LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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.```
Date
December 2016

Definition at line 100 of file zqrt11.f.

100 *
101 * -- LAPACK test routine (version 3.7.0) --
102 * -- LAPACK is a software package provided by Univ. of Tennessee, --
103 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
104 * December 2016
105 *
106 * .. Scalar Arguments ..
107  INTEGER k, lda, lwork, m
108 * ..
109 * .. Array Arguments ..
110  COMPLEX*16 a( lda, * ), tau( * ), work( lwork )
111 * ..
112 *
113 * =====================================================================
114 *
115 * .. Parameters ..
116  DOUBLE PRECISION zero, one
117  parameter( zero = 0.0d0, one = 1.0d0 )
118 * ..
119 * .. Local Scalars ..
120  INTEGER info, j
121 * ..
122 * .. External Functions ..
123  DOUBLE PRECISION dlamch, zlange
124  EXTERNAL dlamch, zlange
125 * ..
126 * .. External Subroutines ..
127  EXTERNAL xerbla, zlaset, zunm2r
128 * ..
129 * .. Intrinsic Functions ..
130  INTRINSIC dble, dcmplx
131 * ..
132 * .. Local Arrays ..
133  DOUBLE PRECISION rdummy( 1 )
134 * ..
135 * .. Executable Statements ..
136 *
137  zqrt11 = zero
138 *
139 * Test for sufficient workspace
140 *
141  IF( lwork.LT.m*m+m ) THEN
142  CALL xerbla( 'ZQRT11', 7 )
143  RETURN
144  END IF
145 *
146 * Quick return if possible
147 *
148  IF( m.LE.0 )
149  \$ RETURN
150 *
151  CALL zlaset( 'Full', m, m, dcmplx( zero ), dcmplx( one ), work,
152  \$ m )
153 *
154 * Form Q
155 *
156  CALL zunm2r( 'Left', 'No transpose', m, m, k, a, lda, tau, work,
157  \$ m, work( m*m+1 ), info )
158 *
159 * Form Q'*Q
160 *
161  CALL zunm2r( 'Left', 'Conjugate transpose', m, m, k, a, lda, tau,
162  \$ work, m, work( m*m+1 ), info )
163 *
164  DO 10 j = 1, m
165  work( ( j-1 )*m+j ) = work( ( j-1 )*m+j ) - one
166  10 CONTINUE
167 *
168  zqrt11 = zlange( 'One-norm', m, m, work, m, rdummy ) /
169  \$ ( dble( m )*dlamch( 'Epsilon' ) )
170 *
171  RETURN
172 *
173 * End of ZQRT11
174 *
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:117
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:161
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:108
double precision function zqrt11(M, K, A, LDA, TAU, WORK, LWORK)
ZQRT11
Definition: zqrt11.f:100
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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