sla_syrcond()

real function sla_syrcond	(	character	uplo,
		integer	n,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( ldaf, * )	af,
		integer	ldaf,
		integer, dimension( * )	ipiv,
		integer	cmode,
		real, dimension( * )	c,
		integer	info,
		real, dimension( * )	work,
		integer, dimension( * )	iwork )

SLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix.

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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.
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
[in]	N	!> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !>
[in]	A	!> A is REAL array, dimension (LDA,N) !> On entry, the N-by-N matrix A. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[in]	AF	!> AF is 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. !>
[in]	LDAF	!> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !>
[in]	IPIV	!> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by SSYTRF. !>
[in]	CMODE	!> CMODE is 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) !>
[in]	C	!> C is REAL array, dimension (N) !> The vector C in the formula op(A) * op2(C). !>
[out]	INFO	!> INFO is INTEGER !> = 0: Successful exit. !> i > 0: The ith argument is invalid. !>
[out]	WORK	!> WORK is REAL array, dimension (3*N). !> Workspace. !>
[out]	IWORK	!> IWORK is INTEGER array, dimension (N). !> Workspace. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 142 of file sla_syrcond.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            N, LDA, LDAF, INFO, CMODE
*     ..
*     .. Array Arguments
      INTEGER            IWORK( * ), IPIV( * )
      REAL               A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      CHARACTER          NORMIN
      INTEGER            KASE, I, J
      REAL               AINVNM, SMLNUM, TMP
      LOGICAL            UP
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SLAMCH
      EXTERNAL           lsame, slamch
*     ..
*     .. External Subroutines ..
      EXTERNAL           slacn2, xerbla, ssytrs
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max
*     ..
*     .. Executable Statements ..
*
      sla_syrcond = 0.0
*
      info = 0
      IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -4
      ELSE IF( ldaf.LT.max( 1, n ) ) THEN
         info = -6
      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**T).
*
            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 of SLA_SYRCOND
*

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