LAPACK 3.3.1
Linear Algebra PACKage

ztrt03.f

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00001       SUBROUTINE ZTRT03( UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE,
00002      $                   CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID )
00003 *
00004 *  -- LAPACK test routine (version 3.1) --
00005 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          DIAG, TRANS, UPLO
00010       INTEGER            LDA, LDB, LDX, N, NRHS
00011       DOUBLE PRECISION   RESID, SCALE, TSCAL
00012 *     ..
00013 *     .. Array Arguments ..
00014       DOUBLE PRECISION   CNORM( * )
00015       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * ),
00016      $                   X( LDX, * )
00017 *     ..
00018 *
00019 *  Purpose
00020 *  =======
00021 *
00022 *  ZTRT03 computes the residual for the solution to a scaled triangular
00023 *  system of equations A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b.
00024 *  Here A is a triangular matrix, A**T denotes the transpose of A, A**H
00025 *  denotes the conjugate transpose of A, s is a scalar, and x and b are
00026 *  N by NRHS matrices.  The test ratio is the maximum over the number of
00027 *  right hand sides of
00028 *     norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
00029 *  where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
00030 *
00031 *  Arguments
00032 *  =========
00033 *
00034 *  UPLO    (input) CHARACTER*1
00035 *          Specifies whether the matrix A is upper or lower triangular.
00036 *          = 'U':  Upper triangular
00037 *          = 'L':  Lower triangular
00038 *
00039 *  TRANS   (input) CHARACTER*1
00040 *          Specifies the operation applied to A.
00041 *          = 'N':  A *x = s*b     (No transpose)
00042 *          = 'T':  A**T *x = s*b  (Transpose)
00043 *          = 'C':  A**H *x = s*b  (Conjugate transpose)
00044 *
00045 *  DIAG    (input) CHARACTER*1
00046 *          Specifies whether or not the matrix A is unit triangular.
00047 *          = 'N':  Non-unit triangular
00048 *          = 'U':  Unit triangular
00049 *
00050 *  N       (input) INTEGER
00051 *          The order of the matrix A.  N >= 0.
00052 *
00053 *  NRHS    (input) INTEGER
00054 *          The number of right hand sides, i.e., the number of columns
00055 *          of the matrices X and B.  NRHS >= 0.
00056 *
00057 *  A       (input) COMPLEX*16 array, dimension (LDA,N)
00058 *          The triangular matrix A.  If UPLO = 'U', the leading n by n
00059 *          upper triangular part of the array A contains the upper
00060 *          triangular matrix, and the strictly lower triangular part of
00061 *          A is not referenced.  If UPLO = 'L', the leading n by n lower
00062 *          triangular part of the array A contains the lower triangular
00063 *          matrix, and the strictly upper triangular part of A is not
00064 *          referenced.  If DIAG = 'U', the diagonal elements of A are
00065 *          also not referenced and are assumed to be 1.
00066 *
00067 *  LDA     (input) INTEGER
00068 *          The leading dimension of the array A.  LDA >= max(1,N).
00069 *
00070 *  SCALE   (input) DOUBLE PRECISION
00071 *          The scaling factor s used in solving the triangular system.
00072 *
00073 *  CNORM   (input) DOUBLE PRECISION array, dimension (N)
00074 *          The 1-norms of the columns of A, not counting the diagonal.
00075 *
00076 *  TSCAL   (input) DOUBLE PRECISION
00077 *          The scaling factor used in computing the 1-norms in CNORM.
00078 *          CNORM actually contains the column norms of TSCAL*A.
00079 *
00080 *  X       (input) COMPLEX*16 array, dimension (LDX,NRHS)
00081 *          The computed solution vectors for the system of linear
00082 *          equations.
00083 *
00084 *  LDX     (input) INTEGER
00085 *          The leading dimension of the array X.  LDX >= max(1,N).
00086 *
00087 *  B       (input) COMPLEX*16 array, dimension (LDB,NRHS)
00088 *          The right hand side vectors for the system of linear
00089 *          equations.
00090 *
00091 *  LDB     (input) INTEGER
00092 *          The leading dimension of the array B.  LDB >= max(1,N).
00093 *
00094 *  WORK    (workspace) COMPLEX*16 array, dimension (N)
00095 *
00096 *  RESID   (output) DOUBLE PRECISION
00097 *          The maximum over the number of right hand sides of
00098 *          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
00099 *
00100 *  =====================================================================
00101 *
00102 *     .. Parameters ..
00103       DOUBLE PRECISION   ONE, ZERO
00104       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00105 *     ..
00106 *     .. Local Scalars ..
00107       INTEGER            IX, J
00108       DOUBLE PRECISION   EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
00109 *     ..
00110 *     .. External Functions ..
00111       LOGICAL            LSAME
00112       INTEGER            IZAMAX
00113       DOUBLE PRECISION   DLAMCH
00114       EXTERNAL           LSAME, IZAMAX, DLAMCH
00115 *     ..
00116 *     .. External Subroutines ..
00117       EXTERNAL           ZAXPY, ZCOPY, ZDSCAL, ZTRMV
00118 *     ..
00119 *     .. Intrinsic Functions ..
00120       INTRINSIC          ABS, DBLE, DCMPLX, MAX
00121 *     ..
00122 *     .. Executable Statements ..
00123 *
00124 *     Quick exit if N = 0
00125 *
00126       IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
00127          RESID = ZERO
00128          RETURN
00129       END IF
00130       EPS = DLAMCH( 'Epsilon' )
00131       SMLNUM = DLAMCH( 'Safe minimum' )
00132 *
00133 *     Compute the norm of the triangular matrix A using the column
00134 *     norms already computed by ZLATRS.
00135 *
00136       TNORM = ZERO
00137       IF( LSAME( DIAG, 'N' ) ) THEN
00138          DO 10 J = 1, N
00139             TNORM = MAX( TNORM, TSCAL*ABS( A( J, J ) )+CNORM( J ) )
00140    10    CONTINUE
00141       ELSE
00142          DO 20 J = 1, N
00143             TNORM = MAX( TNORM, TSCAL+CNORM( J ) )
00144    20    CONTINUE
00145       END IF
00146 *
00147 *     Compute the maximum over the number of right hand sides of
00148 *        norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
00149 *
00150       RESID = ZERO
00151       DO 30 J = 1, NRHS
00152          CALL ZCOPY( N, X( 1, J ), 1, WORK, 1 )
00153          IX = IZAMAX( N, WORK, 1 )
00154          XNORM = MAX( ONE, ABS( X( IX, J ) ) )
00155          XSCAL = ( ONE / XNORM ) / DBLE( N )
00156          CALL ZDSCAL( N, XSCAL, WORK, 1 )
00157          CALL ZTRMV( UPLO, TRANS, DIAG, N, A, LDA, WORK, 1 )
00158          CALL ZAXPY( N, DCMPLX( -SCALE*XSCAL ), B( 1, J ), 1, WORK, 1 )
00159          IX = IZAMAX( N, WORK, 1 )
00160          ERR = TSCAL*ABS( WORK( IX ) )
00161          IX = IZAMAX( N, X( 1, J ), 1 )
00162          XNORM = ABS( X( IX, J ) )
00163          IF( ERR*SMLNUM.LE.XNORM ) THEN
00164             IF( XNORM.GT.ZERO )
00165      $         ERR = ERR / XNORM
00166          ELSE
00167             IF( ERR.GT.ZERO )
00168      $         ERR = ONE / EPS
00169          END IF
00170          IF( ERR*SMLNUM.LE.TNORM ) THEN
00171             IF( TNORM.GT.ZERO )
00172      $         ERR = ERR / TNORM
00173          ELSE
00174             IF( ERR.GT.ZERO )
00175      $         ERR = ONE / EPS
00176          END IF
00177          RESID = MAX( RESID, ERR )
00178    30 CONTINUE
00179 *
00180       RETURN
00181 *
00182 *     End of ZTRT03
00183 *
00184       END
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