table of contents
| geqr(3) | LAPACK | geqr(3) |
NAME¶
geqr - geqr: QR factor, flexible
SYNOPSIS¶
Functions¶
subroutine cgeqr (m, n, a, lda, t, tsize, work, lwork,
info)
CGEQR subroutine dgeqr (m, n, a, lda, t, tsize, work, lwork,
info)
DGEQR subroutine sgeqr (m, n, a, lda, t, tsize, work, lwork,
info)
SGEQR subroutine zgeqr (m, n, a, lda, t, tsize, work, lwork,
info)
ZGEQR
Detailed Description¶
Function Documentation¶
subroutine cgeqr (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) t, integer tsize, complex, dimension( * ) work, integer lwork, integer info)¶
CGEQR
Purpose:
CGEQR computes a QR factorization of a complex M-by-N matrix A:
A = Q * ( R ),
( 0 )
where:
Q is a M-by-M orthogonal matrix;
R is an upper-triangular N-by-N matrix;
0 is a (M-N)-by-N zero matrix, if M > N.
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 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 used to store part of the
data structure to represent Q.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is COMPLEX array, dimension (MAX(5,TSIZE))
On exit, if INFO = 0, T(1) returns optimal (or either minimal
or optimal, if query is assumed) TSIZE. See TSIZE for details.
Remaining T contains part of the data structure used to represent Q.
If one wants to apply or construct Q, then one needs to keep T
(in addition to A) and pass it to further subroutines.
TSIZE
TSIZE is INTEGER
If TSIZE >= 5, the dimension of the array T.
If TSIZE = -1 or -2, then a workspace query is assumed. The routine
only calculates the sizes of the T and WORK arrays, returns these
values as the first entries of the T and WORK arrays, and no error
message related to T or WORK is issued by XERBLA.
If TSIZE = -1, the routine calculates optimal size of T for the
optimum performance and returns this value in T(1).
If TSIZE = -2, the routine calculates minimal size of T and
returns this value in T(1).
WORK
(workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
or optimal, if query was assumed) LWORK.
See LWORK for details.
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1 or -2, then a workspace query is assumed. The routine
only calculates the sizes of the T and WORK arrays, returns these
values as the first entries of the T and WORK arrays, and no error
message related to T or WORK is issued by XERBLA.
If LWORK = -1, the routine calculates optimal size of WORK for the
optimal performance and returns this value in WORK(1).
If LWORK = -2, the routine calculates minimal size of WORK and
returns this value in WORK(1).
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 goal of the interface is to give maximum freedom to the developers for
creating any QR factorization algorithm they wish. The triangular
(trapezoidal) R has to be stored in the upper part of A. The lower part of A
and the array T can be used to store any relevant information for applying or
constructing the Q factor. The WORK array can safely be discarded after exit.
Caution: One should not expect the sizes of T and WORK to be the same from one
LAPACK implementation to the other, or even from one execution to the other.
A workspace query (for T and WORK) is needed at each execution. However,
for a given execution, the size of T and WORK are fixed and will not change
from one query to the next.
Further Details particular to this LAPACK implementation:
These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.
In this version,
T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
CLATSQR or CGEQRT
Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, CGEQR will use either
CLATSQR (if the matrix is tall-and-skinny) or CGEQRT to compute
the QR factorization.
subroutine dgeqr (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) t, integer tsize, double precision, dimension( * ) work, integer lwork, integer info)¶
DGEQR
Purpose:
DGEQR computes a QR factorization of a real M-by-N matrix A:
A = Q * ( R ),
( 0 )
where:
Q is a M-by-M orthogonal matrix;
R is an upper-triangular N-by-N matrix;
0 is a (M-N)-by-N zero matrix, if M > N.
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 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 used to store part of the
data structure to represent Q.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE))
On exit, if INFO = 0, T(1) returns optimal (or either minimal
or optimal, if query is assumed) TSIZE. See TSIZE for details.
Remaining T contains part of the data structure used to represent Q.
If one wants to apply or construct Q, then one needs to keep T
(in addition to A) and pass it to further subroutines.
TSIZE
TSIZE is INTEGER
If TSIZE >= 5, the dimension of the array T.
If TSIZE = -1 or -2, then a workspace query is assumed. The routine
only calculates the sizes of the T and WORK arrays, returns these
values as the first entries of the T and WORK arrays, and no error
message related to T or WORK is issued by XERBLA.
If TSIZE = -1, the routine calculates optimal size of T for the
optimum performance and returns this value in T(1).
If TSIZE = -2, the routine calculates minimal size of T and
returns this value in T(1).
WORK
(workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
or optimal, if query was assumed) LWORK.
See LWORK for details.
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1 or -2, then a workspace query is assumed. The routine
only calculates the sizes of the T and WORK arrays, returns these
values as the first entries of the T and WORK arrays, and no error
message related to T or WORK is issued by XERBLA.
If LWORK = -1, the routine calculates optimal size of WORK for the
optimal performance and returns this value in WORK(1).
If LWORK = -2, the routine calculates minimal size of WORK and
returns this value in WORK(1).
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 goal of the interface is to give maximum freedom to the developers for
creating any QR factorization algorithm they wish. The triangular
(trapezoidal) R has to be stored in the upper part of A. The lower part of A
and the array T can be used to store any relevant information for applying or
constructing the Q factor. The WORK array can safely be discarded after exit.
Caution: One should not expect the sizes of T and WORK to be the same from one
LAPACK implementation to the other, or even from one execution to the other.
A workspace query (for T and WORK) is needed at each execution. However,
for a given execution, the size of T and WORK are fixed and will not change
from one query to the next.
Further Details particular to this LAPACK implementation:
These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.
In this version,
T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
DLATSQR or DGEQRT
Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, DGEQR will use either
DLATSQR (if the matrix is tall-and-skinny) or DGEQRT to compute
the QR factorization.
subroutine sgeqr (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) t, integer tsize, real, dimension( * ) work, integer lwork, integer info)¶
SGEQR
Purpose:
SGEQR computes a QR factorization of a real M-by-N matrix A:
A = Q * ( R ),
( 0 )
where:
Q is a M-by-M orthogonal matrix;
R is an upper-triangular N-by-N matrix;
0 is a (M-N)-by-N zero matrix, if M > N.
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 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 used to store part of the
data structure to represent Q.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is REAL array, dimension (MAX(5,TSIZE))
On exit, if INFO = 0, T(1) returns optimal (or either minimal
or optimal, if query is assumed) TSIZE. See TSIZE for details.
Remaining T contains part of the data structure used to represent Q.
If one wants to apply or construct Q, then one needs to keep T
(in addition to A) and pass it to further subroutines.
TSIZE
TSIZE is INTEGER
If TSIZE >= 5, the dimension of the array T.
If TSIZE = -1 or -2, then a workspace query is assumed. The routine
only calculates the sizes of the T and WORK arrays, returns these
values as the first entries of the T and WORK arrays, and no error
message related to T or WORK is issued by XERBLA.
If TSIZE = -1, the routine calculates optimal size of T for the
optimum performance and returns this value in T(1).
If TSIZE = -2, the routine calculates minimal size of T and
returns this value in T(1).
WORK
(workspace) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
or optimal, if query was assumed) LWORK.
See LWORK for details.
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1 or -2, then a workspace query is assumed. The routine
only calculates the sizes of the T and WORK arrays, returns these
values as the first entries of the T and WORK arrays, and no error
message related to T or WORK is issued by XERBLA.
If LWORK = -1, the routine calculates optimal size of WORK for the
optimal performance and returns this value in WORK(1).
If LWORK = -2, the routine calculates minimal size of WORK and
returns this value in WORK(1).
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 goal of the interface is to give maximum freedom to the developers for
creating any QR factorization algorithm they wish. The triangular
(trapezoidal) R has to be stored in the upper part of A. The lower part of A
and the array T can be used to store any relevant information for applying or
constructing the Q factor. The WORK array can safely be discarded after exit.
Caution: One should not expect the sizes of T and WORK to be the same from one
LAPACK implementation to the other, or even from one execution to the other.
A workspace query (for T and WORK) is needed at each execution. However,
for a given execution, the size of T and WORK are fixed and will not change
from one query to the next.
Further Details particular to this LAPACK implementation:
These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.
In this version,
T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
SLATSQR or SGEQRT
Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, SGEQR will use either
SLATSQR (if the matrix is tall-and-skinny) or SGEQRT to compute
the QR factorization.
subroutine zgeqr (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) t, integer tsize, complex*16, dimension( * ) work, integer lwork, integer info)¶
ZGEQR
Purpose:
ZGEQR computes a QR factorization of a complex M-by-N matrix A:
A = Q * ( R ),
( 0 )
where:
Q is a M-by-M orthogonal matrix;
R is an upper-triangular N-by-N matrix;
0 is a (M-N)-by-N zero matrix, if M > N.
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*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 used to store part of the
data structure to represent Q.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is COMPLEX*16 array, dimension (MAX(5,TSIZE))
On exit, if INFO = 0, T(1) returns optimal (or either minimal
or optimal, if query is assumed) TSIZE. See TSIZE for details.
Remaining T contains part of the data structure used to represent Q.
If one wants to apply or construct Q, then one needs to keep T
(in addition to A) and pass it to further subroutines.
TSIZE
TSIZE is INTEGER
If TSIZE >= 5, the dimension of the array T.
If TSIZE = -1 or -2, then a workspace query is assumed. The routine
only calculates the sizes of the T and WORK arrays, returns these
values as the first entries of the T and WORK arrays, and no error
message related to T or WORK is issued by XERBLA.
If TSIZE = -1, the routine calculates optimal size of T for the
optimum performance and returns this value in T(1).
If TSIZE = -2, the routine calculates minimal size of T and
returns this value in T(1).
WORK
(workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
or optimal, if query was assumed) LWORK.
See LWORK for details.
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1 or -2, then a workspace query is assumed. The routine
only calculates the sizes of the T and WORK arrays, returns these
values as the first entries of the T and WORK arrays, and no error
message related to T or WORK is issued by XERBLA.
If LWORK = -1, the routine calculates optimal size of WORK for the
optimal performance and returns this value in WORK(1).
If LWORK = -2, the routine calculates minimal size of WORK and
returns this value in WORK(1).
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 goal of the interface is to give maximum freedom to the developers for
creating any QR factorization algorithm they wish. The triangular
(trapezoidal) R has to be stored in the upper part of A. The lower part of A
and the array T can be used to store any relevant information for applying or
constructing the Q factor. The WORK array can safely be discarded after exit.
Caution: One should not expect the sizes of T and WORK to be the same from one
LAPACK implementation to the other, or even from one execution to the other.
A workspace query (for T and WORK) is needed at each execution. However,
for a given execution, the size of T and WORK are fixed and will not change
from one query to the next.
Further Details particular to this LAPACK implementation:
These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.
In this version,
T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
ZLATSQR or ZGEQRT
Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, ZGEQR will use either
ZLATSQR (if the matrix is tall-and-skinny) or ZGEQRT to compute
the QR factorization.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |