Attachment 615120 Details for Bug 831690 – fortran source code that reproduces the problem

fortran source code that reproduces the problem

stpt05.f (text/plain), 7.81 KB, created by Mark Sienkiewicz on 2012-09-20 20:52:52 UTC

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Creator: Mark Sienkiewicz

Created: 2012-09-20 20:52:52 UTC

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>      SUBROUTINE STPT05( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX,
>     $                   XACT, LDXACT, FERR, BERR, RESLTS )
>*
>*  -- LAPACK test routine (version 3.1) --
>*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
>*     November 2006
>*
>*     .. Scalar Arguments ..
>      CHARACTER          DIAG, TRANS, UPLO
>      INTEGER            LDB, LDX, LDXACT, N, NRHS
>*     ..
>*     .. Array Arguments ..
>      REAL               AP( * ), B( LDB, * ), BERR( * ), FERR( * ),
>     $                   RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
>*     ..
>*
>*  Purpose
>*  =======
>*
>*  STPT05 tests the error bounds from iterative refinement for the
>*  computed solution to a system of equations A*X = B, where A is a
>*  triangular matrix in packed storage format.
>*
>*  RESLTS(1) = test of the error bound
>*            = norm(X - XACT) / ( norm(X) * FERR )
>*
>*  A large value is returned if this ratio is not less than one.
>*
>*  RESLTS(2) = residual from the iterative refinement routine
>*            = the maximum of BERR / ( (n+1)*EPS + (*) ), where
>*              (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
>*
>*  Arguments
>*  =========
>*
>*  UPLO    (input) CHARACTER*1
>*          Specifies whether the matrix A is upper or lower triangular.
>*          = 'U':  Upper triangular
>*          = 'L':  Lower triangular
>*
>*  TRANS   (input) CHARACTER*1
>*          Specifies the form of the system of equations.
>*          = 'N':  A * X = B  (No transpose)
>*          = 'T':  A'* X = B  (Transpose)
>*          = 'C':  A'* X = B  (Conjugate transpose = Transpose)
>*
>*  DIAG    (input) CHARACTER*1
>*          Specifies whether or not the matrix A is unit triangular.
>*          = 'N':  Non-unit triangular
>*          = 'U':  Unit triangular
>*
>*  N       (input) INTEGER
>*          The number of rows of the matrices X, B, and XACT, and the
>*          order of the matrix A.  N >= 0.
>*
>*  NRHS    (input) INTEGER
>*          The number of columns of the matrices X, B, and XACT.
>*          NRHS >= 0.
>*
>*  AP      (input) REAL array, dimension (N*(N+1)/2)
>*          The upper or lower triangular matrix A, packed columnwise in
>*          a linear array.  The j-th column of A is stored in the array
>*          AP as follows:
>*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
>*          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
>*          If DIAG = 'U', the diagonal elements of A are not referenced
>*          and are assumed to be 1.
>*
>*  B       (input) REAL array, dimension (LDB,NRHS)
>*          The right hand side vectors for the system of linear
>*          equations.
>*
>*  LDB     (input) INTEGER
>*          The leading dimension of the array B.  LDB >= max(1,N).
>*
>*  X       (input) REAL array, dimension (LDX,NRHS)
>*          The computed solution vectors.  Each vector is stored as a
>*          column of the matrix X.
>*
>*  LDX     (input) INTEGER
>*          The leading dimension of the array X.  LDX >= max(1,N).
>*
>*  XACT    (input) REAL array, dimension (LDX,NRHS)
>*          The exact solution vectors.  Each vector is stored as a
>*          column of the matrix XACT.
>*
>*  LDXACT  (input) INTEGER
>*          The leading dimension of the array XACT.  LDXACT >= max(1,N).
>*
>*  FERR    (input) REAL array, dimension (NRHS)
>*          The estimated forward error bounds for each solution vector
>*          X.  If XTRUE is the true solution, FERR bounds the magnitude
>*          of the largest entry in (X - XTRUE) divided by the magnitude
>*          of the largest entry in X.
>*
>*  BERR    (input) REAL array, dimension (NRHS)
>*          The componentwise relative backward error of each solution
>*          vector (i.e., the smallest relative change in any entry of A
>*          or B that makes X an exact solution).
>*
>*  RESLTS  (output) REAL array, dimension (2)
>*          The maximum over the NRHS solution vectors of the ratios:
>*          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
>*          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
>*
>*  =====================================================================
>*
>*     .. Parameters ..
>      REAL               ZERO, ONE
>      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
>*     ..
>*     .. Local Scalars ..
>      LOGICAL            NOTRAN, UNIT, UPPER
>      INTEGER            I, IFU, IMAX, J, JC, K
>      REAL               AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM
>*     ..
>*     .. External Functions ..
>      LOGICAL            LSAME
>      INTEGER            ISAMAX
>      REAL               SLAMCH
>      EXTERNAL           LSAME, ISAMAX, SLAMCH
>*     ..
>*     .. Intrinsic Functions ..
>      INTRINSIC          ABS, MAX, MIN
>*     ..
>*     .. Executable Statements ..
>*
>*     Quick exit if N = 0 or NRHS = 0.
>*
>      IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
>         RESLTS( 1 ) = ZERO
>         RESLTS( 2 ) = ZERO
>         RETURN
>      END IF
>*
>      EPS = SLAMCH( 'Epsilon' )
>      UNFL = SLAMCH( 'Safe minimum' )
>      OVFL = ONE / UNFL
>      UPPER = LSAME( UPLO, 'U' )
>      NOTRAN = LSAME( TRANS, 'N' )
>      UNIT = LSAME( DIAG, 'U' )
>*
>*     Test 1:  Compute the maximum of
>*        norm(X - XACT) / ( norm(X) * FERR )
>*     over all the vectors X and XACT using the infinity-norm.
>*
>      ERRBND = ZERO
>      DO 30 J = 1, NRHS
>         IMAX = ISAMAX( N, X( 1, J ), 1 )
>         XNORM = MAX( ABS( X( IMAX, J ) ), UNFL )
>         DIFF = ZERO
>         DO 10 I = 1, N
>            DIFF = MAX( DIFF, ABS( X( I, J )-XACT( I, J ) ) )
>   10    CONTINUE
>*
>         IF( XNORM.GT.ONE ) THEN
>            GO TO 20
>         ELSE IF( DIFF.LE.OVFL*XNORM ) THEN
>            GO TO 20
>         ELSE
>            ERRBND = ONE / EPS
>            GO TO 30
>         END IF
>*
>   20    CONTINUE
>         IF( DIFF / XNORM.LE.FERR( J ) ) THEN
>            ERRBND = MAX( ERRBND, ( DIFF / XNORM ) / FERR( J ) )
>         ELSE
>            ERRBND = ONE / EPS
>         END IF
>   30 CONTINUE
>      RESLTS( 1 ) = ERRBND
>*
>*     Test 2:  Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where
>*     (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
>*
>      IFU = 0
>      IF( UNIT )
>     $   IFU = 1
>      DO 90 K = 1, NRHS
>         DO 80 I = 1, N
>            TMP = ABS( B( I, K ) )
>            IF( UPPER ) THEN
>               JC = ( ( I-1 )*I ) / 2
>               IF( .NOT.NOTRAN ) THEN
>                  DO 40 J = 1, I - IFU
>                     TMP = TMP + ABS( AP( JC+J ) )*ABS( X( J, K ) )
>   40             CONTINUE
>                  IF( UNIT )
>     $               TMP = TMP + ABS( X( I, K ) )
>               ELSE
>                  JC = JC + I
>                  IF( UNIT ) THEN
>                     TMP = TMP + ABS( X( I, K ) )
>                     JC = JC + I
>                  END IF
>                  DO 50 J = I + IFU, N
>                     TMP = TMP + ABS( AP( JC ) )*ABS( X( J, K ) )
>                     JC = JC + J
>   50             CONTINUE
>               END IF
>            ELSE
>               IF( NOTRAN ) THEN
>                  JC = I
>                  DO 60 J = 1, I - IFU
>                     TMP = TMP + ABS( AP( JC ) )*ABS( X( J, K ) )
>                     JC = JC + N - J
>   60             CONTINUE
>                  IF( UNIT )
>     $               TMP = TMP + ABS( X( I, K ) )
>               ELSE
>                  JC = ( I-1 )*( N-I ) + ( I*( I+1 ) ) / 2
>                  IF( UNIT )
>     $               TMP = TMP + ABS( X( I, K ) )
>                  DO 70 J = I + IFU, N
>                     TMP = TMP + ABS( AP( JC+J-I ) )*ABS( X( J, K ) )
>   70             CONTINUE
>               END IF
>            END IF
>            IF( I.EQ.1 ) THEN
>               AXBI = TMP
>            ELSE
>               AXBI = MIN( AXBI, TMP )
>            END IF
>   80    CONTINUE
>         TMP = BERR( K ) / ( ( N+1 )*EPS+( N+1 )*UNFL /
>     $         MAX( AXBI, ( N+1 )*UNFL ) )
>         IF( K.EQ.1 ) THEN
>            RESLTS( 2 ) = TMP
>         ELSE
>            RESLTS( 2 ) = MAX( RESLTS( 2 ), TMP )
>         END IF
>   90 CONTINUE
>*
>      RETURN
>*
>*     End of STPT05
>*
>      END

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Attachments on bug 831690: 591536 | 615120