LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ crzt02()

real function crzt02 ( integer  M,
integer  N,
complex, dimension( lda, * )  AF,
integer  LDA,
complex, dimension( * )  TAU,
complex, dimension( lwork )  WORK,
integer  LWORK 
)

CRZT02

Purpose:
 CRZT02 returns
      || I - Q'*Q || / ( M * eps)
 where the matrix Q is defined by the Householder transformations
 generated by CTZRZF.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix AF.
[in]N
          N is INTEGER
          The number of columns of the matrix AF.
[in]AF
          AF is COMPLEX array, dimension (LDA,N)
          The output of CTZRZF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array AF.
[in]TAU
          TAU is COMPLEX array, dimension (M)
          Details of the Householder transformations as returned by
          CTZRZF.
[out]WORK
          WORK is COMPLEX array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          Length of WORK array. LWORK >= N*N+N.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 93 of file crzt02.f.

93 *
94 * -- LAPACK test routine (version 3.7.0) --
95 * -- LAPACK is a software package provided by Univ. of Tennessee, --
96 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
97 * December 2016
98 *
99 * .. Scalar Arguments ..
100  INTEGER lda, lwork, m, n
101 * ..
102 * .. Array Arguments ..
103  COMPLEX af( lda, * ), tau( * ), work( lwork )
104 * ..
105 *
106 * =====================================================================
107 *
108 * .. Parameters ..
109  REAL zero, one
110  parameter( zero = 0.0e0, one = 1.0e0 )
111 * ..
112 * .. Local Scalars ..
113  INTEGER i, info
114 * ..
115 * .. Local Arrays ..
116  REAL rwork( 1 )
117 * ..
118 * .. External Functions ..
119  REAL clange, slamch
120  EXTERNAL clange, slamch
121 * ..
122 * .. External Subroutines ..
123  EXTERNAL claset, cunmrz, xerbla
124 * ..
125 * .. Intrinsic Functions ..
126  INTRINSIC cmplx, max, real
127 * ..
128 * .. Executable Statements ..
129 *
130  crzt02 = zero
131 *
132  IF( lwork.LT.n*n+n ) THEN
133  CALL xerbla( 'CRZT02', 7 )
134  RETURN
135  END IF
136 *
137 * Quick return if possible
138 *
139  IF( m.LE.0 .OR. n.LE.0 )
140  $ RETURN
141 *
142 * Q := I
143 *
144  CALL claset( 'Full', n, n, cmplx( zero ), cmplx( one ), work, n )
145 *
146 * Q := P(1) * ... * P(m) * Q
147 *
148  CALL cunmrz( 'Left', 'No transpose', n, n, m, n-m, af, lda, tau,
149  $ work, n, work( n*n+1 ), lwork-n*n, info )
150 *
151 * Q := P(m)' * ... * P(1)' * Q
152 *
153  CALL cunmrz( 'Left', 'Conjugate transpose', n, n, m, n-m, af, lda,
154  $ tau, work, n, work( n*n+1 ), lwork-n*n, info )
155 *
156 * Q := Q - I
157 *
158  DO 10 i = 1, n
159  work( ( i-1 )*n+i ) = work( ( i-1 )*n+i ) - one
160  10 CONTINUE
161 *
162  crzt02 = clange( 'One-norm', n, n, work, n, rwork ) /
163  $ ( slamch( 'Epsilon' )*REAL( MAX( M, N ) ) )
164  RETURN
165 *
166 * End of CRZT02
167 *
subroutine cunmrz(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
CUNMRZ
Definition: cunmrz.f:189
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: claset.f:108
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:117
real function crzt02(M, N, AF, LDA, TAU, WORK, LWORK)
CRZT02
Definition: crzt02.f:93
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
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