 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ ztrt01()

 subroutine ztrt01 ( character UPLO, character DIAG, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldainv, * ) AINV, integer LDAINV, double precision RCOND, double precision, dimension( * ) RWORK, double precision RESID )

ZTRT01

Purpose:
``` ZTRT01 computes the residual for a triangular matrix A times its
inverse:
RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
where EPS is the machine epsilon.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular``` [in] DIAG ``` DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] AINV ``` AINV is COMPLEX*16 array, dimension (LDAINV,N) On entry, the (triangular) inverse of the matrix A, in the same storage format as A. On exit, the contents of AINV are destroyed.``` [in] LDAINV ``` LDAINV is INTEGER The leading dimension of the array AINV. LDAINV >= max(1,N).``` [out] RCOND ``` RCOND is DOUBLE PRECISION The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )```

Definition at line 123 of file ztrt01.f.

125 *
126 * -- LAPACK test routine --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 *
130 * .. Scalar Arguments ..
131  CHARACTER DIAG, UPLO
132  INTEGER LDA, LDAINV, N
133  DOUBLE PRECISION RCOND, RESID
134 * ..
135 * .. Array Arguments ..
136  DOUBLE PRECISION RWORK( * )
137  COMPLEX*16 A( LDA, * ), AINV( LDAINV, * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  DOUBLE PRECISION ZERO, ONE
144  parameter( zero = 0.0d+0, one = 1.0d+0 )
145 * ..
146 * .. Local Scalars ..
147  INTEGER J
148  DOUBLE PRECISION AINVNM, ANORM, EPS
149 * ..
150 * .. External Functions ..
151  LOGICAL LSAME
152  DOUBLE PRECISION DLAMCH, ZLANTR
153  EXTERNAL lsame, dlamch, zlantr
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL ztrmv
157 * ..
158 * .. Intrinsic Functions ..
159  INTRINSIC dble
160 * ..
161 * .. Executable Statements ..
162 *
163 * Quick exit if N = 0
164 *
165  IF( n.LE.0 ) THEN
166  rcond = one
167  resid = zero
168  RETURN
169  END IF
170 *
171 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
172 *
173  eps = dlamch( 'Epsilon' )
174  anorm = zlantr( '1', uplo, diag, n, n, a, lda, rwork )
175  ainvnm = zlantr( '1', uplo, diag, n, n, ainv, ldainv, rwork )
176  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
177  rcond = zero
178  resid = one / eps
179  RETURN
180  END IF
181  rcond = ( one / anorm ) / ainvnm
182 *
183 * Set the diagonal of AINV to 1 if AINV has unit diagonal.
184 *
185  IF( lsame( diag, 'U' ) ) THEN
186  DO 10 j = 1, n
187  ainv( j, j ) = one
188  10 CONTINUE
189  END IF
190 *
191 * Compute A * AINV, overwriting AINV.
192 *
193  IF( lsame( uplo, 'U' ) ) THEN
194  DO 20 j = 1, n
195  CALL ztrmv( 'Upper', 'No transpose', diag, j, a, lda,
196  \$ ainv( 1, j ), 1 )
197  20 CONTINUE
198  ELSE
199  DO 30 j = 1, n
200  CALL ztrmv( 'Lower', 'No transpose', diag, n-j+1, a( j, j ),
201  \$ lda, ainv( j, j ), 1 )
202  30 CONTINUE
203  END IF
204 *
205 * Subtract 1 from each diagonal element to form A*AINV - I.
206 *
207  DO 40 j = 1, n
208  ainv( j, j ) = ainv( j, j ) - one
209  40 CONTINUE
210 *
211 * Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
212 *
213  resid = zlantr( '1', uplo, 'Non-unit', n, n, ainv, ldainv, rwork )
214 *
215  resid = ( ( resid*rcond ) / dble( n ) ) / eps
216 *
217  RETURN
218 *
219 * End of ZTRT01
220 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ztrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
ZTRMV
Definition: ztrmv.f:147
double precision function zlantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
ZLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlantr.f:142
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