 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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
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