LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dppt01()

subroutine dppt01 ( character  UPLO,
integer  N,
double precision, dimension( * )  A,
double precision, dimension( * )  AFAC,
double precision, dimension( * )  RWORK,
double precision  RESID 
)

DPPT01

Purpose:
 DPPT01 reconstructs a symmetric positive definite packed 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 DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The original symmetric matrix A, stored as a packed
          triangular matrix.
[in,out]AFAC
          AFAC is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          On entry, the factor L or U from the L*L' or U'*U
          factorization of A, stored as a packed triangular matrix.
          Overwritten with the reconstructed matrix, and then with the
          difference L*L' - A (or U'*U - A).
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]RESID
          RESID is DOUBLE PRECISION
          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 95 of file dppt01.f.

95 *
96 * -- LAPACK test routine (version 3.7.0) --
97 * -- LAPACK is a software package provided by Univ. of Tennessee, --
98 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
99 * December 2016
100 *
101 * .. Scalar Arguments ..
102  CHARACTER uplo
103  INTEGER n
104  DOUBLE PRECISION resid
105 * ..
106 * .. Array Arguments ..
107  DOUBLE PRECISION a( * ), afac( * ), rwork( * )
108 * ..
109 *
110 * =====================================================================
111 *
112 * .. Parameters ..
113  DOUBLE PRECISION zero, one
114  parameter( zero = 0.0d+0, one = 1.0d+0 )
115 * ..
116 * .. Local Scalars ..
117  INTEGER i, k, kc, npp
118  DOUBLE PRECISION anorm, eps, t
119 * ..
120 * .. External Functions ..
121  LOGICAL lsame
122  DOUBLE PRECISION ddot, dlamch, dlansp
123  EXTERNAL lsame, ddot, dlamch, dlansp
124 * ..
125 * .. External Subroutines ..
126  EXTERNAL dscal, dspr, dtpmv
127 * ..
128 * .. Intrinsic Functions ..
129  INTRINSIC dble
130 * ..
131 * .. Executable Statements ..
132 *
133 * Quick exit if N = 0
134 *
135  IF( n.LE.0 ) THEN
136  resid = zero
137  RETURN
138  END IF
139 *
140 * Exit with RESID = 1/EPS if ANORM = 0.
141 *
142  eps = dlamch( 'Epsilon' )
143  anorm = dlansp( '1', uplo, n, a, rwork )
144  IF( anorm.LE.zero ) THEN
145  resid = one / eps
146  RETURN
147  END IF
148 *
149 * Compute the product U'*U, overwriting U.
150 *
151  IF( lsame( uplo, 'U' ) ) THEN
152  kc = ( n*( n-1 ) ) / 2 + 1
153  DO 10 k = n, 1, -1
154 *
155 * Compute the (K,K) element of the result.
156 *
157  t = ddot( k, afac( kc ), 1, afac( kc ), 1 )
158  afac( kc+k-1 ) = t
159 *
160 * Compute the rest of column K.
161 *
162  IF( k.GT.1 ) THEN
163  CALL dtpmv( 'Upper', 'Transpose', 'Non-unit', k-1, afac,
164  $ afac( kc ), 1 )
165  kc = kc - ( k-1 )
166  END IF
167  10 CONTINUE
168 *
169 * Compute the product L*L', overwriting L.
170 *
171  ELSE
172  kc = ( n*( n+1 ) ) / 2
173  DO 20 k = n, 1, -1
174 *
175 * Add a multiple of column K of the factor L to each of
176 * columns K+1 through N.
177 *
178  IF( k.LT.n )
179  $ CALL dspr( 'Lower', n-k, one, afac( kc+1 ), 1,
180  $ afac( kc+n-k+1 ) )
181 *
182 * Scale column K by the diagonal element.
183 *
184  t = afac( kc )
185  CALL dscal( n-k+1, t, afac( kc ), 1 )
186 *
187  kc = kc - ( n-k+2 )
188  20 CONTINUE
189  END IF
190 *
191 * Compute the difference L*L' - A (or U'*U - A).
192 *
193  npp = n*( n+1 ) / 2
194  DO 30 i = 1, npp
195  afac( i ) = afac( i ) - a( i )
196  30 CONTINUE
197 *
198 * Compute norm( L*U - A ) / ( N * norm(A) * EPS )
199 *
200  resid = dlansp( '1', uplo, n, afac, rwork )
201 *
202  resid = ( ( resid / dble( n ) ) / anorm ) / eps
203 *
204  RETURN
205 *
206 * End of DPPT01
207 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
double precision function ddot(N, DX, INCX, DY, INCY)
DDOT
Definition: ddot.f:84
double precision function dlansp(NORM, UPLO, N, AP, WORK)
DLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.
Definition: dlansp.f:116
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:81
subroutine dspr(UPLO, N, ALPHA, X, INCX, AP)
DSPR
Definition: dspr.f:129
subroutine dtpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
Definition: dtpmv.f:144
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