 LAPACK  3.10.1 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 )```

Definition at line 122 of file strt01.f.

124 *
125 * -- LAPACK test routine --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 *
129 * .. Scalar Arguments ..
130  CHARACTER DIAG, UPLO
131  INTEGER LDA, LDAINV, N
132  REAL RCOND, RESID
133 * ..
134 * .. Array Arguments ..
135  REAL A( LDA, * ), AINV( LDAINV, * ), WORK( * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * .. Parameters ..
141  REAL ZERO, ONE
142  parameter( zero = 0.0e+0, one = 1.0e+0 )
143 * ..
144 * .. Local Scalars ..
145  INTEGER J
146  REAL AINVNM, ANORM, EPS
147 * ..
148 * .. External Functions ..
149  LOGICAL LSAME
150  REAL SLAMCH, SLANTR
151  EXTERNAL lsame, slamch, slantr
152 * ..
153 * .. External Subroutines ..
154  EXTERNAL strmv
155 * ..
156 * .. Intrinsic Functions ..
157  INTRINSIC real
158 * ..
159 * .. Executable Statements ..
160 *
161 * Quick exit if N = 0
162 *
163  IF( n.LE.0 ) THEN
164  rcond = one
165  resid = zero
166  RETURN
167  END IF
168 *
169 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
170 *
171  eps = slamch( 'Epsilon' )
172  anorm = slantr( '1', uplo, diag, n, n, a, lda, work )
173  ainvnm = slantr( '1', uplo, diag, n, n, ainv, ldainv, work )
174  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
175  rcond = zero
176  resid = one / eps
177  RETURN
178  END IF
179  rcond = ( one / anorm ) / ainvnm
180 *
181 * Set the diagonal of AINV to 1 if AINV has unit diagonal.
182 *
183  IF( lsame( diag, 'U' ) ) THEN
184  DO 10 j = 1, n
185  ainv( j, j ) = one
186  10 CONTINUE
187  END IF
188 *
189 * Compute A * AINV, overwriting AINV.
190 *
191  IF( lsame( uplo, 'U' ) ) THEN
192  DO 20 j = 1, n
193  CALL strmv( 'Upper', 'No transpose', diag, j, a, lda,
194  \$ ainv( 1, j ), 1 )
195  20 CONTINUE
196  ELSE
197  DO 30 j = 1, n
198  CALL strmv( 'Lower', 'No transpose', diag, n-j+1, a( j, j ),
199  \$ lda, ainv( j, j ), 1 )
200  30 CONTINUE
201  END IF
202 *
203 * Subtract 1 from each diagonal element to form A*AINV - I.
204 *
205  DO 40 j = 1, n
206  ainv( j, j ) = ainv( j, j ) - one
207  40 CONTINUE
208 *
209 * Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
210 *
211  resid = slantr( '1', uplo, 'Non-unit', n, n, ainv, ldainv, work )
212 *
213  resid = ( ( resid*rcond ) / real( n ) ) / eps
214 *
215  RETURN
216 *
217 * End of STRT01
218 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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,...
Definition: slantr.f:141
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:147
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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