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| ungqr(3) | LAPACK | ungqr(3) |
NAME¶
ungqr - {un,or}gqr: generate explicit Q from geqrf
SYNOPSIS¶
Functions¶
subroutine cungqr (m, n, k, a, lda, tau, work, lwork, info)
CUNGQR subroutine dorgqr (m, n, k, a, lda, tau, work, lwork,
info)
DORGQR subroutine sorgqr (m, n, k, a, lda, tau, work, lwork,
info)
SORGQR subroutine zungqr (m, n, k, a, lda, tau, work, lwork,
info)
ZUNGQR
Detailed Description¶
Function Documentation¶
subroutine cungqr (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)¶
CUNGQR
Purpose:
CUNGQR generates an M-by-N complex matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by CGEQRF.
Parameters
M
M is INTEGER
The number of rows of the matrix Q. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A
A is COMPLEX array, dimension (LDA,N)
On entry, the i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by CGEQRF in the first k columns of its array
argument A.
On exit, the M-by-N matrix Q.
LDA
LDA is INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU
TAU is COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGEQRF.
WORK
WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dorgqr (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)¶
DORGQR
Purpose:
DORGQR generates an M-by-N real matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF.
Parameters
M
M is INTEGER
The number of rows of the matrix Q. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by DGEQRF in the first k columns of its array
argument A.
On exit, the M-by-N matrix Q.
LDA
LDA is INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU
TAU is DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine sorgqr (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)¶
SORGQR
Purpose:
SORGQR generates an M-by-N real matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by SGEQRF.
Parameters
M
M is INTEGER
The number of rows of the matrix Q. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A
A is REAL array, dimension (LDA,N)
On entry, the i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by SGEQRF in the first k columns of its array
argument A.
On exit, the M-by-N matrix Q.
LDA
LDA is INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU
TAU is REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGEQRF.
WORK
WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zungqr (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)¶
ZUNGQR
Purpose:
ZUNGQR generates an M-by-N complex matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by ZGEQRF.
Parameters
M
M is INTEGER
The number of rows of the matrix Q. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A
A is COMPLEX*16 array, dimension (LDA,N)
On entry, the i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by ZGEQRF in the first k columns of its array
argument A.
On exit, the M-by-N matrix Q.
LDA
LDA is INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU
TAU is COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF.
WORK
WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |