 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ 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*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.```

Definition at line 118 of file sqpt01.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 REAL A( LDA, * ), AF( LDA, * ), TAU( * ),
131 \$ WORK( LWORK )
132* ..
133*
134* =====================================================================
135*
136* .. Parameters ..
137 REAL ZERO, ONE
138 parameter( zero = 0.0e0, one = 1.0e0 )
139* ..
140* .. Local Scalars ..
141 INTEGER I, INFO, J
142 REAL NORMA
143* ..
144* .. Local Arrays ..
145 REAL RWORK( 1 )
146* ..
147* .. External Functions ..
148 REAL SLAMCH, SLANGE
149 EXTERNAL slamch, slange
150* ..
151* .. External Subroutines ..
152 EXTERNAL saxpy, scopy, sormqr, xerbla
153* ..
154* .. Intrinsic Functions ..
155 INTRINSIC max, min, real
156* ..
157* .. Executable Statements ..
158*
159 sqpt01 = zero
160*
161* Test if there is enough workspace
162*
163 IF( lwork.LT.m*n+n ) THEN
164 CALL xerbla( 'SQPT01', 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 = slange( 'One-norm', m, n, a, lda, rwork )
174*
175 DO 30 j = 1, k
176 DO 10 i = 1, min( j, m )
177 work( ( j-1 )*m+i ) = af( i, j )
178 10 CONTINUE
179 DO 20 i = j + 1, m
180 work( ( j-1 )*m+i ) = zero
181 20 CONTINUE
182 30 CONTINUE
183 DO 40 j = k + 1, n
184 CALL scopy( m, af( 1, j ), 1, work( ( j-1 )*m+1 ), 1 )
185 40 CONTINUE
186*
187 CALL sormqr( 'Left', 'No transpose', m, n, k, af, lda, tau, work,
188 \$ m, work( m*n+1 ), lwork-m*n, info )
189*
190 DO 50 j = 1, n
191*
192* Compare i-th column of QR and jpvt(i)-th column of A
193*
194 CALL saxpy( m, -one, a( 1, jpvt( j ) ), 1, work( ( j-1 )*m+1 ),
195 \$ 1 )
196 50 CONTINUE
197*
198 sqpt01 = slange( 'One-norm', m, n, work, m, rwork ) /
199 \$ ( real( max( m, n ) )*slamch( 'Epsilon' ) )
200 IF( norma.NE.zero )
201 \$ sqpt01 = sqpt01 / norma
202*
203 RETURN
204*
205* End of SQPT01
206*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
real function sqpt01(M, N, K, A, AF, LDA, TAU, JPVT, WORK, LWORK)
SQPT01
Definition: sqpt01.f:120
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: