LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ zrzt01()

double precision function zrzt01 ( integer  M,
integer  N,
complex*16, dimension( lda, * )  A,
complex*16, dimension( lda, * )  AF,
integer  LDA,
complex*16, dimension( * )  TAU,
complex*16, dimension( lwork )  WORK,
integer  LWORK 
)

ZRZT01

Purpose:
 ZRZT01 returns
      || A - R*Q || / ( M * eps * ||A|| )
 for an upper trapezoidal A that was factored with ZTZRZF.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrices A and AF.
[in]N
          N is INTEGER
          The number of columns of the matrices A and AF.
[in]A
          A is COMPLEX*16 array, dimension (LDA,N)
          The original upper trapezoidal M by N matrix A.
[in]AF
          AF is COMPLEX*16 array, dimension (LDA,N)
          The output of ZTZRZF for input matrix A.
          The lower triangle is not referenced.
[in]LDA
          LDA is INTEGER
          The leading dimension of the arrays A and 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
          The length of the array WORK.  LWORK >= m*n + m.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 96 of file zrzt01.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 LDA, LWORK, M, N
105* ..
106* .. Array Arguments ..
107 COMPLEX*16 A( LDA, * ), AF( LDA, * ), TAU( * ),
108 $ WORK( LWORK )
109* ..
110*
111* =====================================================================
112*
113* .. Parameters ..
114 DOUBLE PRECISION ZERO, ONE
115 parameter( zero = 0.0d0, one = 1.0d0 )
116* ..
117* .. Local Scalars ..
118 INTEGER I, INFO, J
119 DOUBLE PRECISION NORMA
120* ..
121* .. Local Arrays ..
122 DOUBLE PRECISION RWORK( 1 )
123* ..
124* .. External Functions ..
125 DOUBLE PRECISION DLAMCH, ZLANGE
126 EXTERNAL dlamch, zlange
127* ..
128* .. External Subroutines ..
129 EXTERNAL xerbla, zaxpy, zlaset, zunmrz
130* ..
131* .. Intrinsic Functions ..
132 INTRINSIC dble, dcmplx, max
133* ..
134* .. Executable Statements ..
135*
136 zrzt01 = zero
137*
138 IF( lwork.LT.m*n+m ) THEN
139 CALL xerbla( 'ZRZT01', 8 )
140 RETURN
141 END IF
142*
143* Quick return if possible
144*
145 IF( m.LE.0 .OR. n.LE.0 )
146 $ RETURN
147*
148 norma = zlange( 'One-norm', m, n, a, lda, rwork )
149*
150* Copy upper triangle R
151*
152 CALL zlaset( 'Full', m, n, dcmplx( zero ), dcmplx( zero ), work,
153 $ m )
154 DO 20 j = 1, m
155 DO 10 i = 1, j
156 work( ( j-1 )*m+i ) = af( i, j )
157 10 CONTINUE
158 20 CONTINUE
159*
160* R = R * P(1) * ... *P(m)
161*
162 CALL zunmrz( 'Right', 'No tranpose', m, n, m, n-m, af, lda, tau,
163 $ work, m, work( m*n+1 ), lwork-m*n, info )
164*
165* R = R - A
166*
167 DO 30 i = 1, n
168 CALL zaxpy( m, dcmplx( -one ), a( 1, i ), 1,
169 $ work( ( i-1 )*m+1 ), 1 )
170 30 CONTINUE
171*
172 zrzt01 = zlange( 'One-norm', m, n, work, m, rwork )
173*
174 zrzt01 = zrzt01 / ( dlamch( 'Epsilon' )*dble( max( m, n ) ) )
175 IF( norma.NE.zero )
176 $ zrzt01 = zrzt01 / norma
177*
178 RETURN
179*
180* End of ZRZT01
181*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
double precision function zrzt01(M, N, A, AF, LDA, TAU, WORK, LWORK)
ZRZT01
Definition: zrzt01.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 zunmrz(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMRZ
Definition: zunmrz.f:187
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