148 lines
4.2 KiB
FortranFixed
148 lines
4.2 KiB
FortranFixed
SUBROUTINE SPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
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$ RWORK, RCOND, RESID )
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*
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* -- LAPACK test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER LDA, LDAINV, LDWORK, N
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REAL RCOND, RESID
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
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$ WORK( LDWORK, * )
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* ..
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*
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* Purpose
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* =======
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*
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* SPOT03 computes the residual for a symmetric matrix times its
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* inverse:
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* norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
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* where EPS is the machine epsilon.
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*
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* Arguments
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* ==========
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*
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* UPLO (input) CHARACTER*1
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* Specifies whether the upper or lower triangular part of the
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* symmetric matrix A is stored:
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* = 'U': Upper triangular
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* = 'L': Lower triangular
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*
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* N (input) INTEGER
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* The number of rows and columns of the matrix A. N >= 0.
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*
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* A (input) REAL array, dimension (LDA,N)
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* The original symmetric matrix A.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,N)
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*
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* AINV (input/output) REAL array, dimension (LDAINV,N)
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* On entry, the inverse of the matrix A, stored as a symmetric
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* matrix in the same format as A.
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* In this version, AINV is expanded into a full matrix and
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* multiplied by A, so the opposing triangle of AINV will be
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* changed; i.e., if the upper triangular part of AINV is
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* stored, the lower triangular part will be used as work space.
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*
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* LDAINV (input) INTEGER
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* The leading dimension of the array AINV. LDAINV >= max(1,N).
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*
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* WORK (workspace) REAL array, dimension (LDWORK,N)
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*
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* LDWORK (input) INTEGER
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* The leading dimension of the array WORK. LDWORK >= max(1,N).
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*
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* RWORK (workspace) REAL array, dimension (N)
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*
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* RCOND (output) REAL
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* The reciprocal of the condition number of A, computed as
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* ( 1/norm(A) ) / norm(AINV).
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*
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* RESID (output) REAL
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* norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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REAL AINVNM, ANORM, EPS
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL SLAMCH, SLANGE, SLANSY
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EXTERNAL LSAME, SLAMCH, SLANGE, SLANSY
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* ..
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* .. External Subroutines ..
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EXTERNAL SSYMM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC REAL
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0.
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*
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IF( N.LE.0 ) THEN
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RCOND = ONE
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RESID = ZERO
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RETURN
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END IF
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*
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* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
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*
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EPS = SLAMCH( 'Epsilon' )
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ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
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AINVNM = SLANSY( '1', UPLO, N, AINV, LDAINV, RWORK )
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IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
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RCOND = ZERO
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RESID = ONE / EPS
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RETURN
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END IF
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RCOND = ( ONE / ANORM ) / AINVNM
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*
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* Expand AINV into a full matrix and call SSYMM to multiply
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* AINV on the left by A.
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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DO 20 J = 1, N
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DO 10 I = 1, J - 1
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AINV( J, I ) = AINV( I, J )
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10 CONTINUE
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20 CONTINUE
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ELSE
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DO 40 J = 1, N
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DO 30 I = J + 1, N
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AINV( J, I ) = AINV( I, J )
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30 CONTINUE
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40 CONTINUE
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END IF
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CALL SSYMM( 'Left', UPLO, N, N, -ONE, A, LDA, AINV, LDAINV, ZERO,
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$ WORK, LDWORK )
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*
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* Add the identity matrix to WORK .
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*
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DO 50 I = 1, N
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WORK( I, I ) = WORK( I, I ) + ONE
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50 CONTINUE
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*
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* Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
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*
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RESID = SLANGE( '1', N, N, WORK, LDWORK, RWORK )
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*
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RESID = ( ( RESID*RCOND ) / EPS ) / REAL( N )
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*
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RETURN
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*
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* End of SPOT03
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*
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END
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