sla_gercond()

real function sla_gercond	(	character	trans,
		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_GERCOND estimates the Skeel condition number for a general matrix.

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Purpose:

!>
!>    SLA_GERCOND 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]	TRANS	!> TRANS is CHARACTER*1 !> Specifies the form of the system of equations: !> = 'N': A * X = B (No transpose) !> = 'T': A**T * X = B (Transpose) !> = 'C': A**H * X = B (Conjugate Transpose = Transpose) !>
[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 factors L and U from the factorization !> A = P*L*U as computed by SGETRF. !>
[in]	LDAF	!> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !>
[in]	IPIV	!> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by SGETRF; row i of the matrix was interchanged !> with row IPIV(i). !>
[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.2 !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 146 of file sla_gercond.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          TRANS
      INTEGER            N, LDA, LDAF, INFO, CMODE
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * ), IWORK( * )
      REAL               A( LDA, * ), AF( LDAF, * ), WORK( * ),
     $                   C( * )
*    ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            NOTRANS
      INTEGER            KASE, I, J
      REAL               AINVNM, TMP
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           slacn2, sgetrs, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max
*     ..
*     .. Executable Statements ..
*
      sla_gercond = 0.0
*
      info = 0
      notrans = lsame( trans, 'N' )
      IF ( .NOT. notrans .AND. .NOT. lsame(trans, 'T')
     $     .AND. .NOT. lsame(trans, 'C') ) THEN
         info = -1
      ELSE 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_GERCOND', -info )
         RETURN
      END IF
      IF( n.EQ.0 ) THEN
         sla_gercond = 1.0
         RETURN
      END IF
*
*     Compute the equilibration matrix R such that
*     inv(R)*A*C has unit 1-norm.
*
      IF (notrans) THEN
         DO i = 1, n
            tmp = 0.0
            IF ( cmode .EQ. 1 ) THEN
               DO j = 1, n
                  tmp = tmp + abs( a( i, j ) * c( j ) )
               END DO
            ELSE IF ( cmode .EQ. 0 ) THEN
               DO j = 1, n
                  tmp = tmp + abs( a( i, j ) )
               END DO
            ELSE
               DO j = 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, n
                  tmp = tmp + abs( a( j, i ) * c( j ) )
               END DO
            ELSE IF ( cmode .EQ. 0 ) THEN
               DO j = 1, n
                  tmp = tmp + abs( a( j, i ) )
               END DO
            ELSE
               DO j = 1, n
                  tmp = tmp + abs( a( j, i ) / c( j ) )
               END DO
            END IF
            work( 2*n+i ) = tmp
         END DO
      END IF
*
*     Estimate the norm of inv(op(A)).
*
      ainvnm = 0.0
 
      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 (notrans) THEN
               CALL sgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
     $            work, n, info )
            ELSE
               CALL sgetrs( 'Transpose', n, 1, af, ldaf, ipiv,
     $            work, n, info )
            END IF
*
*           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 (notrans) THEN
               CALL sgetrs( 'Transpose', n, 1, af, ldaf, ipiv,
     $            work, n, info )
            ELSE
               CALL sgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
     $            work, n, info )
            END IF
*
*           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_gercond = ( 1.0 / ainvnm )
*
      RETURN
*
*     End of SLA_GERCOND
*

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