LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ 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 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
double precision function zrzt02(M, N, AF, LDA, TAU, WORK, LWORK)
ZRZT02
Definition: zrzt02.f:91
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 zunmrz(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMRZ
Definition: zunmrz.f:187
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