LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ dgerq2()

 subroutine dgerq2 ( integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info )

DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:
DGERQ2 computes an RQ factorization of a real m by n matrix A:
A = R * Q.
Parameters
 [in] M M is INTEGER The number of rows of the matrix A. M >= 0. [in] N N is INTEGER The number of columns of the matrix A. N >= 0. [in,out] A A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the m by n matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details). [in] LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). [out] TAU TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). [out] WORK WORK is DOUBLE PRECISION array, dimension (M) [out] INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Further Details:
The matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) . . . H(k), where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v**T

where tau is a real scalar, and v is a real vector with
v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
A(m-k+i,1:n-k+i-1), and tau in TAU(i).

Definition at line 122 of file dgerq2.f.

123*
124* -- LAPACK computational routine --
125* -- LAPACK is a software package provided by Univ. of Tennessee, --
126* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127*
128* .. Scalar Arguments ..
129 INTEGER INFO, LDA, M, N
130* ..
131* .. Array Arguments ..
132 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 DOUBLE PRECISION ONE
139 parameter( one = 1.0d+0 )
140* ..
141* .. Local Scalars ..
142 INTEGER I, K
143 DOUBLE PRECISION AII
144* ..
145* .. External Subroutines ..
146 EXTERNAL dlarf, dlarfg, xerbla
147* ..
148* .. Intrinsic Functions ..
149 INTRINSIC max, min
150* ..
151* .. Executable Statements ..
152*
153* Test the input arguments
154*
155 info = 0
156 IF( m.LT.0 ) THEN
157 info = -1
158 ELSE IF( n.LT.0 ) THEN
159 info = -2
160 ELSE IF( lda.LT.max( 1, m ) ) THEN
161 info = -4
162 END IF
163 IF( info.NE.0 ) THEN
164 CALL xerbla( 'DGERQ2', -info )
165 RETURN
166 END IF
167*
168 k = min( m, n )
169*
170 DO 10 i = k, 1, -1
171*
172* Generate elementary reflector H(i) to annihilate
173* A(m-k+i,1:n-k+i-1)
174*
175 CALL dlarfg( n-k+i, a( m-k+i, n-k+i ), a( m-k+i, 1 ), lda,
176 \$ tau( i ) )
177*
178* Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
179*
180 aii = a( m-k+i, n-k+i )
181 a( m-k+i, n-k+i ) = one
182 CALL dlarf( 'Right', m-k+i-1, n-k+i, a( m-k+i, 1 ), lda,
183 \$ tau( i ), a, lda, work )
184 a( m-k+i, n-k+i ) = aii
185 10 CONTINUE
186 RETURN
187*
188* End of DGERQ2
189*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dlarf(side, m, n, v, incv, tau, c, ldc, work)
DLARF applies an elementary reflector to a general rectangular matrix.
Definition dlarf.f:124
subroutine dlarfg(n, alpha, x, incx, tau)
DLARFG generates an elementary reflector (Householder matrix).
Definition dlarfg.f:106
Here is the call graph for this function:
Here is the caller graph for this function: