spocon.f

          SUBROUTINE SPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
         $                   INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH.
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, LDA, N
          REAL               ANORM, RCOND
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          REAL               A( LDA, * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SPOCON estimates the reciprocal of the condition number (in the
    *  1-norm) of a real symmetric positive definite matrix using the
    *  Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF.
    *
    *  An estimate is obtained for norm(inv(A)), and the reciprocal of the
    *  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
    *
    *  Arguments
    *  =========
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  Upper triangle of A is stored;
    *          = 'L':  Lower triangle of A is stored.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  A       (input) REAL array, dimension (LDA,N)
    *          The triangular factor U or L from the Cholesky factorization
    *          A = U**T*U or A = L*L**T, as computed by SPOTRF.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  ANORM   (input) REAL
    *          The 1-norm (or infinity-norm) of the symmetric matrix A.
    *
    *  RCOND   (output) REAL
    *          The reciprocal of the condition number of the matrix A,
    *          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
    *          estimate of the 1-norm of inv(A) computed in this routine.
    *
    *  WORK    (workspace) REAL array, dimension (3*N)
    *
    *  IWORK   (workspace) INTEGER array, dimension (N)
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ONE, ZERO
          PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            UPPER
          CHARACTER          NORMIN
          INTEGER            IX, KASE
          REAL               AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
    *     ..
    *     .. Local Arrays ..
          INTEGER            ISAVE( 3 )
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ISAMAX
          REAL               SLAMCH
          EXTERNAL           LSAME, ISAMAX, SLAMCH
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SLACN2, SLATRS, SRSCL, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, MAX
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          UPPER = LSAME( UPLO, 'U' )
          IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -4
          ELSE IF( ANORM.LT.ZERO ) THEN
             INFO = -5
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'SPOCON', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          RCOND = ZERO
          IF( N.EQ.0 ) THEN
             RCOND = ONE
             RETURN
          ELSE IF( ANORM.EQ.ZERO ) THEN
             RETURN
          END IF
    *
          SMLNUM = SLAMCH( 'Safe minimum' )
    *
    *     Estimate the 1-norm of inv(A).
    *
          KASE = 0
          NORMIN = 'N'
       10 CONTINUE
          CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
          IF( KASE.NE.0 ) THEN
             IF( UPPER ) THEN
    *
    *           Multiply by inv(U').
    *
                CALL SLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A,
         $                   LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
                NORMIN = 'Y'
    *
    *           Multiply by inv(U).
    *
                CALL SLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
         $                   A, LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
             ELSE
    *
    *           Multiply by inv(L).
    *
                CALL SLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
         $                   A, LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
                NORMIN = 'Y'
    *
    *           Multiply by inv(L').
    *
                CALL SLATRS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, A,
         $                   LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
             END IF
    *
    *        Multiply by 1/SCALE if doing so will not cause overflow.
    *
             SCALE = SCALEL*SCALEU
             IF( SCALE.NE.ONE ) THEN
                IX = ISAMAX( N, WORK, 1 )
                IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
         $         GO TO 20
                CALL SRSCL( N, SCALE, WORK, 1 )
             END IF
             GO TO 10
          END IF
    *
    *     Compute the estimate of the reciprocal condition number.
    *
          IF( AINVNM.NE.ZERO )
         $   RCOND = ( ONE / AINVNM ) / ANORM
    *
       20 CONTINUE
          RETURN
    *
    *     End of SPOCON
    *
          END