 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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*M)```
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.```
Date
November 2011

Definition at line 122 of file sqpt01.f.

122 *
123 * -- LAPACK test routine (version 3.4.0) --
124 * -- LAPACK is a software package provided by Univ. of Tennessee, --
125 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126 * November 2011
127 *
128 * .. Scalar Arguments ..
129  INTEGER k, lda, lwork, m, n
130 * ..
131 * .. Array Arguments ..
132  INTEGER jpvt( * )
133  REAL a( lda, * ), af( lda, * ), tau( * ),
134  \$ work( lwork )
135 * ..
136 *
137 * =====================================================================
138 *
139 * .. Parameters ..
140  REAL zero, one
141  parameter ( zero = 0.0e0, one = 1.0e0 )
142 * ..
143 * .. Local Scalars ..
144  INTEGER i, info, j
145  REAL norma
146 * ..
147 * .. Local Arrays ..
148  REAL rwork( 1 )
149 * ..
150 * .. External Functions ..
151  REAL slamch, slange
152  EXTERNAL slamch, slange
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL saxpy, scopy, sormqr, xerbla
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC max, min, real
159 * ..
160 * .. Executable Statements ..
161 *
162  sqpt01 = zero
163 *
164 * Test if there is enough workspace
165 *
166  IF( lwork.LT.m*n+n ) THEN
167  CALL xerbla( 'SQPT01', 10 )
168  RETURN
169  END IF
170 *
171 * Quick return if possible
172 *
173  IF( m.LE.0 .OR. n.LE.0 )
174  \$ RETURN
175 *
176  norma = slange( 'One-norm', m, n, a, lda, rwork )
177 *
178  DO 30 j = 1, k
179  DO 10 i = 1, min( j, m )
180  work( ( j-1 )*m+i ) = af( i, j )
181  10 CONTINUE
182  DO 20 i = j + 1, m
183  work( ( j-1 )*m+i ) = zero
184  20 CONTINUE
185  30 CONTINUE
186  DO 40 j = k + 1, n
187  CALL scopy( m, af( 1, j ), 1, work( ( j-1 )*m+1 ), 1 )
188  40 CONTINUE
189 *
190  CALL sormqr( 'Left', 'No transpose', m, n, k, af, lda, tau, work,
191  \$ m, work( m*n+1 ), lwork-m*n, info )
192 *
193  DO 50 j = 1, n
194 *
195 * Compare i-th column of QR and jpvt(i)-th column of A
196 *
197  CALL saxpy( m, -one, a( 1, jpvt( j ) ), 1, work( ( j-1 )*m+1 ),
198  \$ 1 )
199  50 CONTINUE
200 *
201  sqpt01 = slange( 'One-norm', m, n, work, m, rwork ) /
202  \$ ( REAL( MAX( M, N ) )*slamch( 'Epsilon' ) )
203  IF( norma.NE.zero )
204  \$ sqpt01 = sqpt01 / norma
205 *
206  RETURN
207 *
208 * End of SQPT01
209 *
subroutine sormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMQR
Definition: sormqr.f:170
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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:116
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:54
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
real function sqpt01(M, N, K, A, AF, LDA, TAU, JPVT, WORK, LWORK)
SQPT01
Definition: sqpt01.f:122
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:53

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