ungl2 - {un,or}gl2: generate explicit Q, level 2, step in unglq

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subroutinecungl2(integerm,integern,integerk,complex,dimension(lda,*)a,integerlda,complex,dimension(*)tau,complex,dimension(*)work,integerinfo)CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm). Purpose: CUNGL2 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 (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. subroutinedorgl2(integerm,integern,integerk,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)tau,doubleprecision,dimension(*)work,integerinfo)DORGL2Purpose: DORGL2 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 (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. subroutinesorgl2(integerm,integern,integerk,real,dimension(lda,*)a,integerlda,real,dimension(*)tau,real,dimension(*)work,integerinfo)SORGL2Purpose: SORGL2 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 (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. subroutinezungl2(integerm,integern,integerk,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)tau,complex*16,dimension(*)work,integerinfo)ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm). Purpose: ZUNGL2 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 (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.

ungl2 - {un,or}gl2: generate explicit Q, level 2, step in unglq

Functions subroutine cungl2 (m, n, k, a, lda, tau, work, info) CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm). subroutine dorgl2 (m, n, k, a, lda, tau, work, info) DORGL2 subroutine sorgl2 (m, n, k, a, lda, tau, work, info) SORGL2 subroutine zungl2 (m, n, k, a, lda, tau, work, info) ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).