LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ crzt01()

real function crzt01 ( integer  M,
integer  N,
complex, dimension( lda, * )  A,
complex, dimension( lda, * )  AF,
integer  LDA,
complex, dimension( * )  TAU,
complex, dimension( lwork )  WORK,
integer  LWORK 
)

CRZT01

Purpose:
 CRZT01 returns
      || A - R*Q || / ( M * eps * ||A|| )
 for an upper trapezoidal A that was factored with CTZRZF.
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 array, dimension (LDA,N)
          The original upper trapezoidal M by N matrix A.
[in]AF
          AF is COMPLEX array, dimension (LDA,N)
          The output of CTZRZF 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 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
          The length of the array WORK.  LWORK >= m*n + m.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 100 of file crzt01.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 lda, lwork, m, n
108 * ..
109 * .. Array Arguments ..
110  COMPLEX a( lda, * ), af( lda, * ), tau( * ),
111  $ work( lwork )
112 * ..
113 *
114 * =====================================================================
115 *
116 * .. Parameters ..
117  REAL zero, one
118  parameter( zero = 0.0e0, one = 1.0e0 )
119 * ..
120 * .. Local Scalars ..
121  INTEGER i, info, j
122  REAL norma
123 * ..
124 * .. Local Arrays ..
125  REAL rwork( 1 )
126 * ..
127 * .. External Functions ..
128  REAL clange, slamch
129  EXTERNAL clange, slamch
130 * ..
131 * .. External Subroutines ..
132  EXTERNAL caxpy, claset, cunmrz, xerbla
133 * ..
134 * .. Intrinsic Functions ..
135  INTRINSIC cmplx, max, real
136 * ..
137 * .. Executable Statements ..
138 *
139  crzt01 = zero
140 *
141  IF( lwork.LT.m*n+m ) THEN
142  CALL xerbla( 'CRZT01', 8 )
143  RETURN
144  END IF
145 *
146 * Quick return if possible
147 *
148  IF( m.LE.0 .OR. n.LE.0 )
149  $ RETURN
150 *
151  norma = clange( 'One-norm', m, n, a, lda, rwork )
152 *
153 * Copy upper triangle R
154 *
155  CALL claset( 'Full', m, n, cmplx( zero ), cmplx( zero ), work, m )
156  DO 20 j = 1, m
157  DO 10 i = 1, j
158  work( ( j-1 )*m+i ) = af( i, j )
159  10 CONTINUE
160  20 CONTINUE
161 *
162 * R = R * P(1) * ... *P(m)
163 *
164  CALL cunmrz( 'Right', 'No tranpose', m, n, m, n-m, af, lda, tau,
165  $ work, m, work( m*n+1 ), lwork-m*n, info )
166 *
167 * R = R - A
168 *
169  DO 30 i = 1, n
170  CALL caxpy( m, cmplx( -one ), a( 1, i ), 1,
171  $ work( ( i-1 )*m+1 ), 1 )
172  30 CONTINUE
173 *
174  crzt01 = clange( 'One-norm', m, n, work, m, rwork )
175 *
176  crzt01 = crzt01 / ( slamch( 'Epsilon' )*REAL( MAX( M, N ) ) )
177  IF( norma.NE.zero )
178  $ crzt01 = crzt01 / norma
179 *
180  RETURN
181 *
182 * End of CRZT01
183 *
subroutine cunmrz(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
CUNMRZ
Definition: cunmrz.f:189
real function crzt01(M, N, A, AF, LDA, TAU, WORK, LWORK)
CRZT01
Definition: crzt01.f:100
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
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:90
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