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

Definition at line 131 of file cgeqrt3.f.

recursive subroutine dgeqrt3 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)

DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

``` DGEQRT3 recursively computes a QR 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
above the diagonal contain the N-by-N upper triangular matrix R; the
elements below the diagonal are the columns 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 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.  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 131 of file dgeqrt3.f.

recursive subroutine sgeqrt3 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)

SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

``` SGEQRT3 recursively computes a QR 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
above the diagonal contain the N-by-N upper triangular matrix R; the
elements below the diagonal are the columns 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 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.  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 131 of file sgeqrt3.f.

recursive subroutine zgeqrt3 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

``` ZGEQRT3 recursively computes a QR 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 above the diagonal contain the N-by-N upper triangular matrix R;
the elements below the diagonal are the columns 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 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.  The
block reflector H is then given by

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

where V**H is the conjugate transpose of V.

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

Definition at line 131 of file zgeqrt3.f.

Author

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