RZ factorization: trapezoidal reduction and its reflectors. More...

Functions/Subroutines
pure subroutine, public	la_slarz (side, m, n, l, v, incv, tau, c, ldc, work)
	SLARZ: applies a real elementary reflector H to a real M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**T where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix. H is a product of k elementary reflectors as returned by STZRZF.

pure subroutine, public	la_dlarz (side, m, n, l, v, incv, tau, c, ldc, work)
	DLARZ: applies a real elementary reflector H to a real M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**T where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix. H is a product of k elementary reflectors as returned by DTZRZF.

pure subroutine, public	la_qlarz (side, m, n, l, v, incv, tau, c, ldc, work)
	QLARZ: applies a real elementary reflector H to a real M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**T where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix. H is a product of k elementary reflectors as returned by QTZRZF.

pure subroutine, public	la_slarzb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)
	SLARZB: applies a real block reflector H or its transpose H**T to a real distributed M-by-N C from the left or the right. Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

pure subroutine, public	la_dlarzb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)
	DLARZB: applies a real block reflector H or its transpose H**T to a real distributed M-by-N C from the left or the right. Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

pure subroutine, public	la_qlarzb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)
	QLARZB: applies a real block reflector H or its transpose H**T to a real distributed M-by-N C from the left or the right. Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

pure subroutine, public	la_slarzt (direct, storev, n, k, v, ldv, tau, t, ldt)
	SLARZT: forms the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * VT If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - VT * T * V Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

pure subroutine, public	la_dlarzt (direct, storev, n, k, v, ldv, tau, t, ldt)
	DLARZT: forms the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * VT If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - VT * T * V Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

pure subroutine, public	la_qlarzt (direct, storev, n, k, v, ldv, tau, t, ldt)
	QLARZT: forms the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * VT If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - VT * T * V Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

pure subroutine, public	la_sormr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
	SORMR3: 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 = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'C', where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) . . . H(k) as returned by STZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_dormr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
	DORMR3: 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 = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'C', where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) . . . H(k) as returned by DTZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_qormr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
	QORMR3: 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 = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q**T if SIDE = 'R' and TRANS = 'C', where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) . . . H(k) as returned by QTZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_sormrz (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)
	SORMRZ: 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(1) H(2) . . . H(k) as returned by STZRZF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_dormrz (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)
	DORMRZ: 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(1) H(2) . . . H(k) as returned by DTZRZF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_qormrz (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)
	QORMRZ: 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(1) H(2) . . . H(k) as returned by QTZRZF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_slatrz (m, n, l, a, lda, tau, work)
	SLATRZ: factors the M-by-(M+L) real upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal matrix and, R and A1 are M-by-M upper triangular matrices.

pure subroutine, public	la_dlatrz (m, n, l, a, lda, tau, work)
	DLATRZ: factors the M-by-(M+L) real upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal matrix and, R and A1 are M-by-M upper triangular matrices.

pure subroutine, public	la_qlatrz (m, n, l, a, lda, tau, work)
	QLATRZ: factors the M-by-(M+L) real upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal matrix and, R and A1 are M-by-M upper triangular matrices.

pure subroutine, public	la_stzrzf (m, n, a, lda, tau, work, lwork, info)
	STZRZF: reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N orthogonal matrix and R is an M-by-M upper triangular matrix.

pure subroutine, public	la_dtzrzf (m, n, a, lda, tau, work, lwork, info)
	DTZRZF: reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N orthogonal matrix and R is an M-by-M upper triangular matrix.

pure subroutine, public	la_qtzrzf (m, n, a, lda, tau, work, lwork, info)
	QTZRZF: reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N orthogonal matrix and R is an M-by-M upper triangular matrix.

pure subroutine, public	la_clarz (side, m, n, l, v, incv, tau, c, ldc, work)
	CLARZ: applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * vH where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix. To apply HH (the conjugate transpose of H), supply conjg(tau) instead tau. H is a product of k elementary reflectors as returned by CTZRZF.

pure subroutine, public	la_zlarz (side, m, n, l, v, incv, tau, c, ldc, work)
	ZLARZ: applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * vH where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix. To apply HH (the conjugate transpose of H), supply conjg(tau) instead tau. H is a product of k elementary reflectors as returned by ZTZRZF.

pure subroutine, public	la_wlarz (side, m, n, l, v, incv, tau, c, ldc, work)
	WLARZ: applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * vH where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix. To apply HH (the conjugate transpose of H), supply conjg(tau) instead tau. H is a product of k elementary reflectors as returned by WTZRZF.

pure subroutine, public	la_clarzb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)
	CLARZB: applies a complex block reflector H or its transpose H**H to a complex distributed M-by-N C from the left or the right. Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

pure subroutine, public	la_zlarzb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)
	ZLARZB: applies a complex block reflector H or its transpose H**H to a complex distributed M-by-N C from the left or the right. Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

pure subroutine, public	la_wlarzb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)
	WLARZB: applies a complex block reflector H or its transpose H**H to a complex distributed M-by-N C from the left or the right. Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

pure subroutine, public	la_clarzt (direct, storev, n, k, v, ldv, tau, t, ldt)
	CLARZT: forms the triangular factor T of a complex block reflector H of order > n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * VH If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - VH * T * V Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

pure subroutine, public	la_zlarzt (direct, storev, n, k, v, ldv, tau, t, ldt)
	ZLARZT: forms the triangular factor T of a complex block reflector H of order > n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * VH If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - VH * T * V Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

pure subroutine, public	la_wlarzt (direct, storev, n, k, v, ldv, tau, t, ldt)
	WLARZT: forms the triangular factor T of a complex block reflector H of order > n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * VH If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - VH * T * V Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

pure subroutine, public	la_clatrz (m, n, l, a, lda, tau, work)
	CLATRZ: factors the M-by-(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means of unitary transformations, where Z is an (M+L)-by-(M+L) unitary matrix and, R and A1 are M-by-M upper triangular matrices.

pure subroutine, public	la_zlatrz (m, n, l, a, lda, tau, work)
	ZLATRZ: factors the M-by-(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means of unitary transformations, where Z is an (M+L)-by-(M+L) unitary matrix and, R and A1 are M-by-M upper triangular matrices.

pure subroutine, public	la_wlatrz (m, n, l, a, lda, tau, work)
	WLATRZ: factors the M-by-(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means of unitary transformations, where Z is an (M+L)-by-(M+L) unitary matrix and, R and A1 are M-by-M upper triangular matrices.

pure subroutine, public	la_ctzrzf (m, n, a, lda, tau, work, lwork, info)
	CTZRZF: reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix.

pure subroutine, public	la_ztzrzf (m, n, a, lda, tau, work, lwork, info)
	ZTZRZF: reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix.

pure subroutine, public	la_wtzrzf (m, n, a, lda, tau, work, lwork, info)
	WTZRZF: reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix.

pure subroutine, public	la_cunmr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
	CUNMR3: 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(1) H(2) . . . H(k) as returned by CTZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_zunmr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
	ZUNMR3: 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(1) H(2) . . . H(k) as returned by ZTZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_wunmr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
	WUNMR3: 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(1) H(2) . . . H(k) as returned by WTZRZF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

pure subroutine, public	la_cunmrz (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)
	CUNMRZ: 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(1) H(2) . . . H(k) as returned by CTZRZF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_zunmrz (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)
	ZUNMRZ: 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(1) H(2) . . . H(k) as returned by ZTZRZF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

pure subroutine, public	la_wunmrz (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)
	WUNMRZ: 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(1) H(2) . . . H(k) as returned by WTZRZF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

Detailed Description

RZ factorization: trapezoidal reduction and its reflectors.

Function/Subroutine Documentation

◆ la_clarz()

pure subroutine, public la_lapack_orthogonal_factors_rz::la_clarz	(	character, intent(in)	side,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	l,
		complex(sp), dimension(*), intent(in)	v,
		integer(ilp), intent(in)	incv,
		complex(sp), intent(in)	tau,
		complex(sp), dimension(ldc,*), intent(inout)	c,
		integer(ilp), intent(in)	ldc,
		complex(sp), dimension(*), intent(out)	work )

CLARZ: applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**H where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix. To apply H**H (the conjugate transpose of H), supply conjg(tau) instead tau. H is a product of k elementary reflectors as returned by CTZRZF.