REAL FUNCTION SLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF, IPIV, CMODE, \$ C, INFO, WORK, IWORK ) * * -- LAPACK routine (version 3.2.1) -- * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- * -- Jason Riedy of Univ. of California Berkeley. -- * -- April 2009 -- * * -- 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( * ) * .. * * Purpose * ======= * * 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. * * Arguments * ========== * * UPLO (input) CHARACTER*1 * = 'U': Upper triangle of A is stored; * = 'L': Lower triangle of A is stored. * * N (input) INTEGER * The number of linear equations, i.e., the order of the * matrix A. N >= 0. * * A (input) REAL array, dimension (LDA,N) * On entry, the N-by-N matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * AF (input) REAL array, dimension (LDAF,N) * The block diagonal matrix D and the multipliers used to * obtain the factor U or L as computed by SSYTRF. * * LDAF (input) INTEGER * The leading dimension of the array AF. LDAF >= max(1,N). * * IPIV (input) INTEGER array, dimension (N) * Details of the interchanges and the block structure of D * as determined by SSYTRF. * * CMODE (input) INTEGER * Determines op2(C) in the formula op(A) * op2(C) as follows: * CMODE = 1 op2(C) = C * CMODE = 0 op2(C) = I * CMODE = -1 op2(C) = inv(C) * * C (input) REAL array, dimension (N) * The vector C in the formula op(A) * op2(C). * * INFO (output) INTEGER * = 0: Successful exit. * i > 0: The ith argument is invalid. * * WORK (input) REAL array, dimension (3*N). * Workspace. * * IWORK (input) INTEGER array, dimension (N). * Workspace. * * ===================================================================== * * .. 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