LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zqrt11()

 double precision function zqrt11 ( integer M, integer K, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) TAU, complex*16, dimension( lwork ) WORK, integer LWORK )

ZQRT11

Purpose:
``` ZQRT11 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 COMPLEX*16 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 COMPLEX*16 array, dimension (K) The scaling factors tau for the elementary transformations as computed by the QR factorization routine.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The length of the array WORK. LWORK >= M*M + M.```

Definition at line 97 of file zqrt11.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 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( LWORK )
108* ..
109*
110* =====================================================================
111*
112* .. Parameters ..
113 DOUBLE PRECISION ZERO, ONE
114 parameter( zero = 0.0d0, one = 1.0d0 )
115* ..
116* .. Local Scalars ..
117 INTEGER INFO, J
118* ..
119* .. External Functions ..
120 DOUBLE PRECISION DLAMCH, ZLANGE
121 EXTERNAL dlamch, zlange
122* ..
123* .. External Subroutines ..
124 EXTERNAL xerbla, zlaset, zunm2r
125* ..
126* .. Intrinsic Functions ..
127 INTRINSIC dble, dcmplx
128* ..
129* .. Local Arrays ..
130 DOUBLE PRECISION RDUMMY( 1 )
131* ..
132* .. Executable Statements ..
133*
134 zqrt11 = zero
135*
136* Test for sufficient workspace
137*
138 IF( lwork.LT.m*m+m ) THEN
139 CALL xerbla( 'ZQRT11', 7 )
140 RETURN
141 END IF
142*
143* Quick return if possible
144*
145 IF( m.LE.0 )
146 \$ RETURN
147*
148 CALL zlaset( 'Full', m, m, dcmplx( zero ), dcmplx( one ), work,
149 \$ m )
150*
151* Form Q
152*
153 CALL zunm2r( 'Left', 'No transpose', m, m, k, a, lda, tau, work,
154 \$ m, work( m*m+1 ), info )
155*
156* Form Q'*Q
157*
158 CALL zunm2r( 'Left', 'Conjugate transpose', m, m, k, a, lda, tau,
159 \$ work, m, work( m*m+1 ), info )
160*
161 DO 10 j = 1, m
162 work( ( j-1 )*m+j ) = work( ( j-1 )*m+j ) - one
163 10 CONTINUE
164*
165 zqrt11 = zlange( 'One-norm', m, m, work, m, rdummy ) /
166 \$ ( dble( m )*dlamch( 'Epsilon' ) )
167*
168 RETURN
169*
170* End of ZQRT11
171*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
double precision function zqrt11(M, K, A, LDA, TAU, WORK, LWORK)
ZQRT11
Definition: zqrt11.f:98
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 zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
subroutine zunm2r(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf...
Definition: zunm2r.f:159
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