LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ dorgl2()

 subroutine dorgl2 ( integer M, integer N, integer K, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( * ) WORK, integer INFO )

DORGL2

Purpose:
``` 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.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix Q. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix Q. N >= M.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.``` [in,out] 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.``` [in] LDA ``` LDA is INTEGER The first dimension of the array A. LDA >= max(1,M).``` [in] 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.``` [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 has an illegal value```

Definition at line 112 of file dorgl2.f.

113 *
114 * -- LAPACK computational routine --
115 * -- LAPACK is a software package provided by Univ. of Tennessee, --
116 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117 *
118 * .. Scalar Arguments ..
119  INTEGER INFO, K, LDA, M, N
120 * ..
121 * .. Array Arguments ..
122  DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  DOUBLE PRECISION ONE, ZERO
129  parameter( one = 1.0d+0, zero = 0.0d+0 )
130 * ..
131 * .. Local Scalars ..
132  INTEGER I, J, L
133 * ..
134 * .. External Subroutines ..
135  EXTERNAL dlarf, dscal, xerbla
136 * ..
137 * .. Intrinsic Functions ..
138  INTRINSIC max
139 * ..
140 * .. Executable Statements ..
141 *
142 * Test the input arguments
143 *
144  info = 0
145  IF( m.LT.0 ) THEN
146  info = -1
147  ELSE IF( n.LT.m ) THEN
148  info = -2
149  ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
150  info = -3
151  ELSE IF( lda.LT.max( 1, m ) ) THEN
152  info = -5
153  END IF
154  IF( info.NE.0 ) THEN
155  CALL xerbla( 'DORGL2', -info )
156  RETURN
157  END IF
158 *
159 * Quick return if possible
160 *
161  IF( m.LE.0 )
162  \$ RETURN
163 *
164  IF( k.LT.m ) THEN
165 *
166 * Initialise rows k+1:m to rows of the unit matrix
167 *
168  DO 20 j = 1, n
169  DO 10 l = k + 1, m
170  a( l, j ) = zero
171  10 CONTINUE
172  IF( j.GT.k .AND. j.LE.m )
173  \$ a( j, j ) = one
174  20 CONTINUE
175  END IF
176 *
177  DO 40 i = k, 1, -1
178 *
179 * Apply H(i) to A(i:m,i:n) from the right
180 *
181  IF( i.LT.n ) THEN
182  IF( i.LT.m ) THEN
183  a( i, i ) = one
184  CALL dlarf( 'Right', m-i, n-i+1, a( i, i ), lda,
185  \$ tau( i ), a( i+1, i ), lda, work )
186  END IF
187  CALL dscal( n-i, -tau( i ), a( i, i+1 ), lda )
188  END IF
189  a( i, i ) = one - tau( i )
190 *
191 * Set A(i,1:i-1) to zero
192 *
193  DO 30 l = 1, i - 1
194  a( i, l ) = zero
195  30 CONTINUE
196  40 CONTINUE
197  RETURN
198 *
199 * End of DORGL2
200 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
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
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