LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ zrzt02()

double precision function zrzt02 ( integer m,
integer n,
complex*16, dimension( lda, * ) af,
integer lda,
complex*16, dimension( * ) tau,
complex*16, dimension( lwork ) work,
integer lwork )

ZRZT02

Purpose:
!>
!> ZRZT02 returns
!>      || I - Q'*Q || / ( M * eps)
!> where the matrix Q is defined by the Householder transformations
!> generated by ZTZRZF.
!>
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*16 array, dimension (LDA,N)
!>          The output of ZTZRZF.
!>
[in]LDA
!>          LDA is INTEGER
!>          The leading dimension of the array AF.
!>
[in]TAU
!>          TAU is COMPLEX*16 array, dimension (M)
!>          Details of the Householder transformations as returned by
!>          ZTZRZF.
!>
[out]WORK
!>          WORK is COMPLEX*16 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.

Definition at line 89 of file zrzt02.f.

91*
92* -- LAPACK test routine --
93* -- LAPACK is a software package provided by Univ. of Tennessee, --
94* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
95*
96* .. Scalar Arguments ..
97 INTEGER LDA, LWORK, M, N
98* ..
99* .. Array Arguments ..
100 COMPLEX*16 AF( LDA, * ), TAU( * ), WORK( LWORK )
101* ..
102*
103* =====================================================================
104*
105* .. Parameters ..
106 DOUBLE PRECISION ZERO, ONE
107 parameter( zero = 0.0d0, one = 1.0d0 )
108* ..
109* .. Local Scalars ..
110 INTEGER I, INFO
111* ..
112* .. Local Arrays ..
113 DOUBLE PRECISION RWORK( 1 )
114* ..
115* .. External Functions ..
116 DOUBLE PRECISION DLAMCH, ZLANGE
117 EXTERNAL dlamch, zlange
118* ..
119* .. External Subroutines ..
120 EXTERNAL xerbla, zlaset, zunmrz
121* ..
122* .. Intrinsic Functions ..
123 INTRINSIC dble, dcmplx, max
124* ..
125* .. Executable Statements ..
126*
127 zrzt02 = zero
128*
129 IF( lwork.LT.n*n+n ) THEN
130 CALL xerbla( 'ZRZT02', 7 )
131 RETURN
132 END IF
133*
134* Quick return if possible
135*
136 IF( m.LE.0 .OR. n.LE.0 )
137 $ RETURN
138*
139* Q := I
140*
141 CALL zlaset( 'Full', n, n, dcmplx( zero ), dcmplx( one ), work,
142 $ n )
143*
144* Q := P(1) * ... * P(m) * Q
145*
146 CALL zunmrz( 'Left', 'No transpose', n, n, m, n-m, af, lda, tau,
147 $ work, n, work( n*n+1 ), lwork-n*n, info )
148*
149* Q := P(m)' * ... * P(1)' * Q
150*
151 CALL zunmrz( 'Left', 'Conjugate transpose', n, n, m, n-m, af, lda,
152 $ tau, work, n, work( n*n+1 ), lwork-n*n, info )
153*
154* Q := Q - I
155*
156 DO 10 i = 1, n
157 work( ( i-1 )*n+i ) = work( ( i-1 )*n+i ) - one
158 10 CONTINUE
159*
160 zrzt02 = zlange( 'One-norm', n, n, work, n, rwork ) /
161 $ ( dlamch( 'Epsilon' )*dble( max( m, n ) ) )
162 RETURN
163*
164* End of ZRZT02
165*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
zlange
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:113
zlaset
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:104
zunmrz
subroutine zunmrz(side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)
ZUNMRZ
Definition zunmrz.f:186
zrzt02
double precision function zrzt02(m, n, af, lda, tau, work, lwork)
ZRZT02
Definition zrzt02.f:91
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