--- name: "ungr2" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/ungr2" --- # ungr2(3) {un,or}gr2: step in ungrq ## NAME ungr2 - {un,or}gr2: step in ungrq ## SYNOPSIS ### Functions subroutine **cungr2** (m, n, k, a, lda, tau, work, info)\ **CUNGR2** generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm). subroutine **dorgr2** (m, n, k, a, lda, tau, work, info)\ **DORGR2** generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm). subroutine **sorgr2** (m, n, k, a, lda, tau, work, info)\ **SORGR2** generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm). subroutine **zungr2** (m, n, k, a, lda, tau, work, info)\ **ZUNGR2** generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm). ## Detailed Description ## Function Documentation ### subroutine cungr2 (integer m, integer n, integer k, complex, dimension( lda, \* ) a, integer lda, complex, dimension( \* ) tau, complex, dimension( \* ) work, integer info) **CUNGR2** generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm). **Purpose:** ``` !> !> CUNGR2 generates an m by n complex matrix Q with orthonormal rows, !> which is defined as the last m rows of a product of k elementary !> reflectors of order n !> !> Q = H(1)**H H(2)**H . . . H(k)**H !> !> as returned by CGERQF. !> ``` **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. N >= M. !> ``` *K* ``` !> K is INTEGER !> The number of elementary reflectors whose product defines the !> matrix Q. M >= K >= 0. !> ``` *A* ``` !> A is COMPLEX array, dimension (LDA,N) !> On entry, the (m-k+i)-th row must contain the vector which !> defines the elementary reflector H(i), for i = 1,2,...,k, as !> returned by CGERQF in the last k rows 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 CGERQF. !> ``` *WORK* ``` !> WORK is COMPLEX array, dimension (M) !> ``` *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 **113** of file **cungr2.f**. ### subroutine dorgr2 (integer m, integer n, integer k, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) tau, double precision, dimension( \* ) work, integer info) **DORGR2** generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm). **Purpose:** ``` !> !> DORGR2 generates an m by n real matrix Q with orthonormal rows, !> which is defined as the last m rows of a product of k elementary !> reflectors of order n !> !> Q = H(1) H(2) . . . H(k) !> !> as returned by DGERQF. !> ``` **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. N >= M. !> ``` *K* ``` !> K is INTEGER !> The number of elementary reflectors whose product defines the !> matrix Q. M >= K >= 0. !> ``` *A* ``` !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the (m-k+i)-th row must contain the vector which !> defines the elementary reflector H(i), for i = 1,2,...,k, as !> returned by DGERQF in the last k rows 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 DGERQF. !> ``` *WORK* ``` !> WORK is DOUBLE PRECISION array, dimension (M) !> ``` *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 **113** of file **dorgr2.f**. ### subroutine sorgr2 (integer m, integer n, integer k, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) tau, real, dimension( \* ) work, integer info) **SORGR2** generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm). **Purpose:** ``` !> !> SORGR2 generates an m by n real matrix Q with orthonormal rows, !> which is defined as the last m rows of a product of k elementary !> reflectors of order n !> !> Q = H(1) H(2) . . . H(k) !> !> as returned by SGERQF. !> ``` **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. N >= M. !> ``` *K* ``` !> K is INTEGER !> The number of elementary reflectors whose product defines the !> matrix Q. M >= K >= 0. !> ``` *A* ``` !> A is REAL array, dimension (LDA,N) !> On entry, the (m-k+i)-th row must contain the vector which !> defines the elementary reflector H(i), for i = 1,2,...,k, as !> returned by SGERQF in the last k rows 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 SGERQF. !> ``` *WORK* ``` !> WORK is REAL array, dimension (M) !> ``` *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 **113** of file **sorgr2.f**. ### subroutine zungr2 (integer m, integer n, integer k, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( \* ) tau, complex\*16, dimension( \* ) work, integer info) **ZUNGR2** generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm). **Purpose:** ``` !> !> ZUNGR2 generates an m by n complex matrix Q with orthonormal rows, !> which is defined as the last m rows of a product of k elementary !> reflectors of order n !> !> Q = H(1)**H H(2)**H . . . H(k)**H !> !> as returned by ZGERQF. !> ``` **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. N >= M. !> ``` *K* ``` !> K is INTEGER !> The number of elementary reflectors whose product defines the !> matrix Q. M >= K >= 0. !> ``` *A* ``` !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the (m-k+i)-th row must contain the vector which !> defines the elementary reflector H(i), for i = 1,2,...,k, as !> returned by ZGERQF in the last k rows 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 ZGERQF. !> ``` *WORK* ``` !> WORK is COMPLEX*16 array, dimension (M) !> ``` *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 **113** of file **zungr2.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.