 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sspt01()

 subroutine sspt01 ( character UPLO, integer N, real, dimension( * ) A, real, dimension( * ) AFAC, integer, dimension( * ) IPIV, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) RWORK, real RESID )

SSPT01

Purpose:
``` SSPT01 reconstructs a symmetric indefinite packed matrix A from its
block L*D*L' or U*D*U' factorization and computes the residual
norm( C - A ) / ( N * norm(A) * EPS ),
where C is the reconstructed matrix and 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 (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.``` [in] AFAC ``` AFAC is REAL array, dimension (N*(N+1)/2) The factored form of the matrix A, stored as a packed triangular matrix. AFAC contains the block diagonal matrix D and the multipliers used to obtain the factor L or U from the block L*D*L' or U*D*U' factorization as computed by SSPTRF.``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) The pivot indices from SSPTRF.``` [out] C ` C is REAL array, dimension (LDC,N)` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,N).``` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] RESID ``` RESID is REAL If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )```

Definition at line 109 of file sspt01.f.

110 *
111 * -- LAPACK test routine --
112 * -- LAPACK is a software package provided by Univ. of Tennessee, --
113 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114 *
115 * .. Scalar Arguments ..
116  CHARACTER UPLO
117  INTEGER LDC, N
118  REAL RESID
119 * ..
120 * .. Array Arguments ..
121  INTEGER IPIV( * )
122  REAL A( * ), AFAC( * ), C( LDC, * ), RWORK( * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  REAL ZERO, ONE
129  parameter( zero = 0.0e+0, one = 1.0e+0 )
130 * ..
131 * .. Local Scalars ..
132  INTEGER I, INFO, J, JC
133  REAL ANORM, EPS
134 * ..
135 * .. External Functions ..
136  LOGICAL LSAME
137  REAL SLAMCH, SLANSP, SLANSY
138  EXTERNAL lsame, slamch, slansp, slansy
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL slavsp, slaset
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC real
145 * ..
146 * .. Executable Statements ..
147 *
148 * Quick exit if N = 0.
149 *
150  IF( n.LE.0 ) THEN
151  resid = zero
152  RETURN
153  END IF
154 *
155 * Determine EPS and the norm of A.
156 *
157  eps = slamch( 'Epsilon' )
158  anorm = slansp( '1', uplo, n, a, rwork )
159 *
160 * Initialize C to the identity matrix.
161 *
162  CALL slaset( 'Full', n, n, zero, one, c, ldc )
163 *
164 * Call SLAVSP to form the product D * U' (or D * L' ).
165 *
166  CALL slavsp( uplo, 'Transpose', 'Non-unit', n, n, afac, ipiv, c,
167  \$ ldc, info )
168 *
169 * Call SLAVSP again to multiply by U ( or L ).
170 *
171  CALL slavsp( uplo, 'No transpose', 'Unit', n, n, afac, ipiv, c,
172  \$ ldc, info )
173 *
174 * Compute the difference C - A .
175 *
176  IF( lsame( uplo, 'U' ) ) THEN
177  jc = 0
178  DO 20 j = 1, n
179  DO 10 i = 1, j
180  c( i, j ) = c( i, j ) - a( jc+i )
181  10 CONTINUE
182  jc = jc + j
183  20 CONTINUE
184  ELSE
185  jc = 1
186  DO 40 j = 1, n
187  DO 30 i = j, n
188  c( i, j ) = c( i, j ) - a( jc+i-j )
189  30 CONTINUE
190  jc = jc + n - j + 1
191  40 CONTINUE
192  END IF
193 *
194 * Compute norm( C - A ) / ( N * norm(A) * EPS )
195 *
196  resid = slansy( '1', uplo, n, c, ldc, rwork )
197 *
198  IF( anorm.LE.zero ) THEN
199  IF( resid.NE.zero )
200  \$ resid = one / eps
201  ELSE
202  resid = ( ( resid / real( n ) ) / anorm ) / eps
203  END IF
204 *
205  RETURN
206 *
207 * End of SSPT01
208 *
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slansp(NORM, UPLO, N, AP, WORK)
SLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansp.f:114
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 slavsp(UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
SLAVSP
Definition: slavsp.f:130
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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