LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ spot01()

subroutine spot01 ( character  UPLO,
integer  N,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldafac, * )  AFAC,
integer  LDAFAC,
real, dimension( * )  RWORK,
real  RESID 
)

SPOT01

Purpose:
 SPOT01 reconstructs a symmetric positive definite matrix  A  from
 its L*L' or U'*U factorization and computes the residual
    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
    norm( U'*U - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.
Parameters
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.
[in]A
          A is REAL array, dimension (LDA,N)
          The original symmetric matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)
[in,out]AFAC
          AFAC is REAL array, dimension (LDAFAC,N)
          On entry, the factor L or U from the L * L**T or U**T * U
          factorization of A.
          Overwritten with the reconstructed matrix, and then with
          the difference L * L**T - A (or U**T * U - A).
[in]LDAFAC
          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
[out]RWORK
          RWORK is REAL array, dimension (N)
[out]RESID
          RESID is REAL
          If UPLO = 'L', norm(L * L**T - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U**T * U - A) / ( N * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 103 of file spot01.f.

104 *
105 * -- LAPACK test routine --
106 * -- LAPACK is a software package provided by Univ. of Tennessee, --
107 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
108 *
109 * .. Scalar Arguments ..
110  CHARACTER UPLO
111  INTEGER LDA, LDAFAC, N
112  REAL RESID
113 * ..
114 * .. Array Arguments ..
115  REAL A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
116 * ..
117 *
118 * =====================================================================
119 *
120 * .. Parameters ..
121  REAL ZERO, ONE
122  parameter( zero = 0.0e+0, one = 1.0e+0 )
123 * ..
124 * .. Local Scalars ..
125  INTEGER I, J, K
126  REAL ANORM, EPS, T
127 * ..
128 * .. External Functions ..
129  LOGICAL LSAME
130  REAL SDOT, SLAMCH, SLANSY
131  EXTERNAL lsame, sdot, slamch, slansy
132 * ..
133 * .. External Subroutines ..
134  EXTERNAL sscal, ssyr, strmv
135 * ..
136 * .. Intrinsic Functions ..
137  INTRINSIC real
138 * ..
139 * .. Executable Statements ..
140 *
141 * Quick exit if N = 0.
142 *
143  IF( n.LE.0 ) THEN
144  resid = zero
145  RETURN
146  END IF
147 *
148 * Exit with RESID = 1/EPS if ANORM = 0.
149 *
150  eps = slamch( 'Epsilon' )
151  anorm = slansy( '1', uplo, n, a, lda, rwork )
152  IF( anorm.LE.zero ) THEN
153  resid = one / eps
154  RETURN
155  END IF
156 *
157 * Compute the product U**T * U, overwriting U.
158 *
159  IF( lsame( uplo, 'U' ) ) THEN
160  DO 10 k = n, 1, -1
161 *
162 * Compute the (K,K) element of the result.
163 *
164  t = sdot( k, afac( 1, k ), 1, afac( 1, k ), 1 )
165  afac( k, k ) = t
166 *
167 * Compute the rest of column K.
168 *
169  CALL strmv( 'Upper', 'Transpose', 'Non-unit', k-1, afac,
170  $ ldafac, afac( 1, k ), 1 )
171 *
172  10 CONTINUE
173 *
174 * Compute the product L * L**T, overwriting L.
175 *
176  ELSE
177  DO 20 k = n, 1, -1
178 *
179 * Add a multiple of column K of the factor L to each of
180 * columns K+1 through N.
181 *
182  IF( k+1.LE.n )
183  $ CALL ssyr( 'Lower', n-k, one, afac( k+1, k ), 1,
184  $ afac( k+1, k+1 ), ldafac )
185 *
186 * Scale column K by the diagonal element.
187 *
188  t = afac( k, k )
189  CALL sscal( n-k+1, t, afac( k, k ), 1 )
190 *
191  20 CONTINUE
192  END IF
193 *
194 * Compute the difference L * L**T - A (or U**T * U - A).
195 *
196  IF( lsame( uplo, 'U' ) ) THEN
197  DO 40 j = 1, n
198  DO 30 i = 1, j
199  afac( i, j ) = afac( i, j ) - a( i, j )
200  30 CONTINUE
201  40 CONTINUE
202  ELSE
203  DO 60 j = 1, n
204  DO 50 i = j, n
205  afac( i, j ) = afac( i, j ) - a( i, j )
206  50 CONTINUE
207  60 CONTINUE
208  END IF
209 *
210 * Compute norm(L*U - A) / ( N * norm(A) * EPS )
211 *
212  resid = slansy( '1', uplo, n, afac, ldafac, rwork )
213 *
214  resid = ( ( resid / real( n ) ) / anorm ) / eps
215 *
216  RETURN
217 *
218 * End of SPOT01
219 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slansy(NORM, UPLO, N, A, LDA, WORK)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansy.f:122
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
real function sdot(N, SX, INCX, SY, INCY)
SDOT
Definition: sdot.f:82
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:147
subroutine ssyr(UPLO, N, ALPHA, X, INCX, A, LDA)
SSYR
Definition: ssyr.f:132
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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