matrix.f90

CLM集合卡曼滤波数据同化算法

      DO 20 I = 1, P
         Z = Z*RECBAS
         IF( Y.LT.ONE )&
           OLDY = Y
         Y = SLAMC3( Y, Z )
   20 CONTINUE
      IF( Y.GE.ONE )&
        Y = OLDY

      DO 30 I = 1, EMAX
         Y = SLAMC3( Y*BETA, ZERO )
   30 CONTINUE

      RMAX = Y
      RETURN

      END
!============================================================================



      REAL             FUNCTION SLAPY2( X, Y )

      REAL               X, Y


      REAL               ZERO
      PARAMETER          ( ZERO = 0.0E0 )
      REAL               ONE
      PARAMETER          ( ONE = 1.0E0 )

      REAL               W, XABS, YABS, Z

      INTRINSIC          ABS, MAX, MIN, SQRT

      XABS = ABS( X )
      YABS = ABS( Y )
      W = MAX( XABS, YABS )
      Z = MIN( XABS, YABS )
      IF( Z.EQ.ZERO ) THEN
         SLAPY2 = W
      ELSE
         SLAPY2 = W*SQRT( ONE+( Z / W )**2 )
      END IF
      RETURN

      END
!============================================================================


      SUBROUTINE SLARFG( N, ALPHA, X, INCX, TAU )

      INTEGER            INCX, N
      REAL               ALPHA, TAU

      REAL               X( * )

      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )

      INTEGER            J, KNT
      REAL               BETA, RSAFMN, SAFMIN, XNORM

      REAL               SLAMCH, SLAPY2, SNRM2
      EXTERNAL           SLAMCH, SLAPY2, SNRM2

      INTRINSIC          ABS, SIGN

      EXTERNAL           SSCAL

      IF( N.LE.1 ) THEN
         TAU = ZERO
         RETURN
      END IF

      XNORM = SNRM2( N-1, X, INCX )

      IF( XNORM.EQ.ZERO ) THEN

         TAU = ZERO
      ELSE

         BETA = -SIGN( SLAPY2( ALPHA, XNORM ), ALPHA )
         SAFMIN = SLAMCH( 'S' ) / SLAMCH( 'E' )
         IF( ABS( BETA ).LT.SAFMIN ) THEN

            RSAFMN = ONE / SAFMIN
            KNT = 0
   10       CONTINUE
            KNT = KNT + 1
            CALL SSCAL( N-1, RSAFMN, X, INCX )
            BETA = BETA*RSAFMN
            ALPHA = ALPHA*RSAFMN
            IF( ABS( BETA ).LT.SAFMIN )&
              GO TO 10

            XNORM = SNRM2( N-1, X, INCX )
            BETA = -SIGN( SLAPY2( ALPHA, XNORM ), ALPHA )
            TAU = ( BETA-ALPHA ) / BETA
            CALL SSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX )

            ALPHA = BETA
            DO 20 J = 1, KNT
               ALPHA = ALPHA*SAFMIN
   20       CONTINUE
         ELSE
            TAU = ( BETA-ALPHA ) / BETA
            CALL SSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX )
            ALPHA = BETA
         END IF
      END IF

      RETURN

      END
!============================================================================


      SUBROUTINE SLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )

      CHARACTER          UPLO
      INTEGER            LDA, LDW, N, NB

      REAL               A( LDA, * ), E( * ), TAU( * ), W( LDW, * )





      REAL               ZERO, ONE, HALF
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0, HALF = 0.5E+0 )

      INTEGER            I, IW
      REAL               ALPHA

      EXTERNAL           SAXPY, SGEMV, SLARFG, SSCAL, SSYMV

      LOGICAL            LSAME
      REAL               SDOT
      EXTERNAL           LSAME, SDOT

      INTRINSIC          MIN

      IF( N.LE.0 )&
        RETURN

      IF( LSAME( UPLO, 'U' ) ) THEN

         DO 10 I = N, N - NB + 1, -1
            IW = I - N + NB
            IF( I.LT.N ) THEN

               CALL SGEMV( 'No transpose', I, N-I, -ONE, A( 1, I+1 ),&
                          LDA, W( I, IW+1 ), LDW, ONE, A( 1, I ), 1 )
               CALL SGEMV( 'No transpose', I, N-I, -ONE, W( 1, IW+1 ),&
                          LDW, A( I, I+1 ), LDA, ONE, A( 1, I ), 1 )
            END IF
            IF( I.GT.1 ) THEN

               CALL SLARFG( I-1, A( I-1, I ), A( 1, I ), 1, TAU( I-1 ) )
               E( I-1 ) = A( I-1, I )
               A( I-1, I ) = ONE

               CALL SSYMV( 'Upper', I-1, ONE, A, LDA, A( 1, I ), 1,&
                          ZERO, W( 1, IW ), 1 )
               IF( I.LT.N ) THEN
                  CALL SGEMV( 'Transpose', I-1, N-I, ONE, W( 1, IW+1 ),&
                             LDW, A( 1, I ), 1, ZERO, W( I+1, IW ), 1 )
                  CALL SGEMV( 'No transpose', I-1, N-I, -ONE,&
                             A( 1, I+1 ), LDA, W( I+1, IW ), 1, ONE,&
                             W( 1, IW ), 1 )
                  CALL SGEMV( 'Transpose', I-1, N-I, ONE, A( 1, I+1 ),&
                             LDA, A( 1, I ), 1, ZERO, W( I+1, IW ), 1 )
                  CALL SGEMV( 'No transpose', I-1, N-I, -ONE,&
                             W( 1, IW+1 ), LDW, W( I+1, IW ), 1, ONE,&
                             W( 1, IW ), 1 )
               END IF
               CALL SSCAL( I-1, TAU( I-1 ), W( 1, IW ), 1 )
               ALPHA = -HALF*TAU( I-1 )*SDOT( I-1, W( 1, IW ), 1,&
                      A( 1, I ), 1 )
               CALL SAXPY( I-1, ALPHA, A( 1, I ), 1, W( 1, IW ), 1 )
            END IF

   10    CONTINUE
      ELSE

         DO 20 I = 1, NB

            CALL SGEMV( 'No transpose', N-I+1, I-1, -ONE, A( I, 1 ),&
                       LDA, W( I, 1 ), LDW, ONE, A( I, I ), 1 )
            CALL SGEMV( 'No transpose', N-I+1, I-1, -ONE, W( I, 1 ),&
                       LDW, A( I, 1 ), LDA, ONE, A( I, I ), 1 )
            IF( I.LT.N ) THEN

               CALL SLARFG( N-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1,&
                           TAU( I ) )
               E( I ) = A( I+1, I )
               A( I+1, I ) = ONE

               CALL SSYMV( 'Lower', N-I, ONE, A( I+1, I+1 ), LDA,&
                          A( I+1, I ), 1, ZERO, W( I+1, I ), 1 )
               CALL SGEMV( 'Transpose', N-I, I-1, ONE, W( I+1, 1 ), LDW,&
                          A( I+1, I ), 1, ZERO, W( 1, I ), 1 )
               CALL SGEMV( 'No transpose', N-I, I-1, -ONE, A( I+1, 1 ),&
                          LDA, W( 1, I ), 1, ONE, W( I+1, I ), 1 )
               CALL SGEMV( 'Transpose', N-I, I-1, ONE, A( I+1, 1 ), LDA,&
                          A( I+1, I ), 1, ZERO, W( 1, I ), 1 )
               CALL SGEMV( 'No transpose', N-I, I-1, -ONE, W( I+1, 1 ),&
                          LDW, W( 1, I ), 1, ONE, W( I+1, I ), 1 )
               CALL SSCAL( N-I, TAU( I ), W( I+1, I ), 1 )
               ALPHA = -HALF*TAU( I )*SDOT( N-I, W( I+1, I ), 1,&
                      A( I+1, I ), 1 )
               CALL SAXPY( N-I, ALPHA, A( I+1, I ), 1, W( I+1, I ), 1 )
            END IF

   20    CONTINUE
      END IF

      RETURN

      END
!============================================================================




      REAL             FUNCTION SNRM2 ( N, X, INCX )

      INTEGER                           INCX, N

      REAL                              X( * )

      REAL                  ONE         , ZERO
      PARAMETER           ( ONE = 1.0E+0, ZERO = 0.0E+0 )

      INTEGER               IX
      REAL                  ABSXI, NORM, SCALE, SSQ

      INTRINSIC             ABS, SQRT

      IF( N.LT.1 .OR. INCX.LT.1 )THEN
         NORM  = ZERO
      ELSE IF( N.EQ.1 )THEN
         NORM  = ABS( X( 1 ) )
      ELSE
         SCALE = ZERO
         SSQ   = ONE

         DO 10, IX = 1, 1 + ( N - 1 )*INCX, INCX
            IF( X( IX ).NE.ZERO )THEN
               ABSXI = ABS( X( IX ) )
               IF( SCALE.LT.ABSXI )THEN
                  SSQ   = ONE   + SSQ*( SCALE/ABSXI )**2
                  SCALE = ABSXI
               ELSE
                  SSQ   = SSQ   +     ( ABSXI/SCALE )**2
               END IF
            END IF
   10    CONTINUE
         NORM  = SCALE * SQRT( SSQ )
      END IF

      SNRM2 = NORM
      RETURN

      END
!============================================================================



      SUBROUTINE SPTTRF( N, D, E, INFO )

      INTEGER            INFO, N

      REAL               D( * ), E( * )


      REAL               ZERO
      PARAMETER          ( ZERO = 0.0E+0 )

      INTEGER            I, I4
      REAL               EI

      EXTERNAL           XERBLA

      INTRINSIC          MOD

      INFO = 0
      IF( N.LT.0 ) THEN
         INFO = -1
         CALL XERBLA( 'SPTTRF', -INFO )
         RETURN
      END IF

      IF( N.EQ.0 )&
        RETURN

      I4 = MOD( N-1, 4 )
      DO 10 I = 1, I4
         IF( D( I ).LE.ZERO ) THEN
            INFO = I
            GO TO 30
         END IF
         EI = E( I )
         E( I ) = EI / D( I )
         D( I+1 ) = D( I+1 ) - E( I )*EI
   10 CONTINUE

      DO 20 I = I4 + 1, N - 4, 4

         IF( D( I ).LE.ZERO ) THEN
            INFO = I
            GO TO 30
         END IF

         EI = E( I )
         E( I ) = EI / D( I )
         D( I+1 ) = D( I+1 ) - E( I )*EI

         IF( D( I+1 ).LE.ZERO ) THEN
            INFO = I + 1
            GO TO 30
         END IF

         EI = E( I+1 )
         E( I+1 ) = EI / D( I+1 )
         D( I+2 ) = D( I+2 ) - E( I+1 )*EI

         IF( D( I+2 ).LE.ZERO ) THEN
            INFO = I + 2
            GO TO 30
         END IF

         EI = E( I+2 )
         E( I+2 ) = EI / D( I+2 )
         D( I+3 ) = D( I+3 ) - E( I+2 )*EI

         IF( D( I+3 ).LE.ZERO ) THEN
            INFO = I + 3
            GO TO 30
         END IF

         EI = E( I+3 )
         E( I+3 ) = EI / D( I+3 )
         D( I+4 ) = D( I+4 ) - E( I+3 )*EI
   20 CONTINUE

      IF( D( N ).LE.ZERO )&
        INFO = N

   30 CONTINUE
      RETURN

      END
!============================================================================


      subroutine sscal(n,sa,sx,incx)

      real sa,sx(*)
      integer i,incx,m,mp1,n,nincx

      if( n.le.0 .or. incx.le.0 )return
      if(incx.eq.1)go to 20

      nincx = n*incx
      do 10 i = 1,nincx,incx
        sx(i) = sa*sx(i)
   10 continue
      return

   20 m = mod(n,5)
      if( m .eq. 0 ) go to 40
      do 30 i = 1,m
        sx(i) = sa*sx(i)
   30 continue
      if( n .lt. 5 ) return
   40 mp1 = m + 1
      do 50 i = mp1,n,5
        sx(i) = sa*sx(i)
        sx(i + 1) = sa*sx(i + 1)
        sx(i + 2) = sa*sx(i + 2)
        sx(i + 3) = sa*sx(i + 3)
        sx(i + 4) = sa*sx(i + 4)
   50 continue
      return
      end
!============================================================================





      SUBROUTINE SSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E,&
                        M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK,&
                        INFO )

      CHARACTER          ORDER, RANGE
      INTEGER            IL, INFO, IU, M, N, NSPLIT
      REAL               ABSTOL, VL, VU

      INTEGER            IBLOCK( * ), ISPLIT( * ), IWORK( * )
      REAL               D( * ), E( * ), W( * ), WORK( * )

      COMMON             / LATIME / OPS, ITCNT

      REAL               ITCNT, OPS

      REAL               ZERO, ONE, TWO, HALF
      PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0,&
                        HALF = 1.0E0 / TWO )
      REAL               FUDGE, RELFAC
      PARAMETER          ( FUDGE = 2.0E0, RELFAC = 2.0E0 )

      LOGICAL            NCNVRG, TOOFEW
      INTEGER            IB, IBEGIN, IDISCL, IDISCU, IE, IEND, IINFO,&
                        IM, IN, IOFF, IORDER, IOUT, IRANGE, ITMAX,&
                        ITMP1, IW, IWOFF, J, JB, JDISC, JE, NB, NWL,&
                        NWU
      REAL               ATOLI, BNORM, GL, GU, PIVMIN, RTOLI, SAFEMN,&
                        TMP1, TMP2, TNORM, ULP, WKILL, WL, WLU, WU, WUL

      INTEGER            IDUMMA( 1 )

      LOGICAL            LSAME
      INTEGER            ILAENV
      REAL               SLAMCH
      EXTERNAL           LSAME, ILAENV, SLAMCH

      EXTERNAL           SLAEBZ, XERBLA

      INTRINSIC          ABS, INT, LOG, MAX, MIN, SQRT

      INFO = 0

      IF( LSAME( RANGE, 'A' ) ) THEN
         IRANGE = 1
      ELSE IF( LSAME( RANGE, 'V' ) ) THEN
         IRANGE = 2
      ELSE IF( LSAME( RANGE, 'I' ) ) THEN
         IRANGE = 3
      ELSE
         IRANGE = 0
      END IF

      IF( LSAME( ORDER, 'B' ) ) THEN
         IORDER = 2
      ELSE IF( LSAME( ORDER, 'E' ) ) THEN
         IORDER = 1
      ELSE
         IORDER = 0
      END IF

      IF( IRANGE.LE.0 ) THEN
         INFO = -1
      ELSE IF( IORDER.LE.0 ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( IRANGE.EQ.2 ) THEN
         IF( VL.GE.VU ) INFO = -5
      ELSE IF( IRANGE.EQ.3 .AND. ( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) )&
               THEN
         INFO = -6
      ELSE IF( IRANGE.EQ.3 .AND. ( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) )&
               THEN
         INFO = -7
      END IF

      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'SSTEBZ', -INFO )
         RETURN
      END IF

      INFO = 0
      NCNVRG = .FALSE.
      TOOFEW = .FALSE.

      M = 0
      IF( N.EQ.0 )&
        RETURN

      IF( IRANGE.EQ.3 .AND. IL.EQ.1 .AND. IU.EQ.N )&
        IRANGE = 1

      SAFEMN = SLAMCH( 'S' )
      ULP = SLAMCH( 'P' )
      OPS = OPS + 1
      RTOLI = ULP*RELFAC
      NB = ILAEN