--- name: "ung2l" 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/ung2l" --- # ung2l(3) {un,or}g2l: step in ungql ## NAME ung2l - {un,or}g2l: step in ungql ## SYNOPSIS ### Functions subroutine **cung2l** (m, n, k, a, lda, tau, work, info)\ **CUNG2L** generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm). subroutine **dorg2l** (m, n, k, a, lda, tau, work, info)\ **DORG2L** generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm). subroutine **sorg2l** (m, n, k, a, lda, tau, work, info)\ **SORG2L** generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm). subroutine **zung2l** (m, n, k, a, lda, tau, work, info)\ **ZUNG2L** generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm). ## Detailed Description ## Function Documentation ### subroutine cung2l (integer m, integer n, integer k, complex, dimension( lda, \* ) a, integer lda, complex, dimension( \* ) tau, complex, dimension( \* ) work, integer info) **CUNG2L** generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm). **Purpose:** ``` !> !> CUNG2L generates an m by n complex matrix Q with orthonormal columns, !> which is defined as the last n columns of a product of k elementary !> reflectors of order m !> !> Q = H(k) . . . H(2) H(1) !> !> as returned by CGEQLF. !> ``` **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 (n-k+i)-th column must contain the vector which !> defines the elementary reflector H(i), for i = 1,2,...,k, as !> returned by CGEQLF in the last 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 CGEQLF. !> ``` *WORK* ``` !> WORK is COMPLEX array, dimension (N) !> ``` *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 **cung2l.f**. ### subroutine dorg2l (integer m, integer n, integer k, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) tau, double precision, dimension( \* ) work, integer info) **DORG2L** generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm). **Purpose:** ``` !> !> DORG2L generates an m by n real matrix Q with orthonormal columns, !> which is defined as the last n columns of a product of k elementary !> reflectors of order m !> !> Q = H(k) . . . H(2) H(1) !> !> as returned by DGEQLF. !> ``` **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 (n-k+i)-th column must contain the vector which !> defines the elementary reflector H(i), for i = 1,2,...,k, as !> returned by DGEQLF in the last 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 DGEQLF. !> ``` *WORK* ``` !> WORK is DOUBLE PRECISION array, dimension (N) !> ``` *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 **dorg2l.f**. ### subroutine sorg2l (integer m, integer n, integer k, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) tau, real, dimension( \* ) work, integer info) **SORG2L** generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm). **Purpose:** ``` !> !> SORG2L generates an m by n real matrix Q with orthonormal columns, !> which is defined as the last n columns of a product of k elementary !> reflectors of order m !> !> Q = H(k) . . . H(2) H(1) !> !> as returned by SGEQLF. !> ``` **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 (n-k+i)-th column must contain the vector which !> defines the elementary reflector H(i), for i = 1,2,...,k, as !> returned by SGEQLF in the last 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 SGEQLF. !> ``` *WORK* ``` !> WORK is REAL array, dimension (N) !> ``` *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 **sorg2l.f**. ### subroutine zung2l (integer m, integer n, integer k, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( \* ) tau, complex\*16, dimension( \* ) work, integer info) **ZUNG2L** generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm). **Purpose:** ``` !> !> ZUNG2L generates an m by n complex matrix Q with orthonormal columns, !> which is defined as the last n columns of a product of k elementary !> reflectors of order m !> !> Q = H(k) . . . H(2) H(1) !> !> as returned by ZGEQLF. !> ``` **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 (n-k+i)-th column must contain the vector which !> defines the elementary reflector H(i), for i = 1,2,...,k, as !> returned by ZGEQLF in the last 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 ZGEQLF. !> ``` *WORK* ``` !> WORK is COMPLEX*16 array, dimension (N) !> ``` *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 **zung2l.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.