ungqr - Man Page
{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.
Definition at line 127 of file cungqr.f.
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.
Definition at line 127 of file dorgqr.f.
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.
Definition at line 127 of file sorgqr.f.
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.
Definition at line 127 of file zungqr.f.
Author
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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK