 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ strt01()

 subroutine strt01 ( character UPLO, character DIAG, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( ldainv, * ) AINV, integer LDAINV, real RCOND, real, dimension( * ) WORK, real RESID )

STRT01

Purpose:
``` STRT01 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 REAL 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,out] AINV ``` AINV is REAL 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 REAL The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).``` [out] WORK ` WORK is REAL array, dimension (N)` [out] RESID ``` RESID is REAL norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )```
Date
December 2016

Definition at line 126 of file strt01.f.

126 *
127 * -- LAPACK test routine (version 3.7.0) --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 * December 2016
131 *
132 * .. Scalar Arguments ..
133  CHARACTER diag, uplo
134  INTEGER lda, ldainv, n
135  REAL rcond, resid
136 * ..
137 * .. Array Arguments ..
138  REAL a( lda, * ), ainv( ldainv, * ), work( * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  REAL zero, one
145  parameter( zero = 0.0e+0, one = 1.0e+0 )
146 * ..
147 * .. Local Scalars ..
148  INTEGER j
149  REAL ainvnm, anorm, eps
150 * ..
151 * .. External Functions ..
152  LOGICAL lsame
153  REAL slamch, slantr
154  EXTERNAL lsame, slamch, slantr
155 * ..
156 * .. External Subroutines ..
157  EXTERNAL strmv
158 * ..
159 * .. Intrinsic Functions ..
160  INTRINSIC real
161 * ..
162 * .. Executable Statements ..
163 *
164 * Quick exit if N = 0
165 *
166  IF( n.LE.0 ) THEN
167  rcond = one
168  resid = zero
169  RETURN
170  END IF
171 *
172 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
173 *
174  eps = slamch( 'Epsilon' )
175  anorm = slantr( '1', uplo, diag, n, n, a, lda, work )
176  ainvnm = slantr( '1', uplo, diag, n, n, ainv, ldainv, work )
177  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
178  rcond = zero
179  resid = one / eps
180  RETURN
181  END IF
182  rcond = ( one / anorm ) / ainvnm
183 *
184 * Set the diagonal of AINV to 1 if AINV has unit diagonal.
185 *
186  IF( lsame( diag, 'U' ) ) THEN
187  DO 10 j = 1, n
188  ainv( j, j ) = one
189  10 CONTINUE
190  END IF
191 *
192 * Compute A * AINV, overwriting AINV.
193 *
194  IF( lsame( uplo, 'U' ) ) THEN
195  DO 20 j = 1, n
196  CALL strmv( 'Upper', 'No transpose', diag, j, a, lda,
197  \$ ainv( 1, j ), 1 )
198  20 CONTINUE
199  ELSE
200  DO 30 j = 1, n
201  CALL strmv( 'Lower', 'No transpose', diag, n-j+1, a( j, j ),
202  \$ lda, ainv( j, j ), 1 )
203  30 CONTINUE
204  END IF
205 *
206 * Subtract 1 from each diagonal element to form A*AINV - I.
207 *
208  DO 40 j = 1, n
209  ainv( j, j ) = ainv( j, j ) - one
210  40 CONTINUE
211 *
212 * Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
213 *
214  resid = slantr( '1', uplo, 'Non-unit', n, n, ainv, ldainv, work )
215 *
216  resid = ( ( resid*rcond ) / REAL( N ) ) / eps
217 *
218  RETURN
219 *
220 * End of STRT01
221 *
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:149
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
real function slantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
SLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
Definition: slantr.f:143
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