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SUBROUTINE SPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
$ RWORK, RCOND, RESID )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER LDA, LDAINV, LDWORK, N
REAL RCOND, RESID
* ..
* .. Array Arguments ..
REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
$ WORK( LDWORK, * )
* ..
*
* Purpose
* =======
*
* SPOT03 computes the residual for a symmetric matrix times its
* inverse:
* norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * 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)
*
* AINV (input/output) REAL array, dimension (LDAINV,N)
* On entry, the inverse of the matrix A, stored as a symmetric
* matrix in the same format as A.
* In this version, AINV is expanded into a full matrix and
* multiplied by A, so the opposing triangle of AINV will be
* changed; i.e., if the upper triangular part of AINV is
* stored, the lower triangular part will be used as work space.
*
* LDAINV (input) INTEGER
* The leading dimension of the array AINV. LDAINV >= max(1,N).
*
* WORK (workspace) REAL array, dimension (LDWORK,N)
*
* LDWORK (input) INTEGER
* The leading dimension of the array WORK. LDWORK >= max(1,N).
*
* RWORK (workspace) REAL array, dimension (N)
*
* RCOND (output) REAL
* The reciprocal of the condition number of A, computed as
* ( 1/norm(A) ) / norm(AINV).
*
* RESID (output) REAL
* norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, J
REAL AINVNM, ANORM, EPS
* ..
* .. External Functions ..
LOGICAL LSAME
REAL SLAMCH, SLANGE, SLANSY
EXTERNAL LSAME, SLAMCH, SLANGE, SLANSY
* ..
* .. External Subroutines ..
EXTERNAL SSYMM
* ..
* .. Intrinsic Functions ..
INTRINSIC REAL
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 ) THEN
RCOND = ONE
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
*
EPS = SLAMCH( 'Epsilon' )
ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
AINVNM = SLANSY( '1', UPLO, N, AINV, LDAINV, RWORK )
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCOND = ZERO
RESID = ONE / EPS
RETURN
END IF
RCOND = ( ONE / ANORM ) / AINVNM
*
* Expand AINV into a full matrix and call SSYMM to multiply
* AINV on the left by A.
*
IF( LSAME( UPLO, 'U' ) ) THEN
DO 20 J = 1, N
DO 10 I = 1, J - 1
AINV( J, I ) = AINV( I, J )
10 CONTINUE
20 CONTINUE
ELSE
DO 40 J = 1, N
DO 30 I = J + 1, N
AINV( J, I ) = AINV( I, J )
30 CONTINUE
40 CONTINUE
END IF
CALL SSYMM( 'Left', UPLO, N, N, -ONE, A, LDA, AINV, LDAINV, ZERO,
$ WORK, LDWORK )
*
* Add the identity matrix to WORK .
*
DO 50 I = 1, N
WORK( I, I ) = WORK( I, I ) + ONE
50 CONTINUE
*
* Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
*
RESID = SLANGE( '1', N, N, WORK, LDWORK, RWORK )
*
RESID = ( ( RESID*RCOND ) / EPS ) / REAL( N )
*
RETURN
*
* End of SPOT03
*
END
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