 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ slaqp2()

 subroutine slaqp2 ( integer M, integer N, integer OFFSET, real, dimension( lda, * ) A, integer LDA, integer, dimension( * ) JPVT, real, dimension( * ) TAU, real, dimension( * ) VN1, real, dimension( * ) VN2, real, dimension( * ) WORK )

SLAQP2 computes a QR factorization with column pivoting of the matrix block.

Download SLAQP2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
``` SLAQP2 computes a QR factorization with column pivoting of
the block A(OFFSET+1:M,1:N).
The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.```
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] OFFSET ``` OFFSET is INTEGER The number of rows of the matrix A that must be pivoted but no factorized. OFFSET >= 0.``` [in,out] A ``` A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the upper triangle of block A(OFFSET+1:M,1:N) is the triangular factor obtained; the elements in block A(OFFSET+1:M,1:N) below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors. Block A(1:OFFSET,1:N) has been accordingly pivoted, but no factorized.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).``` [in,out] JPVT ``` JPVT is INTEGER array, dimension (N) On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th column of A is a free column. On exit, if JPVT(i) = k, then the i-th column of A*P was the k-th column of A.``` [out] TAU ``` TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors.``` [in,out] VN1 ``` VN1 is REAL array, dimension (N) The vector with the partial column norms.``` [in,out] VN2 ``` VN2 is REAL array, dimension (N) The vector with the exact column norms.``` [out] WORK ` WORK is REAL array, dimension (N)`
Contributors:
G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA
Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia.
References:
LAPACK Working Note 176 [PDF]

Definition at line 147 of file slaqp2.f.

149 *
150 * -- LAPACK auxiliary routine --
151 * -- LAPACK is a software package provided by Univ. of Tennessee, --
152 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153 *
154 * .. Scalar Arguments ..
155  INTEGER LDA, M, N, OFFSET
156 * ..
157 * .. Array Arguments ..
158  INTEGER JPVT( * )
159  REAL A( LDA, * ), TAU( * ), VN1( * ), VN2( * ),
160  \$ WORK( * )
161 * ..
162 *
163 * =====================================================================
164 *
165 * .. Parameters ..
166  REAL ZERO, ONE
167  parameter( zero = 0.0e+0, one = 1.0e+0 )
168 * ..
169 * .. Local Scalars ..
170  INTEGER I, ITEMP, J, MN, OFFPI, PVT
171  REAL AII, TEMP, TEMP2, TOL3Z
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL slarf, slarfg, sswap
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC abs, max, min, sqrt
178 * ..
179 * .. External Functions ..
180  INTEGER ISAMAX
181  REAL SLAMCH, SNRM2
182  EXTERNAL isamax, slamch, snrm2
183 * ..
184 * .. Executable Statements ..
185 *
186  mn = min( m-offset, n )
187  tol3z = sqrt(slamch('Epsilon'))
188 *
189 * Compute factorization.
190 *
191  DO 20 i = 1, mn
192 *
193  offpi = offset + i
194 *
195 * Determine ith pivot column and swap if necessary.
196 *
197  pvt = ( i-1 ) + isamax( n-i+1, vn1( i ), 1 )
198 *
199  IF( pvt.NE.i ) THEN
200  CALL sswap( m, a( 1, pvt ), 1, a( 1, i ), 1 )
201  itemp = jpvt( pvt )
202  jpvt( pvt ) = jpvt( i )
203  jpvt( i ) = itemp
204  vn1( pvt ) = vn1( i )
205  vn2( pvt ) = vn2( i )
206  END IF
207 *
208 * Generate elementary reflector H(i).
209 *
210  IF( offpi.LT.m ) THEN
211  CALL slarfg( m-offpi+1, a( offpi, i ), a( offpi+1, i ), 1,
212  \$ tau( i ) )
213  ELSE
214  CALL slarfg( 1, a( m, i ), a( m, i ), 1, tau( i ) )
215  END IF
216 *
217  IF( i.LT.n ) THEN
218 *
219 * Apply H(i)**T to A(offset+i:m,i+1:n) from the left.
220 *
221  aii = a( offpi, i )
222  a( offpi, i ) = one
223  CALL slarf( 'Left', m-offpi+1, n-i, a( offpi, i ), 1,
224  \$ tau( i ), a( offpi, i+1 ), lda, work( 1 ) )
225  a( offpi, i ) = aii
226  END IF
227 *
228 * Update partial column norms.
229 *
230  DO 10 j = i + 1, n
231  IF( vn1( j ).NE.zero ) THEN
232 *
233 * NOTE: The following 4 lines follow from the analysis in
234 * Lapack Working Note 176.
235 *
236  temp = one - ( abs( a( offpi, j ) ) / vn1( j ) )**2
237  temp = max( temp, zero )
238  temp2 = temp*( vn1( j ) / vn2( j ) )**2
239  IF( temp2 .LE. tol3z ) THEN
240  IF( offpi.LT.m ) THEN
241  vn1( j ) = snrm2( m-offpi, a( offpi+1, j ), 1 )
242  vn2( j ) = vn1( j )
243  ELSE
244  vn1( j ) = zero
245  vn2( j ) = zero
246  END IF
247  ELSE
248  vn1( j ) = vn1( j )*sqrt( temp )
249  END IF
250  END IF
251  10 CONTINUE
252 *
253  20 CONTINUE
254 *
255  RETURN
256 *
257 * End of SLAQP2
258 *
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:71
subroutine slarfg(N, ALPHA, X, INCX, TAU)
SLARFG generates an elementary reflector (Householder matrix).
Definition: slarfg.f:106
subroutine slarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
SLARF applies an elementary reflector to a general rectangular matrix.
Definition: slarf.f:124
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
Definition: sswap.f:82
real(wp) function snrm2(n, x, incx)
SNRM2
Definition: snrm2.f90:89
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
Here is the call graph for this function:
Here is the caller graph for this function: