LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ sqpt01()

 real function sqpt01 ( integer m, integer n, integer k, real, dimension( lda, * ) a, real, dimension( lda, * ) af, integer lda, real, dimension( * ) tau, integer, dimension( * ) jpvt, real, dimension( lwork ) work, integer lwork )

SQPT01

Purpose:
``` SQPT01 tests the QR-factorization with pivoting of a matrix A.  The
array AF contains the (possibly partial) QR-factorization of A, where
the upper triangle of AF(1:k,1:k) is a partial triangular factor,
the entries below the diagonal in the first k columns are the
Householder vectors, and the rest of AF contains a partially updated
matrix.

This function returns ||A*P - Q*R|| / ( ||norm(A)||*eps*max(M,N) )
where || . || is matrix one norm.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrices A and AF.``` [in] N ``` N is INTEGER The number of columns of the matrices A and AF.``` [in] K ``` K is INTEGER The number of columns of AF that have been reduced to upper triangular form.``` [in] A ``` A is REAL array, dimension (LDA, N) The original matrix A.``` [in] AF ``` AF is REAL array, dimension (LDA,N) The (possibly partial) output of SGEQPF. The upper triangle of AF(1:k,1:k) is a partial triangular factor, the entries below the diagonal in the first k columns are the Householder vectors, and the rest of AF contains a partially updated matrix.``` [in] LDA ``` LDA is INTEGER The leading dimension of the arrays A and AF.``` [in] TAU ``` TAU is REAL array, dimension (K) Details of the Householder transformations as returned by SGEQPF.``` [in] JPVT ``` JPVT is INTEGER array, dimension (N) Pivot information as returned by SGEQPF.``` [out] WORK ` WORK is REAL array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The length of the array WORK. LWORK >= M*N+N.```

Definition at line 119 of file sqpt01.f.

121*
122* -- LAPACK test routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 INTEGER K, LDA, LWORK, M, N
128* ..
129* .. Array Arguments ..
130 INTEGER JPVT( * )
131 REAL A( LDA, * ), AF( LDA, * ), TAU( * ),
132 \$ WORK( LWORK )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 REAL ZERO, ONE
139 parameter( zero = 0.0e0, one = 1.0e0 )
140* ..
141* .. Local Scalars ..
142 INTEGER I, INFO, J
143 REAL NORMA
144* ..
145* .. Local Arrays ..
146 REAL RWORK( 1 )
147* ..
148* .. External Functions ..
149 REAL SLAMCH, SLANGE
150 EXTERNAL slamch, slange
151* ..
152* .. External Subroutines ..
153 EXTERNAL saxpy, scopy, sormqr, xerbla
154* ..
155* .. Intrinsic Functions ..
156 INTRINSIC max, min, real
157* ..
158* .. Executable Statements ..
159*
160 sqpt01 = zero
161*
162* Test if there is enough workspace
163*
164 IF( lwork.LT.m*n+n ) THEN
165 CALL xerbla( 'SQPT01', 10 )
166 RETURN
167 END IF
168*
169* Quick return if possible
170*
171 IF( m.LE.0 .OR. n.LE.0 )
172 \$ RETURN
173*
174 norma = slange( 'One-norm', m, n, a, lda, rwork )
175*
176 DO j = 1, k
177 DO i = 1, min( j, m )
178 work( ( j-1 )*m+i ) = af( i, j )
179 END DO
180 DO i = j + 1, m
181 work( ( j-1 )*m+i ) = zero
182 END DO
183 END DO
184 DO j = k + 1, n
185 CALL scopy( m, af( 1, j ), 1, work( ( j-1 )*m+1 ), 1 )
186 END DO
187*
188 CALL sormqr( 'Left', 'No transpose', m, n, k, af, lda, tau, work,
189 \$ m, work( m*n+1 ), lwork-m*n, info )
190*
191 DO j = 1, n
192*
193* Compare i-th column of QR and jpvt(i)-th column of A
194*
195 CALL saxpy( m, -one, a( 1, jpvt( j ) ), 1, work( ( j-1 )*m+1 ),
196 \$ 1 )
197 END DO
198*
199 sqpt01 = slange( 'One-norm', m, n, work, m, rwork ) /
200 \$ ( real( max( m, n ) )*slamch( 'Epsilon' ) )
201 IF( norma.NE.zero )
202 \$ sqpt01 = sqpt01 / norma
203*
204 RETURN
205*
206* End of SQPT01
207*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine saxpy(n, sa, sx, incx, sy, incy)
SAXPY
Definition saxpy.f:89
subroutine scopy(n, sx, incx, sy, incy)
SCOPY
Definition scopy.f:82
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function slange(norm, m, n, a, lda, work)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition slange.f:114
subroutine sormqr(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
SORMQR
Definition sormqr.f:168
real function sqpt01(m, n, k, a, af, lda, tau, jpvt, work, lwork)
SQPT01
Definition sqpt01.f:121
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