unglq - {un,or}glq: generate explicit Q from gelqf

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Thu Aug 7 2025 17:26:25 unglq(3)

subroutinecunglq(integerm,integern,integerk,complex,dimension(lda,*)a,integerlda,complex,dimension(*)tau,complex,dimension(*)work,integerlwork,integerinfo)CUNGLQPurpose: CUNGLQ generates an M-by-N complex matrix Q with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N Q = H(k)**H . . . H(2)**H H(1)**H as returned by CGELQF. ParametersM 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 i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGELQF in the first 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 CGELQF. 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,M). For optimum performance LWORK >= M*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. subroutinedorglq(integerm,integern,integerk,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)tau,doubleprecision,dimension(*)work,integerlwork,integerinfo)DORGLQPurpose: DORGLQ generates an M-by-N real matrix Q with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N Q = H(k) . . . H(2) H(1) as returned by DGELQF. ParametersM 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 i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGELQF in the first 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 DGELQF. 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,M). For optimum performance LWORK >= M*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. subroutinesorglq(integerm,integern,integerk,real,dimension(lda,*)a,integerlda,real,dimension(*)tau,real,dimension(*)work,integerlwork,integerinfo)SORGLQPurpose: SORGLQ generates an M-by-N real matrix Q with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N Q = H(k) . . . H(2) H(1) as returned by SGELQF. ParametersM 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 i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGELQF in the first 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 SGELQF. 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,M). For optimum performance LWORK >= M*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. subroutinezunglq(integerm,integern,integerk,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)tau,complex*16,dimension(*)work,integerlwork,integerinfo)ZUNGLQPurpose: ZUNGLQ generates an M-by-N complex matrix Q with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N Q = H(k)**H . . . H(2)**H H(1)**H as returned by ZGELQF. ParametersM 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 i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGELQF in the first 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 ZGELQF. 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,M). For optimum performance LWORK >= M*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.

unglq - {un,or}glq: generate explicit Q from gelqf

Functions subroutine cunglq (m, n, k, a, lda, tau, work, lwork, info) CUNGLQ subroutine dorglq (m, n, k, a, lda, tau, work, lwork, info) DORGLQ subroutine sorglq (m, n, k, a, lda, tau, work, lwork, info) SORGLQ subroutine zunglq (m, n, k, a, lda, tau, work, lwork, info) ZUNGLQ