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SUBROUTINE SPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
$ PIV, RWORK, RESID, RANK )
*
* -- LAPACK test routine (version 3.1) --
* Craig Lucas, University of Manchester / NAG Ltd.
* October, 2008
*
* .. Scalar Arguments ..
REAL RESID
INTEGER LDA, LDAFAC, LDPERM, N, RANK
CHARACTER UPLO
* ..
* .. Array Arguments ..
REAL A( LDA, * ), AFAC( LDAFAC, * ),
$ PERM( LDPERM, * ), RWORK( * )
INTEGER PIV( * )
* ..
*
* Purpose
* =======
*
* SPST01 reconstructs a symmetric positive semidefinite matrix A
* from its L or U factors and the permutation matrix P and computes
* the residual
* norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
* norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
* where EPS is the machine epsilon.
*
* Arguments
* ==========
*
* UPLO (input) CHARACTER*1
* Specifies whether the upper or lower triangular part of the
* symmetric matrix A is stored:
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (input) INTEGER
* The number of rows and columns of the matrix A. N >= 0.
*
* A (input) REAL array, dimension (LDA,N)
* The original symmetric matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N)
*
* AFAC (input) REAL array, dimension (LDAFAC,N)
* The factor L or U from the L*L' or U'*U
* factorization of A.
*
* LDAFAC (input) INTEGER
* The leading dimension of the array AFAC. LDAFAC >= max(1,N).
*
* PERM (output) REAL array, dimension (LDPERM,N)
* Overwritten with the reconstructed matrix, and then with the
* difference P*L*L'*P' - A (or P*U'*U*P' - A)
*
* LDPERM (input) INTEGER
* The leading dimension of the array PERM.
* LDAPERM >= max(1,N).
*
* PIV (input) INTEGER array, dimension (N)
* PIV is such that the nonzero entries are
* P( PIV( K ), K ) = 1.
*
* RWORK (workspace) REAL array, dimension (N)
*
* RESID (output) REAL
* If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
* If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
REAL ANORM, EPS, T
INTEGER I, J, K
* ..
* .. External Functions ..
REAL SDOT, SLAMCH, SLANSY
LOGICAL LSAME
EXTERNAL SDOT, SLAMCH, SLANSY, LSAME
* ..
* .. External Subroutines ..
EXTERNAL SSCAL, SSYR, STRMV
* ..
* .. Intrinsic Functions ..
INTRINSIC REAL
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = SLAMCH( 'Epsilon' )
ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
* Compute the product U'*U, overwriting U.
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
IF( RANK.LT.N ) THEN
DO 110 J = RANK + 1, N
DO 100 I = RANK + 1, J
AFAC( I, J ) = ZERO
100 CONTINUE
110 CONTINUE
END IF
*
DO 120 K = N, 1, -1
*
* Compute the (K,K) element of the result.
*
T = SDOT( K, AFAC( 1, K ), 1, AFAC( 1, K ), 1 )
AFAC( K, K ) = T
*
* Compute the rest of column K.
*
CALL STRMV( 'Upper', 'Transpose', 'Non-unit', K-1, AFAC,
$ LDAFAC, AFAC( 1, K ), 1 )
*
120 CONTINUE
*
* Compute the product L*L', overwriting L.
*
ELSE
*
IF( RANK.LT.N ) THEN
DO 140 J = RANK + 1, N
DO 130 I = J, N
AFAC( I, J ) = ZERO
130 CONTINUE
140 CONTINUE
END IF
*
DO 150 K = N, 1, -1
* Add a multiple of column K of the factor L to each of
* columns K+1 through N.
*
IF( K+1.LE.N )
$ CALL SSYR( 'Lower', N-K, ONE, AFAC( K+1, K ), 1,
$ AFAC( K+1, K+1 ), LDAFAC )
*
* Scale column K by the diagonal element.
*
T = AFAC( K, K )
CALL SSCAL( N-K+1, T, AFAC( K, K ), 1 )
150 CONTINUE
*
END IF
*
* Form P*L*L'*P' or P*U'*U*P'
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
DO 170 J = 1, N
DO 160 I = 1, N
IF( PIV( I ).LE.PIV( J ) ) THEN
IF( I.LE.J ) THEN
PERM( PIV( I ), PIV( J ) ) = AFAC( I, J )
ELSE
PERM( PIV( I ), PIV( J ) ) = AFAC( J, I )
END IF
END IF
160 CONTINUE
170 CONTINUE
*
*
ELSE
*
DO 190 J = 1, N
DO 180 I = 1, N
IF( PIV( I ).GE.PIV( J ) ) THEN
IF( I.GE.J ) THEN
PERM( PIV( I ), PIV( J ) ) = AFAC( I, J )
ELSE
PERM( PIV( I ), PIV( J ) ) = AFAC( J, I )
END IF
END IF
180 CONTINUE
190 CONTINUE
*
END IF
*
* Compute the difference P*L*L'*P' - A (or P*U'*U*P' - A).
*
IF( LSAME( UPLO, 'U' ) ) THEN
DO 210 J = 1, N
DO 200 I = 1, J
PERM( I, J ) = PERM( I, J ) - A( I, J )
200 CONTINUE
210 CONTINUE
ELSE
DO 230 J = 1, N
DO 220 I = J, N
PERM( I, J ) = PERM( I, J ) - A( I, J )
220 CONTINUE
230 CONTINUE
END IF
*
* Compute norm( P*L*L'P - A ) / ( N * norm(A) * EPS ), or
* ( P*U'*U*P' - A )/ ( N * norm(A) * EPS ).
*
RESID = SLANSY( '1', UPLO, N, PERM, LDAFAC, RWORK )
*
RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS
*
RETURN
*
* End of SPST01
*
END
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