LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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```
Date
September 2012
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 125 of file dgerq2.f.

125 *
126 * -- LAPACK computational routine (version 3.4.2) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 * September 2012
130 *
131 * .. Scalar Arguments ..
132  INTEGER info, lda, m, n
133 * ..
134 * .. Array Arguments ..
135  DOUBLE PRECISION a( lda, * ), tau( * ), work( * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * .. Parameters ..
141  DOUBLE PRECISION one
142  parameter ( one = 1.0d+0 )
143 * ..
144 * .. Local Scalars ..
145  INTEGER i, k
146  DOUBLE PRECISION aii
147 * ..
148 * .. External Subroutines ..
149  EXTERNAL dlarf, dlarfg, xerbla
150 * ..
151 * .. Intrinsic Functions ..
152  INTRINSIC max, min
153 * ..
154 * .. Executable Statements ..
155 *
156 * Test the input arguments
157 *
158  info = 0
159  IF( m.LT.0 ) THEN
160  info = -1
161  ELSE IF( n.LT.0 ) THEN
162  info = -2
163  ELSE IF( lda.LT.max( 1, m ) ) THEN
164  info = -4
165  END IF
166  IF( info.NE.0 ) THEN
167  CALL xerbla( 'DGERQ2', -info )
168  RETURN
169  END IF
170 *
171  k = min( m, n )
172 *
173  DO 10 i = k, 1, -1
174 *
175 * Generate elementary reflector H(i) to annihilate
176 * A(m-k+i,1:n-k+i-1)
177 *
178  CALL dlarfg( n-k+i, a( m-k+i, n-k+i ), a( m-k+i, 1 ), lda,
179  \$ tau( i ) )
180 *
181 * Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
182 *
183  aii = a( m-k+i, n-k+i )
184  a( m-k+i, n-k+i ) = one
185  CALL dlarf( 'Right', m-k+i-1, n-k+i, a( m-k+i, 1 ), lda,
186  \$ tau( i ), a, lda, work )
187  a( m-k+i, n-k+i ) = aii
188  10 CONTINUE
189  RETURN
190 *
191 * End of DGERQ2
192 *
subroutine dlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
DLARF applies an elementary reflector to a general rectangular matrix.
Definition: dlarf.f:126
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dlarfg(N, ALPHA, X, INCX, TAU)
DLARFG generates an elementary reflector (Householder matrix).
Definition: dlarfg.f:108

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