LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zqpt01()

 double precision function zqpt01 ( integer m, integer n, integer k, complex*16, dimension( lda, * ) a, complex*16, dimension( lda, * ) af, integer lda, complex*16, dimension( * ) tau, integer, dimension( * ) jpvt, complex*16, dimension( lwork ) work, integer lwork )

ZQPT01

Purpose:
``` ZQPT01 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) )```
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 COMPLEX*16 array, dimension (LDA, N) The original matrix A.``` [in] AF ``` AF is COMPLEX*16 array, dimension (LDA,N) The (possibly partial) output of ZGEQPF. 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 COMPLEX*16 array, dimension (K) Details of the Householder transformations as returned by ZGEQPF.``` [in] JPVT ``` JPVT is INTEGER array, dimension (N) Pivot information as returned by ZGEQPF.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The length of the array WORK. LWORK >= M*N+N.```

Definition at line 118 of file zqpt01.f.

120*
121* -- LAPACK test routine --
122* -- LAPACK is a software package provided by Univ. of Tennessee, --
123* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
124*
125* .. Scalar Arguments ..
126 INTEGER K, LDA, LWORK, M, N
127* ..
128* .. Array Arguments ..
129 INTEGER JPVT( * )
130 COMPLEX*16 A( LDA, * ), AF( LDA, * ), TAU( * ),
131 \$ WORK( LWORK )
132* ..
133*
134* =====================================================================
135*
136* .. Parameters ..
137 DOUBLE PRECISION ZERO, ONE
138 parameter( zero = 0.0d0, one = 1.0d0 )
139* ..
140* .. Local Scalars ..
141 INTEGER I, INFO, J
142 DOUBLE PRECISION NORMA
143* ..
144* .. Local Arrays ..
145 DOUBLE PRECISION RWORK( 1 )
146* ..
147* .. External Functions ..
148 DOUBLE PRECISION DLAMCH, ZLANGE
149 EXTERNAL dlamch, zlange
150* ..
151* .. External Subroutines ..
152 EXTERNAL xerbla, zaxpy, zcopy, zunmqr
153* ..
154* .. Intrinsic Functions ..
155 INTRINSIC dble, dcmplx, max, min
156* ..
157* .. Executable Statements ..
158*
159 zqpt01 = zero
160*
161* Test if there is enough workspace
162*
163 IF( lwork.LT.m*n+n ) THEN
164 CALL xerbla( 'ZQPT01', 10 )
165 RETURN
166 END IF
167*
168* Quick return if possible
169*
170 IF( m.LE.0 .OR. n.LE.0 )
171 \$ RETURN
172*
173 norma = zlange( 'One-norm', m, n, a, lda, rwork )
174*
175 DO j = 1, k
176 DO i = 1, min( j, m )
177 work( ( j-1 )*m+i ) = af( i, j )
178 END DO
179 DO i = j + 1, m
180 work( ( j-1 )*m+i ) = zero
181 END DO
182 END DO
183 DO j = k + 1, n
184 CALL zcopy( m, af( 1, j ), 1, work( ( j-1 )*m+1 ), 1 )
185 END DO
186*
187 CALL zunmqr( 'Left', 'No transpose', m, n, k, af, lda, tau, work,
188 \$ m, work( m*n+1 ), lwork-m*n, info )
189*
190 DO j = 1, n
191*
192* Compare i-th column of QR and jpvt(i)-th column of A
193*
194 CALL zaxpy( m, dcmplx( -one ), a( 1, jpvt( j ) ), 1,
195 \$ work( ( j-1 )*m+1 ), 1 )
196 END DO
197*
198 zqpt01 = zlange( 'One-norm', m, n, work, m, rwork ) /
199 \$ ( dble( max( m, n ) )*dlamch( 'Epsilon' ) )
200 IF( norma.NE.zero )
201 \$ zqpt01 = zqpt01 / norma
202*
203 RETURN
204*
205* End of ZQPT01
206*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zaxpy(n, za, zx, incx, zy, incy)
ZAXPY
Definition zaxpy.f:88
subroutine zcopy(n, zx, incx, zy, incy)
ZCOPY
Definition zcopy.f:81
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
double precision function zlange(norm, m, n, a, lda, work)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition zlange.f:115
subroutine zunmqr(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
ZUNMQR
Definition zunmqr.f:167
double precision function zqpt01(m, n, k, a, af, lda, tau, jpvt, work, lwork)
ZQPT01
Definition zqpt01.f:120
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