LAPACK 3.3.1
Linear Algebra PACKage

ztpt03.f

Go to the documentation of this file.
00001       SUBROUTINE ZTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
00002      $                   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            LDB, LDX, N, NRHS
00011       DOUBLE PRECISION   RESID, SCALE, TSCAL
00012 *     ..
00013 *     .. Array Arguments ..
00014       DOUBLE PRECISION   CNORM( * )
00015       COMPLEX*16         AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  ZTPT03 computes the residual for the solution to a scaled triangular
00022 *  system of equations A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b,
00023 *  when the triangular matrix A is stored in packed format.  Here A**T
00024 *  denotes the transpose of A, A**H denotes the conjugate transpose of
00025 *  A, s is a scalar, and x and b are N by NRHS matrices.  The test ratio
00026 *  is the maximum over the number of right hand sides of
00027 *     norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
00028 *  where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
00029 *
00030 *  Arguments
00031 *  =========
00032 *
00033 *  UPLO    (input) CHARACTER*1
00034 *          Specifies whether the matrix A is upper or lower triangular.
00035 *          = 'U':  Upper triangular
00036 *          = 'L':  Lower triangular
00037 *
00038 *  TRANS   (input) CHARACTER*1
00039 *          Specifies the operation applied to A.
00040 *          = 'N':  A *x = s*b     (No transpose)
00041 *          = 'T':  A**T *x = s*b  (Transpose)
00042 *          = 'C':  A**H *x = s*b  (Conjugate transpose)
00043 *
00044 *  DIAG    (input) CHARACTER*1
00045 *          Specifies whether or not the matrix A is unit triangular.
00046 *          = 'N':  Non-unit triangular
00047 *          = 'U':  Unit triangular
00048 *
00049 *  N       (input) INTEGER
00050 *          The order of the matrix A.  N >= 0.
00051 *
00052 *  NRHS    (input) INTEGER
00053 *          The number of right hand sides, i.e., the number of columns
00054 *          of the matrices X and B.  NRHS >= 0.
00055 *
00056 *  AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
00057 *          The upper or lower triangular matrix A, packed columnwise in
00058 *          a linear array.  The j-th column of A is stored in the array
00059 *          AP as follows:
00060 *          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
00061 *          if UPLO = 'L',
00062 *             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
00063 *
00064 *  SCALE   (input) DOUBLE PRECISION
00065 *          The scaling factor s used in solving the triangular system.
00066 *
00067 *  CNORM   (input) DOUBLE PRECISION array, dimension (N)
00068 *          The 1-norms of the columns of A, not counting the diagonal.
00069 *
00070 *  TSCAL   (input) DOUBLE PRECISION
00071 *          The scaling factor used in computing the 1-norms in CNORM.
00072 *          CNORM actually contains the column norms of TSCAL*A.
00073 *
00074 *  X       (input) COMPLEX*16 array, dimension (LDX,NRHS)
00075 *          The computed solution vectors for the system of linear
00076 *          equations.
00077 *
00078 *  LDX     (input) INTEGER
00079 *          The leading dimension of the array X.  LDX >= max(1,N).
00080 *
00081 *  B       (input) COMPLEX*16 array, dimension (LDB,NRHS)
00082 *          The right hand side vectors for the system of linear
00083 *          equations.
00084 *
00085 *  LDB     (input) INTEGER
00086 *          The leading dimension of the array B.  LDB >= max(1,N).
00087 *
00088 *  WORK    (workspace) COMPLEX*16 array, dimension (N)
00089 *
00090 *  RESID   (output) DOUBLE PRECISION
00091 *          The maximum over the number of right hand sides of
00092 *          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
00093 *
00094 *  =====================================================================
00095 *
00096 *     .. Parameters ..
00097       DOUBLE PRECISION   ONE, ZERO
00098       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00099 *     ..
00100 *     .. Local Scalars ..
00101       INTEGER            IX, J, JJ
00102       DOUBLE PRECISION   EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
00103 *     ..
00104 *     .. External Functions ..
00105       LOGICAL            LSAME
00106       INTEGER            IZAMAX
00107       DOUBLE PRECISION   DLAMCH
00108       EXTERNAL           LSAME, IZAMAX, DLAMCH
00109 *     ..
00110 *     .. External Subroutines ..
00111       EXTERNAL           ZAXPY, ZCOPY, ZDSCAL, ZTPMV
00112 *     ..
00113 *     .. Intrinsic Functions ..
00114       INTRINSIC          ABS, DBLE, DCMPLX, MAX
00115 *     ..
00116 *     .. Executable Statements ..
00117 *
00118 *     Quick exit if N = 0.
00119 *
00120       IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
00121          RESID = ZERO
00122          RETURN
00123       END IF
00124       EPS = DLAMCH( 'Epsilon' )
00125       SMLNUM = DLAMCH( 'Safe minimum' )
00126 *
00127 *     Compute the norm of the triangular matrix A using the column
00128 *     norms already computed by ZLATPS.
00129 *
00130       TNORM = 0.D0
00131       IF( LSAME( DIAG, 'N' ) ) THEN
00132          IF( LSAME( UPLO, 'U' ) ) THEN
00133             JJ = 1
00134             DO 10 J = 1, N
00135                TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
00136                JJ = JJ + J
00137    10       CONTINUE
00138          ELSE
00139             JJ = 1
00140             DO 20 J = 1, N
00141                TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
00142                JJ = JJ + N - J + 1
00143    20       CONTINUE
00144          END IF
00145       ELSE
00146          DO 30 J = 1, N
00147             TNORM = MAX( TNORM, TSCAL+CNORM( J ) )
00148    30    CONTINUE
00149       END IF
00150 *
00151 *     Compute the maximum over the number of right hand sides of
00152 *        norm(op(A)*x - s*b) / ( norm(A) * norm(x) * EPS ).
00153 *
00154       RESID = ZERO
00155       DO 40 J = 1, NRHS
00156          CALL ZCOPY( N, X( 1, J ), 1, WORK, 1 )
00157          IX = IZAMAX( N, WORK, 1 )
00158          XNORM = MAX( ONE, ABS( X( IX, J ) ) )
00159          XSCAL = ( ONE / XNORM ) / DBLE( N )
00160          CALL ZDSCAL( N, XSCAL, WORK, 1 )
00161          CALL ZTPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 )
00162          CALL ZAXPY( N, DCMPLX( -SCALE*XSCAL ), B( 1, J ), 1, WORK, 1 )
00163          IX = IZAMAX( N, WORK, 1 )
00164          ERR = TSCAL*ABS( WORK( IX ) )
00165          IX = IZAMAX( N, X( 1, J ), 1 )
00166          XNORM = ABS( X( IX, J ) )
00167          IF( ERR*SMLNUM.LE.XNORM ) THEN
00168             IF( XNORM.GT.ZERO )
00169      $         ERR = ERR / XNORM
00170          ELSE
00171             IF( ERR.GT.ZERO )
00172      $         ERR = ONE / EPS
00173          END IF
00174          IF( ERR*SMLNUM.LE.TNORM ) THEN
00175             IF( TNORM.GT.ZERO )
00176      $         ERR = ERR / TNORM
00177          ELSE
00178             IF( ERR.GT.ZERO )
00179      $         ERR = ONE / EPS
00180          END IF
00181          RESID = MAX( RESID, ERR )
00182    40 CONTINUE
00183 *
00184       RETURN
00185 *
00186 *     End of ZTPT03
00187 *
00188       END
 All Files Functions