REAL FUNCTION SLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV, CMODE, $ C, INFO, WORK, IWORK ) * * -- LAPACK routine (version 3.2) -- * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- * -- Jason Riedy of Univ. of California Berkeley. -- * -- November 2008 -- * * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley and NAG Ltd. -- * IMPLICIT NONE * .. * .. Scalar Arguments .. CHARACTER UPLO INTEGER N, LDA, LDAF, INFO, CMODE * .. * .. Array Arguments INTEGER IWORK( * ), IPIV( * ) REAL A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * ) * * SLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C) * where op2 is determined by CMODE as follows * CMODE = 1 op2(C) = C * CMODE = 0 op2(C) = I * CMODE = -1 op2(C) = inv(C) * The Skeel condition number cond(A) = norminf( |inv(A)||A| ) * is computed by computing scaling factors R such that * diag(R)*A*op2(C) is row equilibrated and computing the standard * infinity-norm condition number. * WORK is a real workspace of size 3*N, and * IWORK is an integer workspace of size N. * .. * .. Local Scalars .. CHARACTER NORMIN INTEGER KASE, I, J REAL AINVNM, SMLNUM, TMP LOGICAL UP * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER ISAMAX REAL SLAMCH EXTERNAL LSAME, ISAMAX, SLAMCH * .. * .. External Subroutines .. EXTERNAL SLACN2, SLATRS, SRSCL, XERBLA, SSYTRS * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * SLA_SYRCOND = 0.0 * INFO = 0 IF( N.LT.0 ) THEN INFO = -2 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SLA_SYRCOND', -INFO ) RETURN END IF IF( N.EQ.0 ) THEN SLA_SYRCOND = 1.0 RETURN END IF UP = .FALSE. IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. * * Compute the equilibration matrix R such that * inv(R)*A*C has unit 1-norm. * IF ( UP ) THEN DO I = 1, N TMP = 0.0 IF ( CMODE .EQ. 1 ) THEN DO J = 1, I TMP = TMP + ABS( A( J, I ) * C( J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( I, J ) * C( J ) ) END DO ELSE IF ( CMODE .EQ. 0 ) THEN DO J = 1, I TMP = TMP + ABS( A( J, I ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( I, J ) ) END DO ELSE DO J = 1, I TMP = TMP + ABS( A( J, I ) / C( J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( I, J ) / C( J ) ) END DO END IF WORK( 2*N+I ) = TMP END DO ELSE DO I = 1, N TMP = 0.0 IF ( CMODE .EQ. 1 ) THEN DO J = 1, I TMP = TMP + ABS( A( I, J ) * C( J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( J, I ) * C( J ) ) END DO ELSE IF ( CMODE .EQ. 0 ) THEN DO J = 1, I TMP = TMP + ABS( A( I, J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( J, I ) ) END DO ELSE DO J = 1, I TMP = TMP + ABS( A( I, J) / C( J ) ) END DO DO J = I+1, N TMP = TMP + ABS( A( J, I) / C( J ) ) END DO END IF WORK( 2*N+I ) = TMP END DO ENDIF * * Estimate the norm of inv(op(A)). * SMLNUM = SLAMCH( 'Safe minimum' ) AINVNM = 0.0 NORMIN = 'N' KASE = 0 10 CONTINUE CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( KASE.EQ.2 ) THEN * * Multiply by R. * DO I = 1, N WORK( I ) = WORK( I ) * WORK( 2*N+I ) END DO IF ( UP ) THEN call ssytrs( 'U', n, 1, af, ldaf, ipiv, work, n, info ) ELSE call ssytrs( 'L', n, 1, af, ldaf, ipiv, work, n, info ) ENDIF * * Multiply by inv(C). * IF ( CMODE .EQ. 1 ) THEN DO I = 1, N WORK( I ) = WORK( I ) / C( I ) END DO ELSE IF ( CMODE .EQ. -1 ) THEN DO I = 1, N WORK( I ) = WORK( I ) * C( I ) END DO END IF ELSE * * Multiply by inv(C'). * IF ( CMODE .EQ. 1 ) THEN DO I = 1, N WORK( I ) = WORK( I ) / C( I ) END DO ELSE IF ( CMODE .EQ. -1 ) THEN DO I = 1, N WORK( I ) = WORK( I ) * C( I ) END DO END IF IF ( UP ) THEN call ssytrs( 'U', n, 1, af, ldaf, ipiv, work, n, info ) ELSE call ssytrs( 'L', n, 1, af, ldaf, ipiv, work, n, info ) ENDIF * * Multiply by R. * DO I = 1, N WORK( I ) = WORK( I ) * WORK( 2*N+I ) END DO END IF * GO TO 10 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM .NE. 0.0 ) $ SLA_SYRCOND = ( 1.0 / AINVNM ) * RETURN * END