zgesvx.f

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*                       solution and error bounds are computed because
*                       there are a number of situations where the
*                       computed solution can be more accurate than the
*                       value of RCOND would suggest.
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            COLEQU, EQUIL, NOFACT, NOTRAN, ROWEQU
      CHARACTER          NORM
      INTEGER            I, INFEQU, J
      DOUBLE PRECISION   AMAX, ANORM, BIGNUM, COLCND, RCMAX, RCMIN,
     $                   ROWCND, RPVGRW, SMLNUM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH, ZLANGE, ZLANTR
      EXTERNAL           LSAME, DLAMCH, ZLANGE, ZLANTR
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA, ZGECON, ZGEEQU, ZGERFS, ZGETRF, ZGETRS,
     $                   ZLACPY, ZLAQGE
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. Executable Statements ..
*
      INFO = 0
      NOFACT = LSAME( FACT, 'N' )
      EQUIL = LSAME( FACT, 'E' )
      NOTRAN = LSAME( TRANS, 'N' )
      IF( NOFACT .OR. EQUIL ) THEN
         EQUED = 'N'
         ROWEQU = .FALSE.
         COLEQU = .FALSE.
      ELSE
         ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' )
         COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' )
         SMLNUM = DLAMCH( 'Safe minimum' )
         BIGNUM = ONE / SMLNUM
      END IF
*
*     Test the input parameters.
*
      IF( .NOT.NOFACT .AND. .NOT.EQUIL .AND. .NOT.LSAME( FACT, 'F' ) )
     $     THEN
         INFO = -1
      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
     $         LSAME( TRANS, 'C' ) ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -6
      ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
         INFO = -8
      ELSE IF( LSAME( FACT, 'F' ) .AND. .NOT.
     $         ( ROWEQU .OR. COLEQU .OR. LSAME( EQUED, 'N' ) ) ) THEN
         INFO = -10
      ELSE
         IF( ROWEQU ) THEN
            RCMIN = BIGNUM
            RCMAX = ZERO
            DO 10 J = 1, N
               RCMIN = MIN( RCMIN, R( J ) )
               RCMAX = MAX( RCMAX, R( J ) )
   10       CONTINUE
            IF( RCMIN.LE.ZERO ) THEN
               INFO = -11
            ELSE IF( N.GT.0 ) THEN
               ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
            ELSE
               ROWCND = ONE
            END IF
         END IF
         IF( COLEQU .AND. INFO.EQ.0 ) THEN
            RCMIN = BIGNUM
            RCMAX = ZERO
            DO 20 J = 1, N
               RCMIN = MIN( RCMIN, C( J ) )
               RCMAX = MAX( RCMAX, C( J ) )
   20       CONTINUE
            IF( RCMIN.LE.ZERO ) THEN
               INFO = -12
            ELSE IF( N.GT.0 ) THEN
               COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
            ELSE
               COLCND = ONE
            END IF
         END IF
         IF( INFO.EQ.0 ) THEN
            IF( LDB.LT.MAX( 1, N ) ) THEN
               INFO = -14
            ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
               INFO = -16
            END IF
         END IF
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'ZGESVX', -INFO )
         RETURN
      END IF
*
      IF( EQUIL ) THEN
*
*        Compute row and column scalings to equilibrate the matrix A.
*
         CALL ZGEEQU( N, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFEQU )
         IF( INFEQU.EQ.0 ) THEN
*
*           Equilibrate the matrix.
*
            CALL ZLAQGE( N, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
     $                   EQUED )
            ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' )
            COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' )
         END IF
      END IF
*
*     Scale the right hand side.
*
      IF( NOTRAN ) THEN
         IF( ROWEQU ) THEN
            DO 40 J = 1, NRHS
               DO 30 I = 1, N
                  B( I, J ) = R( I )*B( I, J )
   30          CONTINUE
   40       CONTINUE
         END IF
      ELSE IF( COLEQU ) THEN
         DO 60 J = 1, NRHS
            DO 50 I = 1, N
               B( I, J ) = C( I )*B( I, J )
   50       CONTINUE
   60    CONTINUE
      END IF
*
      IF( NOFACT .OR. EQUIL ) THEN
*
*        Compute the LU factorization of A.
*
         CALL ZLACPY( 'Full', N, N, A, LDA, AF, LDAF )
         CALL ZGETRF( N, N, AF, LDAF, IPIV, INFO )
*
*        Return if INFO is non-zero.
*
         IF( INFO.GT.0 ) THEN
*
*           Compute the reciprocal pivot growth factor of the
*           leading rank-deficient INFO columns of A.
*
            RPVGRW = ZLANTR( 'M', 'U', 'N', INFO, INFO, AF, LDAF,
     $               RWORK )
            IF( RPVGRW.EQ.ZERO ) THEN
               RPVGRW = ONE
            ELSE
               RPVGRW = ZLANGE( 'M', N, INFO, A, LDA, RWORK ) /
     $                  RPVGRW
            END IF
            RWORK( 1 ) = RPVGRW
            RCOND = ZERO
            RETURN
         END IF
      END IF
*
*     Compute the norm of the matrix A and the
*     reciprocal pivot growth factor RPVGRW.
*
      IF( NOTRAN ) THEN
         NORM = '1'
      ELSE
         NORM = 'I'
      END IF
      ANORM = ZLANGE( NORM, N, N, A, LDA, RWORK )
      RPVGRW = ZLANTR( 'M', 'U', 'N', N, N, AF, LDAF, RWORK )
      IF( RPVGRW.EQ.ZERO ) THEN
         RPVGRW = ONE
      ELSE
         RPVGRW = ZLANGE( 'M', N, N, A, LDA, RWORK ) / RPVGRW
      END IF
*
*     Compute the reciprocal of the condition number of A.
*
      CALL ZGECON( NORM, N, AF, LDAF, ANORM, RCOND, WORK, RWORK, INFO )
*
*     Compute the solution matrix X.
*
      CALL ZLACPY( 'Full', N, NRHS, B, LDB, X, LDX )
      CALL ZGETRS( TRANS, N, NRHS, AF, LDAF, IPIV, X, LDX, INFO )
*
*     Use iterative refinement to improve the computed solution and
*     compute error bounds and backward error estimates for it.
*
      CALL ZGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X,
     $             LDX, FERR, BERR, WORK, RWORK, INFO )
*
*     Transform the solution matrix X to a solution of the original
*     system.
*
      IF( NOTRAN ) THEN
         IF( COLEQU ) THEN
            DO 80 J = 1, NRHS
               DO 70 I = 1, N
                  X( I, J ) = C( I )*X( I, J )
   70          CONTINUE
   80       CONTINUE
            DO 90 J = 1, NRHS
               FERR( J ) = FERR( J ) / COLCND
   90       CONTINUE
         END IF
      ELSE IF( ROWEQU ) THEN
         DO 110 J = 1, NRHS
            DO 100 I = 1, N
               X( I, J ) = R( I )*X( I, J )
  100       CONTINUE
  110    CONTINUE
         DO 120 J = 1, NRHS
            FERR( J ) = FERR( J ) / ROWCND
  120    CONTINUE
      END IF
*
*     Set INFO = N+1 if the matrix is singular to working precision.
*
      IF( RCOND.LT.DLAMCH( 'Epsilon' ) )
     $   INFO = N + 1
*
      RWORK( 1 ) = RPVGRW
      RETURN
*
*     End of ZGESVX
*
      END