LQ and QL factorizations: blocked, short-wide and triangular-pentagonal variants. More...

Functions/Subroutines
pure subroutine, public	la_sorg2l (m, n, k, a, lda, tau, work, info)
	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.

pure subroutine, public	la_dorg2l (m, n, k, a, lda, tau, work, info)
	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.

pure subroutine, public	la_qorg2l (m, n, k, a, lda, tau, work, info)
	QORG2L: 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 QGEQLF.

pure subroutine, public	la_sorgl2 (m, n, k, a, lda, tau, work, info)
	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.

pure subroutine, public	la_dorgl2 (m, n, k, a, lda, tau, work, info)
	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.

pure subroutine, public	la_qorgl2 (m, n, k, a, lda, tau, work, info)
	QORGL2: 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 QGELQF.

pure subroutine, public	la_sorglq (m, n, k, a, lda, tau, work, lwork, info)
	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.

pure subroutine, public	la_dorglq (m, n, k, a, lda, tau, work, lwork, info)
	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.

pure subroutine, public	la_qorglq (m, n, k, a, lda, tau, work, lwork, info)
	QORGLQ: 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 QGELQF.

pure subroutine, public	la_sorgql (m, n, k, a, lda, tau, work, lwork, info)
	SORGQL: 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.

pure subroutine, public	la_dorgql (m, n, k, a, lda, tau, work, lwork, info)
	DORGQL: 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.

pure subroutine, public	la_qorgql (m, n, k, a, lda, tau, work, lwork, info)
	QORGQL: 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 QGEQLF.

pure subroutine, public	la_sorm2l (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
	SORM2L: overwrites the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q*T C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'T', where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by SGEQLF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_dorm2l (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
	DORM2L: overwrites the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q*T C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'T', where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by DGEQLF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_qorm2l (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
	QORM2L: overwrites the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q*T C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'T', where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by QGEQLF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_sorml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
	SORML2: overwrites the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q*T C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'T', where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by SGELQF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_dorml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
	DORML2: overwrites the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q*T C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'T', where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by DGELQF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_qorml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
	QORML2: overwrites the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q*T C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'T', where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by QGELQF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_sormlq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
	SORMLQ: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*T C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by SGELQF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_dormlq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
	DORMLQ: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*T C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by DGELQF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_qormlq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
	QORMLQ: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*T C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by QGELQF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_sormql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
	SORMQL: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*T C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by SGEQLF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_dormql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
	DORMQL: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*T C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by DGEQLF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_qormql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
	QORMQL: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*T C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by QGEQLF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_sgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
	DGEMLQT overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'T': QT C C QT where Q is a real orthogonal matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**T generated using the compact WY representation as returned by SGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_dgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
	DGEMLQT: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'T': QT C C QT where Q is a real orthogonal matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**T generated using the compact WY representation as returned by DGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_qgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
	QGEMLQT: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'T': QT C C QT where Q is a real orthogonal matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**T generated using the compact WY representation as returned by QGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_stplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
	STPLQT2: computes a LQ a factorization of a real "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

pure subroutine, public	la_dtplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
	DTPLQT2: computes a LQ a factorization of a real "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

pure subroutine, public	la_qtplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
	QTPLQT2: computes a LQ a factorization of a real "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

pure subroutine, public	la_stpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
	STPMLQT: applies a real orthogonal matrix Q obtained from a "triangular-pentagonal" real block reflector H to a general real matrix C, which consists of two blocks A and B.

pure subroutine, public	la_dtpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
	DTPMQRT applies a real orthogonal matrix Q obtained from a "triangular-pentagonal" real block reflector H to a general real matrix C, which consists of two blocks A and B.

pure subroutine, public	la_qtpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
	QTPMQRT applies a real orthogonal matrix Q obtained from a "triangular-pentagonal" real block reflector H to a general real matrix C, which consists of two blocks A and B.

pure subroutine, public	la_sgelq2 (m, n, a, lda, tau, work, info)
	SGELQ2: computes an LQ factorization of a real m-by-n matrix A: A = ( L 0 ) * Q where: Q is a n-by-n orthogonal matrix; L is a lower-triangular m-by-m matrix; 0 is a m-by-(n-m) zero matrix, if m < n.

pure subroutine, public	la_dgelq2 (m, n, a, lda, tau, work, info)
	DGELQ2: computes an LQ factorization of a real m-by-n matrix A: A = ( L 0 ) * Q where: Q is a n-by-n orthogonal matrix; L is a lower-triangular m-by-m matrix; 0 is a m-by-(n-m) zero matrix, if m < n.

pure subroutine, public	la_qgelq2 (m, n, a, lda, tau, work, info)
	QGELQ2: computes an LQ factorization of a real m-by-n matrix A: A = ( L 0 ) * Q where: Q is a n-by-n orthogonal matrix; L is a lower-triangular m-by-m matrix; 0 is a m-by-(n-m) zero matrix, if m < n.

pure subroutine, public	la_sgelqf (m, n, a, lda, tau, work, lwork, info)
	SGELQF: computes an LQ factorization of a real M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.

pure subroutine, public	la_dgelqf (m, n, a, lda, tau, work, lwork, info)
	DGELQF: computes an LQ factorization of a real M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.

pure subroutine, public	la_qgelqf (m, n, a, lda, tau, work, lwork, info)
	QGELQF: computes an LQ factorization of a real M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.

pure recursive subroutine, public	la_sgelqt3 (m, n, a, lda, t, ldt, info)
	SGELQT3: recursively computes a LQ factorization of a real M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

pure recursive subroutine, public	la_dgelqt3 (m, n, a, lda, t, ldt, info)
	DGELQT3: recursively computes a LQ factorization of a real M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

pure recursive subroutine, public	la_qgelqt3 (m, n, a, lda, t, ldt, info)
	QGELQT3: recursively computes a LQ factorization of a real M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

pure subroutine, public	la_sgeql2 (m, n, a, lda, tau, work, info)
	SGEQL2: computes a QL factorization of a real m by n matrix A: A = Q * L.

pure subroutine, public	la_dgeql2 (m, n, a, lda, tau, work, info)
	DGEQL2: computes a QL factorization of a real m by n matrix A: A = Q * L.

pure subroutine, public	la_qgeql2 (m, n, a, lda, tau, work, info)
	QGEQL2: computes a QL factorization of a real m by n matrix A: A = Q * L.

pure subroutine, public	la_sgeqlf (m, n, a, lda, tau, work, lwork, info)
	SGEQLF: computes a QL factorization of a real M-by-N matrix A: A = Q * L.

pure subroutine, public	la_dgeqlf (m, n, a, lda, tau, work, lwork, info)
	DGEQLF: computes a QL factorization of a real M-by-N matrix A: A = Q * L.

pure subroutine, public	la_qgeqlf (m, n, a, lda, tau, work, lwork, info)
	QGEQLF: computes a QL factorization of a real M-by-N matrix A: A = Q * L.

pure subroutine, public	la_slamswlq (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
	SLAMSWLQ: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*T C C * Q**T where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (SLASWLQ)

pure subroutine, public	la_dlamswlq (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
	DLAMSWLQ: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*T C C * Q**T where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (DLASWLQ)

pure subroutine, public	la_qlamswlq (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
	QLAMSWLQ: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*T C C * Q**T where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (QLASWLQ)

pure subroutine, public	la_stplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
	STPLQT: computes a blocked LQ factorization of a real "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

pure subroutine, public	la_dtplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
	DTPLQT: computes a blocked LQ factorization of a real "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

pure subroutine, public	la_qtplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
	QTPLQT: computes a blocked LQ factorization of a real "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

pure subroutine, public	la_sgelqt (m, n, mb, a, lda, t, ldt, work, info)
	DGELQT computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of Q.

pure subroutine, public	la_dgelqt (m, n, mb, a, lda, t, ldt, work, info)
	DGELQT: computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of Q.

pure subroutine, public	la_qgelqt (m, n, mb, a, lda, t, ldt, work, info)
	QGELQT: computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of Q.

pure subroutine, public	la_sgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
	SGEMLQ: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*T C C * Q**T where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (SGELQ)

pure subroutine, public	la_dgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
	DGEMLQ: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*T C C * Q**T where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (DGELQ)

pure subroutine, public	la_qgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
	QGEMLQ: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*T C C * Q**T where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (QGELQ)

pure subroutine, public	la_slaswlq (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
	SLASWLQ: computes a blocked Tall-Skinny LQ factorization of a real M-by-N matrix A for M <= N: A = ( L 0 ) * Q, where: Q is a n-by-N orthogonal matrix, stored on exit in an implicit form in the elements above the diagonal of the array A and in the elements of the array T; L is a lower-triangular M-by-M matrix stored on exit in the elements on and below the diagonal of the array A. 0 is a M-by-(N-M) zero matrix, if M < N, and is not stored.

pure subroutine, public	la_dlaswlq (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
	DLASWLQ: computes a blocked Tall-Skinny LQ factorization of a real M-by-N matrix A for M <= N: A = ( L 0 ) * Q, where: Q is a n-by-N orthogonal matrix, stored on exit in an implicit form in the elements above the diagonal of the array A and in the elements of the array T; L is a lower-triangular M-by-M matrix stored on exit in the elements on and below the diagonal of the array A. 0 is a M-by-(N-M) zero matrix, if M < N, and is not stored.

pure subroutine, public	la_qlaswlq (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
	QLASWLQ: computes a blocked Tall-Skinny LQ factorization of a real M-by-N matrix A for M <= N: A = ( L 0 ) * Q, where: Q is a n-by-N orthogonal matrix, stored on exit in an implicit form in the elements above the diagonal of the array A and in the elements of the array T; L is a lower-triangular M-by-M matrix stored on exit in the elements on and below the diagonal of the array A. 0 is a M-by-(N-M) zero matrix, if M < N, and is not stored.

pure subroutine, public	la_sgelq (m, n, a, lda, t, tsize, work, lwork, info)
	SGELQ: computes an LQ factorization of a real M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.

pure subroutine, public	la_dgelq (m, n, a, lda, t, tsize, work, lwork, info)
	DGELQ: computes an LQ factorization of a real M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.

pure subroutine, public	la_qgelq (m, n, a, lda, t, tsize, work, lwork, info)
	QGELQ: computes an LQ factorization of a real M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.

pure subroutine, public	la_ctplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
	CTPLQT2: computes a LQ a factorization of a complex "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

pure subroutine, public	la_ztplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
	ZTPLQT2: computes a LQ a factorization of a complex "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

pure subroutine, public	la_wtplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
	WTPLQT2: computes a LQ a factorization of a complex "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

pure subroutine, public	la_cung2l (m, n, k, a, lda, tau, work, info)
	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.

pure subroutine, public	la_zung2l (m, n, k, a, lda, tau, work, info)
	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.

pure subroutine, public	la_wung2l (m, n, k, a, lda, tau, work, info)
	WUNG2L: 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 WGEQLF.

pure subroutine, public	la_cungl2 (m, n, k, a, lda, tau, work, info)
	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.

pure subroutine, public	la_zungl2 (m, n, k, a, lda, tau, work, info)
	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.

pure subroutine, public	la_wungl2 (m, n, k, a, lda, tau, work, info)
	WUNGL2: 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 WGELQF.

pure subroutine, public	la_cunglq (m, n, k, a, lda, tau, work, lwork, info)
	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.

pure subroutine, public	la_zunglq (m, n, k, a, lda, tau, work, lwork, info)
	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.

pure subroutine, public	la_wunglq (m, n, k, a, lda, tau, work, lwork, info)
	WUNGLQ: 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 WGELQF.

pure subroutine, public	la_cungql (m, n, k, a, lda, tau, work, lwork, info)
	CUNGQL: 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.

pure subroutine, public	la_zungql (m, n, k, a, lda, tau, work, lwork, info)
	ZUNGQL: 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.

pure subroutine, public	la_wungql (m, n, k, a, lda, tau, work, lwork, info)
	WUNGQL: 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 WGEQLF.

pure subroutine, public	la_cunm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)

pure subroutine, public	la_zunm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)

pure subroutine, public	la_wunm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)

pure subroutine, public	la_cunm2l (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
	CUNM2L: overwrites the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q*H C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**H if SIDE = 'R' and TRANS = 'C', where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by CGEQLF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_zunm2l (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
	ZUNM2L: overwrites the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q*H C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**H if SIDE = 'R' and TRANS = 'C', where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by ZGEQLF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_wunm2l (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
	WUNM2L: overwrites the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q*H C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**H if SIDE = 'R' and TRANS = 'C', where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by WGEQLF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_cunml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
	CUNML2: overwrites the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q*H C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * QH if SIDE = 'R' and TRANS = 'C', where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k)H . . . H(2)H H(1)H as returned by CGELQF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_zunml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
	ZUNML2: overwrites the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q*H C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * QH if SIDE = 'R' and TRANS = 'C', where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k)H . . . H(2)H H(1)H as returned by ZGELQF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_wunml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
	WUNML2: overwrites the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q*H C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * QH if SIDE = 'R' and TRANS = 'C', where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k)H . . . H(2)H H(1)H as returned by WGELQF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_cunmlq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
	CUNMLQ: overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q*H C C * QH where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k)H . . . H(2)H H(1)H as returned by CGELQF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_zunmlq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
	ZUNMLQ: overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q*H C C * QH where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k)H . . . H(2)H H(1)H as returned by ZGELQF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_wunmlq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
	WUNMLQ: overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q*H C C * QH where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k)H . . . H(2)H H(1)H as returned by WGELQF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_cunmql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
	CUNMQL: overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q*H C C * Q**H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by CGEQLF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_zunmql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
	ZUNMQL: overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q*H C C * Q**H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by ZGEQLF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_wunmql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
	WUNMQL: overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q*H C C * Q**H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by WGEQLF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_cgelq2 (m, n, a, lda, tau, work, info)
	CGELQ2: computes an LQ factorization of a complex m-by-n matrix A: A = ( L 0 ) * Q where: Q is a n-by-n orthogonal matrix; L is a lower-triangular m-by-m matrix; 0 is a m-by-(n-m) zero matrix, if m < n.

pure subroutine, public	la_zgelq2 (m, n, a, lda, tau, work, info)
	ZGELQ2: computes an LQ factorization of a complex m-by-n matrix A: A = ( L 0 ) * Q where: Q is a n-by-n orthogonal matrix; L is a lower-triangular m-by-m matrix; 0 is a m-by-(n-m) zero matrix, if m < n.

pure subroutine, public	la_wgelq2 (m, n, a, lda, tau, work, info)
	WGELQ2: computes an LQ factorization of a complex m-by-n matrix A: A = ( L 0 ) * Q where: Q is a n-by-n orthogonal matrix; L is a lower-triangular m-by-m matrix; 0 is a m-by-(n-m) zero matrix, if m < n.

pure subroutine, public	la_cgelqf (m, n, a, lda, tau, work, lwork, info)
	CGELQF: computes an LQ factorization of a complex M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.

pure subroutine, public	la_zgelqf (m, n, a, lda, tau, work, lwork, info)
	ZGELQF: computes an LQ factorization of a complex M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.

pure subroutine, public	la_wgelqf (m, n, a, lda, tau, work, lwork, info)
	WGELQF: computes an LQ factorization of a complex M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.

pure recursive subroutine, public	la_cgelqt3 (m, n, a, lda, t, ldt, info)
	CGELQT3: recursively computes a LQ factorization of a complex M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

pure recursive subroutine, public	la_zgelqt3 (m, n, a, lda, t, ldt, info)
	ZGELQT3: recursively computes a LQ factorization of a complex M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

pure recursive subroutine, public	la_wgelqt3 (m, n, a, lda, t, ldt, info)
	WGELQT3: recursively computes a LQ factorization of a complex M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

pure subroutine, public	la_cgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
	CGEMLQT: overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'C': QH C C QH where Q is a complex unitary matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**H generated using the compact WY representation as returned by CGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_zgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
	ZGEMLQT: overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'C': QH C C QH where Q is a complex unitary matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**H generated using the compact WY representation as returned by ZGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_wgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
	WGEMLQT: overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'C': QH C C QH where Q is a complex unitary matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**H generated using the compact WY representation as returned by WGELQT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_cgeql2 (m, n, a, lda, tau, work, info)
	CGEQL2: computes a QL factorization of a complex m by n matrix A: A = Q * L.

pure subroutine, public	la_zgeql2 (m, n, a, lda, tau, work, info)
	ZGEQL2: computes a QL factorization of a complex m by n matrix A: A = Q * L.

pure subroutine, public	la_wgeql2 (m, n, a, lda, tau, work, info)
	WGEQL2: computes a QL factorization of a complex m by n matrix A: A = Q * L.

pure subroutine, public	la_cgeqlf (m, n, a, lda, tau, work, lwork, info)
	CGEQLF: computes a QL factorization of a complex M-by-N matrix A: A = Q * L.

pure subroutine, public	la_zgeqlf (m, n, a, lda, tau, work, lwork, info)
	ZGEQLF: computes a QL factorization of a complex M-by-N matrix A: A = Q * L.

pure subroutine, public	la_wgeqlf (m, n, a, lda, tau, work, lwork, info)
	WGEQLF: computes a QL factorization of a complex M-by-N matrix A: A = Q * L.

pure subroutine, public	la_ctplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
	CTPLQT: computes a blocked LQ factorization of a complex "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

pure subroutine, public	la_ztplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
	ZTPLQT: computes a blocked LQ factorization of a complex "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

pure subroutine, public	la_wtplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
	WTPLQT: computes a blocked LQ factorization of a complex "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.

pure subroutine, public	la_ctpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
	CTPMLQT: applies a complex unitary matrix Q obtained from a "triangular-pentagonal" complex block reflector H to a general complex matrix C, which consists of two blocks A and B.

pure subroutine, public	la_ztpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
	ZTPMLQT: applies a complex unitary matrix Q obtained from a "triangular-pentagonal" complex block reflector H to a general complex matrix C, which consists of two blocks A and B.

pure subroutine, public	la_wtpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
	WTPMLQT: applies a complex unitary matrix Q obtained from a "triangular-pentagonal" complex block reflector H to a general complex matrix C, which consists of two blocks A and B.

pure subroutine, public	la_cgelqt (m, n, mb, a, lda, t, ldt, work, info)
	CGELQT: computes a blocked LQ factorization of a complex M-by-N matrix A using the compact WY representation of Q.

pure subroutine, public	la_zgelqt (m, n, mb, a, lda, t, ldt, work, info)
	ZGELQT: computes a blocked LQ factorization of a complex M-by-N matrix A using the compact WY representation of Q.

pure subroutine, public	la_wgelqt (m, n, mb, a, lda, t, ldt, work, info)
	WGELQT: computes a blocked LQ factorization of a complex M-by-N matrix A using the compact WY representation of Q.

pure subroutine, public	la_clamswlq (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
	CLAMSWLQ: overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q*H C C * Q**H where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (CLASWLQ)

pure subroutine, public	la_zlamswlq (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
	ZLAMSWLQ: overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q*H C C * Q**H where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (ZLASWLQ)

pure subroutine, public	la_wlamswlq (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
	WLAMSWLQ: overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q*H C C * Q**H where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (WLASWLQ)

pure subroutine, public	la_claswlq (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
	CLASWLQ: computes a blocked Tall-Skinny LQ factorization of a complex M-by-N matrix A for M <= N: A = ( L 0 ) * Q, where: Q is a n-by-N orthogonal matrix, stored on exit in an implicit form in the elements above the diagonal of the array A and in the elements of the array T; L is a lower-triangular M-by-M matrix stored on exit in the elements on and below the diagonal of the array A. 0 is a M-by-(N-M) zero matrix, if M < N, and is not stored.

pure subroutine, public	la_zlaswlq (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
	ZLASWLQ: computes a blocked Tall-Skinny LQ factorization of a complexx M-by-N matrix A for M <= N: A = ( L 0 ) * Q, where: Q is a n-by-N orthogonal matrix, stored on exit in an implicit form in the elements above the diagonal of the array A and in the elements of the array T; L is a lower-triangular M-by-M matrix stored on exit in the elements on and below the diagonal of the array A. 0 is a M-by-(N-M) zero matrix, if M < N, and is not stored.

pure subroutine, public	la_wlaswlq (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
	WLASWLQ: computes a blocked Tall-Skinny LQ factorization of a complexx M-by-N matrix A for M <= N: A = ( L 0 ) * Q, where: Q is a n-by-N orthogonal matrix, stored on exit in an implicit form in the elements above the diagonal of the array A and in the elements of the array T; L is a lower-triangular M-by-M matrix stored on exit in the elements on and below the diagonal of the array A. 0 is a M-by-(N-M) zero matrix, if M < N, and is not stored.

pure subroutine, public	la_cgelq (m, n, a, lda, t, tsize, work, lwork, info)
	CGELQ: computes an LQ factorization of a complex M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.

pure subroutine, public	la_zgelq (m, n, a, lda, t, tsize, work, lwork, info)
	ZGELQ: computes an LQ factorization of a complex M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.

pure subroutine, public	la_wgelq (m, n, a, lda, t, tsize, work, lwork, info)
	WGELQ: computes an LQ factorization of a complex M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.

pure subroutine, public	la_cgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
	CGEMLQ: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q*H C C * Q**H where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (CGELQ)

pure subroutine, public	la_zgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
	ZGEMLQ: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q*H C C * Q**H where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (ZGELQ)

pure subroutine, public	la_wgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
	WGEMLQ: overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q*H C C * Q**H where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (WGELQ)

Detailed Description

LQ and QL factorizations: blocked, short-wide and triangular-pentagonal variants.

Function/Subroutine Documentation

◆ la_cgelq()

pure subroutine, public la_lapack_orthogonal_factors_ql::la_cgelq	(	integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		complex(sp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(*), intent(out)	t,
		integer(ilp), intent(in)	tsize,
		complex(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info )

CGELQ: computes an LQ factorization of a complex M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N.