 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ sqrt11()

 real function sqrt11 ( integer M, integer K, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, real, dimension( lwork ) WORK, integer LWORK )

SQRT11

Purpose:
``` SQRT11 computes the test ratio

|| Q'*Q - I || / (eps * m)

where the orthogonal matrix Q is represented as a product of
elementary transformations.  Each transformation has the form

H(k) = I - tau(k) v(k) v(k)'

where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
[ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
in A(k+1:m,k).```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix A.``` [in] K ``` K is INTEGER The number of columns of A whose subdiagonal entries contain information about orthogonal transformations.``` [in] A ``` A is REAL array, dimension (LDA,K) The (possibly partial) output of a QR reduction routine.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A.``` [in] TAU ``` TAU is REAL array, dimension (K) The scaling factors tau for the elementary transformations as computed by the QR factorization routine.``` [out] WORK ` WORK is REAL array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The length of the array WORK. LWORK >= M*M + M.```

Definition at line 97 of file sqrt11.f.

98 *
99 * -- LAPACK test routine --
100 * -- LAPACK is a software package provided by Univ. of Tennessee, --
101 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
102 *
103 * .. Scalar Arguments ..
104  INTEGER K, LDA, LWORK, M
105 * ..
106 * .. Array Arguments ..
107  REAL A( LDA, * ), TAU( * ), WORK( LWORK )
108 * ..
109 *
110 * =====================================================================
111 *
112 * .. Parameters ..
113  REAL ZERO, ONE
114  parameter( zero = 0.0e0, one = 1.0e0 )
115 * ..
116 * .. Local Scalars ..
117  INTEGER INFO, J
118 * ..
119 * .. External Functions ..
120  REAL SLAMCH, SLANGE
121  EXTERNAL slamch, slange
122 * ..
123 * .. External Subroutines ..
124  EXTERNAL slaset, sorm2r, xerbla
125 * ..
126 * .. Intrinsic Functions ..
127  INTRINSIC real
128 * ..
129 * .. Local Arrays ..
130  REAL RDUMMY( 1 )
131 * ..
132 * .. Executable Statements ..
133 *
134  sqrt11 = zero
135 *
136 * Test for sufficient workspace
137 *
138  IF( lwork.LT.m*m+m ) THEN
139  CALL xerbla( 'SQRT11', 7 )
140  RETURN
141  END IF
142 *
143 * Quick return if possible
144 *
145  IF( m.LE.0 )
146  \$ RETURN
147 *
148  CALL slaset( 'Full', m, m, zero, one, work, m )
149 *
150 * Form Q
151 *
152  CALL sorm2r( 'Left', 'No transpose', m, m, k, a, lda, tau, work,
153  \$ m, work( m*m+1 ), info )
154 *
155 * Form Q'*Q
156 *
157  CALL sorm2r( 'Left', 'Transpose', m, m, k, a, lda, tau, work, m,
158  \$ work( m*m+1 ), info )
159 *
160  DO 10 j = 1, m
161  work( ( j-1 )*m+j ) = work( ( j-1 )*m+j ) - one
162  10 CONTINUE
163 *
164  sqrt11 = slange( 'One-norm', m, m, work, m, rdummy ) /
165  \$ ( real( m )*slamch( 'Epsilon' ) )
166 *
167  RETURN
168 *
169 * End of SQRT11
170 *
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
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 sorm2r(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
SORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sge...
Definition: sorm2r.f:159
real function sqrt11(M, K, A, LDA, TAU, WORK, LWORK)
SQRT11
Definition: sqrt11.f:98
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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