216 lines
7.0 KiB
FortranFixed
216 lines
7.0 KiB
FortranFixed
SUBROUTINE CPPT05( UPLO, 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 UPLO
|
|
INTEGER LDB, LDX, LDXACT, N, NRHS
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL BERR( * ), FERR( * ), RESLTS( * )
|
|
COMPLEX AP( * ), B( LDB, * ), X( LDX, * ),
|
|
$ XACT( LDXACT, * )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* CPPT05 tests the error bounds from iterative refinement for the
|
|
* computed solution to a system of equations A*X = B, where A is a
|
|
* Hermitian 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 upper or lower triangular part of the
|
|
* Hermitian matrix A is stored.
|
|
* = 'U': Upper triangular
|
|
* = 'L': Lower 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) COMPLEX array, dimension (N*(N+1)/2)
|
|
* The upper or lower triangle of the Hermitian 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.
|
|
*
|
|
* B (input) COMPLEX 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) COMPLEX 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) COMPLEX 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 UPPER
|
|
INTEGER I, IMAX, J, JC, K
|
|
REAL AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM
|
|
COMPLEX ZDUM
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
INTEGER ICAMAX
|
|
REAL SLAMCH
|
|
EXTERNAL LSAME, ICAMAX, SLAMCH
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, AIMAG, MAX, MIN, REAL
|
|
* ..
|
|
* .. Statement Functions ..
|
|
REAL CABS1
|
|
* ..
|
|
* .. Statement Function definitions ..
|
|
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
|
|
* ..
|
|
* .. 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' )
|
|
*
|
|
* 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 = ICAMAX( N, X( 1, J ), 1 )
|
|
XNORM = MAX( CABS1( X( IMAX, J ) ), UNFL )
|
|
DIFF = ZERO
|
|
DO 10 I = 1, N
|
|
DIFF = MAX( DIFF, CABS1( 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 )
|
|
*
|
|
DO 90 K = 1, NRHS
|
|
DO 80 I = 1, N
|
|
TMP = CABS1( B( I, K ) )
|
|
IF( UPPER ) THEN
|
|
JC = ( ( I-1 )*I ) / 2
|
|
DO 40 J = 1, I - 1
|
|
TMP = TMP + CABS1( AP( JC+J ) )*CABS1( X( J, K ) )
|
|
40 CONTINUE
|
|
TMP = TMP + ABS( REAL( AP( JC+I ) ) )*CABS1( X( I, K ) )
|
|
JC = JC + I + I
|
|
DO 50 J = I + 1, N
|
|
TMP = TMP + CABS1( AP( JC ) )*CABS1( X( J, K ) )
|
|
JC = JC + J
|
|
50 CONTINUE
|
|
ELSE
|
|
JC = I
|
|
DO 60 J = 1, I - 1
|
|
TMP = TMP + CABS1( AP( JC ) )*CABS1( X( J, K ) )
|
|
JC = JC + N - J
|
|
60 CONTINUE
|
|
TMP = TMP + ABS( REAL( AP( JC ) ) )*CABS1( X( I, K ) )
|
|
DO 70 J = I + 1, N
|
|
TMP = TMP + CABS1( AP( JC+J-I ) )*CABS1( X( J, K ) )
|
|
70 CONTINUE
|
|
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 CPPT05
|
|
*
|
|
END
|