LAPACK: TESTING/EIG/zunt03.f Source File

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00001       SUBROUTINE ZUNT03( RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK,
00002      $                   RWORK, RESULT, INFO )
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*( * )    RC
00010       INTEGER            INFO, K, LDU, LDV, LWORK, MU, MV, N
00011       DOUBLE PRECISION   RESULT
00012 *     ..
00013 *     .. Array Arguments ..
00014       DOUBLE PRECISION   RWORK( * )
00015       COMPLEX*16         U( LDU, * ), V( LDV, * ), WORK( * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  ZUNT03 compares two unitary matrices U and V to see if their
00022 *  corresponding rows or columns span the same spaces.  The rows are
00023 *  checked if RC = 'R', and the columns are checked if RC = 'C'.
00024 *
00025 *  RESULT is the maximum of
00026 *
00027 *     | V*V' - I | / ( MV ulp ), if RC = 'R', or
00028 *
00029 *     | V'*V - I | / ( MV ulp ), if RC = 'C',
00030 *
00031 *  and the maximum over rows (or columns) 1 to K of
00032 *
00033 *     | U(i) - S*V(i) |/ ( N ulp )
00034 *
00035 *  where abs(S) = 1 (chosen to minimize the expression), U(i) is the
00036 *  i-th row (column) of U, and V(i) is the i-th row (column) of V.
00037 *
00038 *  Arguments
00039 *  ==========
00040 *
00041 *  RC      (input) CHARACTER*1
00042 *          If RC = 'R' the rows of U and V are to be compared.
00043 *          If RC = 'C' the columns of U and V are to be compared.
00044 *
00045 *  MU      (input) INTEGER
00046 *          The number of rows of U if RC = 'R', and the number of
00047 *          columns if RC = 'C'.  If MU = 0 ZUNT03 does nothing.
00048 *          MU must be at least zero.
00049 *
00050 *  MV      (input) INTEGER
00051 *          The number of rows of V if RC = 'R', and the number of
00052 *          columns if RC = 'C'.  If MV = 0 ZUNT03 does nothing.
00053 *          MV must be at least zero.
00054 *
00055 *  N       (input) INTEGER
00056 *          If RC = 'R', the number of columns in the matrices U and V,
00057 *          and if RC = 'C', the number of rows in U and V.  If N = 0
00058 *          ZUNT03 does nothing.  N must be at least zero.
00059 *
00060 *  K       (input) INTEGER
00061 *          The number of rows or columns of U and V to compare.
00062 *          0 <= K <= max(MU,MV).
00063 *
00064 *  U       (input) COMPLEX*16 array, dimension (LDU,N)
00065 *          The first matrix to compare.  If RC = 'R', U is MU by N, and
00066 *          if RC = 'C', U is N by MU.
00067 *
00068 *  LDU     (input) INTEGER
00069 *          The leading dimension of U.  If RC = 'R', LDU >= max(1,MU),
00070 *          and if RC = 'C', LDU >= max(1,N).
00071 *
00072 *  V       (input) COMPLEX*16 array, dimension (LDV,N)
00073 *          The second matrix to compare.  If RC = 'R', V is MV by N, and
00074 *          if RC = 'C', V is N by MV.
00075 *
00076 *  LDV     (input) INTEGER
00077 *          The leading dimension of V.  If RC = 'R', LDV >= max(1,MV),
00078 *          and if RC = 'C', LDV >= max(1,N).
00079 *
00080 *  WORK    (workspace) COMPLEX*16 array, dimension (LWORK)
00081 *
00082 *  LWORK   (input) INTEGER
00083 *          The length of the array WORK.  For best performance, LWORK
00084 *          should be at least N*N if RC = 'C' or M*M if RC = 'R', but
00085 *          the tests will be done even if LWORK is 0.
00086 *
00087 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (max(MV,N))
00088 *
00089 *  RESULT  (output) DOUBLE PRECISION
00090 *          The value computed by the test described above.  RESULT is
00091 *          limited to 1/ulp to avoid overflow.
00092 *
00093 *  INFO    (output) INTEGER
00094 *          0  indicates a successful exit
00095 *          -k indicates the k-th parameter had an illegal value
00096 *
00097 *  =====================================================================
00098 *
00099 *
00100 *     .. Parameters ..
00101       DOUBLE PRECISION   ZERO, ONE
00102       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
00103 *     ..
00104 *     .. Local Scalars ..
00105       INTEGER            I, IRC, J, LMX
00106       DOUBLE PRECISION   RES1, RES2, ULP
00107       COMPLEX*16         S, SU, SV
00108 *     ..
00109 *     .. External Functions ..
00110       LOGICAL            LSAME
00111       INTEGER            IZAMAX
00112       DOUBLE PRECISION   DLAMCH
00113       EXTERNAL           LSAME, IZAMAX, DLAMCH
00114 *     ..
00115 *     .. Intrinsic Functions ..
00116       INTRINSIC          ABS, DBLE, DCMPLX, MAX, MIN
00117 *     ..
00118 *     .. External Subroutines ..
00119       EXTERNAL           XERBLA, ZUNT01
00120 *     ..
00121 *     .. Executable Statements ..
00122 *
00123 *     Check inputs
00124 *
00125       INFO = 0
00126       IF( LSAME( RC, 'R' ) ) THEN
00127          IRC = 0
00128       ELSE IF( LSAME( RC, 'C' ) ) THEN
00129          IRC = 1
00130       ELSE
00131          IRC = -1
00132       END IF
00133       IF( IRC.EQ.-1 ) THEN
00134          INFO = -1
00135       ELSE IF( MU.LT.0 ) THEN
00136          INFO = -2
00137       ELSE IF( MV.LT.0 ) THEN
00138          INFO = -3
00139       ELSE IF( N.LT.0 ) THEN
00140          INFO = -4
00141       ELSE IF( K.LT.0 .OR. K.GT.MAX( MU, MV ) ) THEN
00142          INFO = -5
00143       ELSE IF( ( IRC.EQ.0 .AND. LDU.LT.MAX( 1, MU ) ) .OR.
00144      $         ( IRC.EQ.1 .AND. LDU.LT.MAX( 1, N ) ) ) THEN
00145          INFO = -7
00146       ELSE IF( ( IRC.EQ.0 .AND. LDV.LT.MAX( 1, MV ) ) .OR.
00147      $         ( IRC.EQ.1 .AND. LDV.LT.MAX( 1, N ) ) ) THEN
00148          INFO = -9
00149       END IF
00150       IF( INFO.NE.0 ) THEN
00151          CALL XERBLA( 'ZUNT03', -INFO )
00152          RETURN
00153       END IF
00154 *
00155 *     Initialize result
00156 *
00157       RESULT = ZERO
00158       IF( MU.EQ.0 .OR. MV.EQ.0 .OR. N.EQ.0 )
00159      $   RETURN
00160 *
00161 *     Machine constants
00162 *
00163       ULP = DLAMCH( 'Precision' )
00164 *
00165       IF( IRC.EQ.0 ) THEN
00166 *
00167 *        Compare rows
00168 *
00169          RES1 = ZERO
00170          DO 20 I = 1, K
00171             LMX = IZAMAX( N, U( I, 1 ), LDU )
00172             IF( V( I, LMX ).EQ.DCMPLX( ZERO ) ) THEN
00173                SV = ONE
00174             ELSE
00175                SV = ABS( V( I, LMX ) ) / V( I, LMX )
00176             END IF
00177             IF( U( I, LMX ).EQ.DCMPLX( ZERO ) ) THEN
00178                SU = ONE
00179             ELSE
00180                SU = ABS( U( I, LMX ) ) / U( I, LMX )
00181             END IF
00182             S = SV / SU
00183             DO 10 J = 1, N
00184                RES1 = MAX( RES1, ABS( U( I, J )-S*V( I, J ) ) )
00185    10       CONTINUE
00186    20    CONTINUE
00187          RES1 = RES1 / ( DBLE( N )*ULP )
00188 *
00189 *        Compute orthogonality of rows of V.
00190 *
00191          CALL ZUNT01( 'Rows', MV, N, V, LDV, WORK, LWORK, RWORK, RES2 )
00192 *
00193       ELSE
00194 *
00195 *        Compare columns
00196 *
00197          RES1 = ZERO
00198          DO 40 I = 1, K
00199             LMX = IZAMAX( N, U( 1, I ), 1 )
00200             IF( V( LMX, I ).EQ.DCMPLX( ZERO ) ) THEN
00201                SV = ONE
00202             ELSE
00203                SV = ABS( V( LMX, I ) ) / V( LMX, I )
00204             END IF
00205             IF( U( LMX, I ).EQ.DCMPLX( ZERO ) ) THEN
00206                SU = ONE
00207             ELSE
00208                SU = ABS( U( LMX, I ) ) / U( LMX, I )
00209             END IF
00210             S = SV / SU
00211             DO 30 J = 1, N
00212                RES1 = MAX( RES1, ABS( U( J, I )-S*V( J, I ) ) )
00213    30       CONTINUE
00214    40    CONTINUE
00215          RES1 = RES1 / ( DBLE( N )*ULP )
00216 *
00217 *        Compute orthogonality of columns of V.
00218 *
00219          CALL ZUNT01( 'Columns', N, MV, V, LDV, WORK, LWORK, RWORK,
00220      $                RES2 )
00221       END IF
00222 *
00223       RESULT = MIN( MAX( RES1, RES2 ), ONE / ULP )
00224       RETURN
00225 *
00226 *     End of ZUNT03
00227 *
00228       END