 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ srzt01()

 real function srzt01 ( integer M, integer N, real, dimension( lda, * ) A, real, dimension( lda, * ) AF, integer LDA, real, dimension( * ) TAU, real, dimension( lwork ) WORK, integer LWORK )

SRZT01

Purpose:
``` SRZT01 returns
|| A - R*Q || / ( M * eps * ||A|| )
for an upper trapezoidal A that was factored with STZRZF.```
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 REAL array, dimension (LDA,N) The original upper trapezoidal M by N matrix A.``` [in] AF ``` AF is REAL array, dimension (LDA,N) The output of STZRZF 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 REAL array, dimension (M) Details of the Householder transformations as returned by STZRZF.``` [out] WORK ` WORK is REAL array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The length of the array WORK. LWORK >= m*n + m*nb.```

Definition at line 96 of file srzt01.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  REAL A( LDA, * ), AF( LDA, * ), TAU( * ),
108  \$ WORK( LWORK )
109 * ..
110 *
111 * =====================================================================
112 *
113 * .. Parameters ..
114  REAL ZERO, ONE
115  parameter( zero = 0.0e+0, one = 1.0e+0 )
116 * ..
117 * .. Local Scalars ..
118  INTEGER I, INFO, J
119  REAL NORMA
120 * ..
121 * .. Local Arrays ..
122  REAL RWORK( 1 )
123 * ..
124 * .. External Functions ..
125  REAL SLAMCH, SLANGE
126  EXTERNAL slamch, slange
127 * ..
128 * .. External Subroutines ..
129  EXTERNAL saxpy, slaset, sormrz, xerbla
130 * ..
131 * .. Intrinsic Functions ..
132  INTRINSIC max, real
133 * ..
134 * .. Executable Statements ..
135 *
136  srzt01 = zero
137 *
138  IF( lwork.LT.m*n+m ) THEN
139  CALL xerbla( 'SRZT01', 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 = slange( 'One-norm', m, n, a, lda, rwork )
149 *
150 * Copy upper triangle R
151 *
152  CALL slaset( 'Full', m, n, zero, zero, work, m )
153  DO 20 j = 1, m
154  DO 10 i = 1, j
155  work( ( j-1 )*m+i ) = af( i, j )
156  10 CONTINUE
157  20 CONTINUE
158 *
159 * R = R * P(1) * ... *P(m)
160 *
161  CALL sormrz( 'Right', 'No tranpose', m, n, m, n-m, af, lda, tau,
162  \$ work, m, work( m*n+1 ), lwork-m*n, info )
163 *
164 * R = R - A
165 *
166  DO 30 i = 1, n
167  CALL saxpy( m, -one, a( 1, i ), 1, work( ( i-1 )*m+1 ), 1 )
168  30 CONTINUE
169 *
170  srzt01 = slange( 'One-norm', m, n, work, m, rwork )
171 *
172  srzt01 = srzt01 / ( slamch( 'Epsilon' )*real( max( m, n ) ) )
173  IF( norma.NE.zero )
174  \$ srzt01 = srzt01 / norma
175 *
176  RETURN
177 *
178 * End of SRZT01
179 *
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:114
subroutine sormrz(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMRZ
Definition: sormrz.f:187
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
real function srzt01(M, N, A, AF, LDA, TAU, WORK, LWORK)
SRZT01
Definition: srzt01.f:98
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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