LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dget51.f
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00001 *> \brief \b DGET51
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE DGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
00012 *                          RESULT )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       INTEGER            ITYPE, LDA, LDB, LDU, LDV, N
00016 *       DOUBLE PRECISION   RESULT
00017 *       ..
00018 *       .. Array Arguments ..
00019 *       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), U( LDU, * ),
00020 *      $                   V( LDV, * ), WORK( * )
00021 *       ..
00022 *  
00023 *
00024 *> \par Purpose:
00025 *  =============
00026 *>
00027 *> \verbatim
00028 *>
00029 *>      DGET51  generally checks a decomposition of the form
00030 *>
00031 *>              A = U B V'
00032 *>
00033 *>      where ' means transpose and U and V are orthogonal.
00034 *>
00035 *>      Specifically, if ITYPE=1
00036 *>
00037 *>              RESULT = | A - U B V' | / ( |A| n ulp )
00038 *>
00039 *>      If ITYPE=2, then:
00040 *>
00041 *>              RESULT = | A - B | / ( |A| n ulp )
00042 *>
00043 *>      If ITYPE=3, then:
00044 *>
00045 *>              RESULT = | I - UU' | / ( n ulp )
00046 *> \endverbatim
00047 *
00048 *  Arguments:
00049 *  ==========
00050 *
00051 *> \param[in] ITYPE
00052 *> \verbatim
00053 *>          ITYPE is INTEGER
00054 *>          Specifies the type of tests to be performed.
00055 *>          =1: RESULT = | A - U B V' | / ( |A| n ulp )
00056 *>          =2: RESULT = | A - B | / ( |A| n ulp )
00057 *>          =3: RESULT = | I - UU' | / ( n ulp )
00058 *> \endverbatim
00059 *>
00060 *> \param[in] N
00061 *> \verbatim
00062 *>          N is INTEGER
00063 *>          The size of the matrix.  If it is zero, DGET51 does nothing.
00064 *>          It must be at least zero.
00065 *> \endverbatim
00066 *>
00067 *> \param[in] A
00068 *> \verbatim
00069 *>          A is DOUBLE PRECISION array, dimension (LDA, N)
00070 *>          The original (unfactored) matrix.
00071 *> \endverbatim
00072 *>
00073 *> \param[in] LDA
00074 *> \verbatim
00075 *>          LDA is INTEGER
00076 *>          The leading dimension of A.  It must be at least 1
00077 *>          and at least N.
00078 *> \endverbatim
00079 *>
00080 *> \param[in] B
00081 *> \verbatim
00082 *>          B is DOUBLE PRECISION array, dimension (LDB, N)
00083 *>          The factored matrix.
00084 *> \endverbatim
00085 *>
00086 *> \param[in] LDB
00087 *> \verbatim
00088 *>          LDB is INTEGER
00089 *>          The leading dimension of B.  It must be at least 1
00090 *>          and at least N.
00091 *> \endverbatim
00092 *>
00093 *> \param[in] U
00094 *> \verbatim
00095 *>          U is DOUBLE PRECISION array, dimension (LDU, N)
00096 *>          The orthogonal matrix on the left-hand side in the
00097 *>          decomposition.
00098 *>          Not referenced if ITYPE=2
00099 *> \endverbatim
00100 *>
00101 *> \param[in] LDU
00102 *> \verbatim
00103 *>          LDU is INTEGER
00104 *>          The leading dimension of U.  LDU must be at least N and
00105 *>          at least 1.
00106 *> \endverbatim
00107 *>
00108 *> \param[in] V
00109 *> \verbatim
00110 *>          V is DOUBLE PRECISION array, dimension (LDV, N)
00111 *>          The orthogonal matrix on the left-hand side in the
00112 *>          decomposition.
00113 *>          Not referenced if ITYPE=2
00114 *> \endverbatim
00115 *>
00116 *> \param[in] LDV
00117 *> \verbatim
00118 *>          LDV is INTEGER
00119 *>          The leading dimension of V.  LDV must be at least N and
00120 *>          at least 1.
00121 *> \endverbatim
00122 *>
00123 *> \param[out] WORK
00124 *> \verbatim
00125 *>          WORK is DOUBLE PRECISION array, dimension (2*N**2)
00126 *> \endverbatim
00127 *>
00128 *> \param[out] RESULT
00129 *> \verbatim
00130 *>          RESULT is DOUBLE PRECISION
00131 *>          The values computed by the test specified by ITYPE.  The
00132 *>          value is currently limited to 1/ulp, to avoid overflow.
00133 *>          Errors are flagged by RESULT=10/ulp.
00134 *> \endverbatim
00135 *
00136 *  Authors:
00137 *  ========
00138 *
00139 *> \author Univ. of Tennessee 
00140 *> \author Univ. of California Berkeley 
00141 *> \author Univ. of Colorado Denver 
00142 *> \author NAG Ltd. 
00143 *
00144 *> \date November 2011
00145 *
00146 *> \ingroup double_eig
00147 *
00148 *  =====================================================================
00149       SUBROUTINE DGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
00150      $                   RESULT )
00151 *
00152 *  -- LAPACK test routine (version 3.4.0) --
00153 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00154 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00155 *     November 2011
00156 *
00157 *     .. Scalar Arguments ..
00158       INTEGER            ITYPE, LDA, LDB, LDU, LDV, N
00159       DOUBLE PRECISION   RESULT
00160 *     ..
00161 *     .. Array Arguments ..
00162       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), U( LDU, * ),
00163      $                   V( LDV, * ), WORK( * )
00164 *     ..
00165 *
00166 *  =====================================================================
00167 *
00168 *     .. Parameters ..
00169       DOUBLE PRECISION   ZERO, ONE, TEN
00170       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0, TEN = 10.0D0 )
00171 *     ..
00172 *     .. Local Scalars ..
00173       INTEGER            JCOL, JDIAG, JROW
00174       DOUBLE PRECISION   ANORM, ULP, UNFL, WNORM
00175 *     ..
00176 *     .. External Functions ..
00177       DOUBLE PRECISION   DLAMCH, DLANGE
00178       EXTERNAL           DLAMCH, DLANGE
00179 *     ..
00180 *     .. External Subroutines ..
00181       EXTERNAL           DGEMM, DLACPY
00182 *     ..
00183 *     .. Intrinsic Functions ..
00184       INTRINSIC          DBLE, MAX, MIN
00185 *     ..
00186 *     .. Executable Statements ..
00187 *
00188       RESULT = ZERO
00189       IF( N.LE.0 )
00190      $   RETURN
00191 *
00192 *     Constants
00193 *
00194       UNFL = DLAMCH( 'Safe minimum' )
00195       ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
00196 *
00197 *     Some Error Checks
00198 *
00199       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
00200          RESULT = TEN / ULP
00201          RETURN
00202       END IF
00203 *
00204       IF( ITYPE.LE.2 ) THEN
00205 *
00206 *        Tests scaled by the norm(A)
00207 *
00208          ANORM = MAX( DLANGE( '1', N, N, A, LDA, WORK ), UNFL )
00209 *
00210          IF( ITYPE.EQ.1 ) THEN
00211 *
00212 *           ITYPE=1: Compute W = A - UBV'
00213 *
00214             CALL DLACPY( ' ', N, N, A, LDA, WORK, N )
00215             CALL DGEMM( 'N', 'N', N, N, N, ONE, U, LDU, B, LDB, ZERO,
00216      $                  WORK( N**2+1 ), N )
00217 *
00218             CALL DGEMM( 'N', 'C', N, N, N, -ONE, WORK( N**2+1 ), N, V,
00219      $                  LDV, ONE, WORK, N )
00220 *
00221          ELSE
00222 *
00223 *           ITYPE=2: Compute W = A - B
00224 *
00225             CALL DLACPY( ' ', N, N, B, LDB, WORK, N )
00226 *
00227             DO 20 JCOL = 1, N
00228                DO 10 JROW = 1, N
00229                   WORK( JROW+N*( JCOL-1 ) ) = WORK( JROW+N*( JCOL-1 ) )
00230      $                - A( JROW, JCOL )
00231    10          CONTINUE
00232    20       CONTINUE
00233          END IF
00234 *
00235 *        Compute norm(W)/ ( ulp*norm(A) )
00236 *
00237          WNORM = DLANGE( '1', N, N, WORK, N, WORK( N**2+1 ) )
00238 *
00239          IF( ANORM.GT.WNORM ) THEN
00240             RESULT = ( WNORM / ANORM ) / ( N*ULP )
00241          ELSE
00242             IF( ANORM.LT.ONE ) THEN
00243                RESULT = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
00244             ELSE
00245                RESULT = MIN( WNORM / ANORM, DBLE( N ) ) / ( N*ULP )
00246             END IF
00247          END IF
00248 *
00249       ELSE
00250 *
00251 *        Tests not scaled by norm(A)
00252 *
00253 *        ITYPE=3: Compute  UU' - I
00254 *
00255          CALL DGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,
00256      $               N )
00257 *
00258          DO 30 JDIAG = 1, N
00259             WORK( ( N+1 )*( JDIAG-1 )+1 ) = WORK( ( N+1 )*( JDIAG-1 )+
00260      $         1 ) - ONE
00261    30    CONTINUE
00262 *
00263          RESULT = MIN( DLANGE( '1', N, N, WORK, N, WORK( N**2+1 ) ),
00264      $            DBLE( N ) ) / ( N*ULP )
00265       END IF
00266 *
00267       RETURN
00268 *
00269 *     End of DGET51
00270 *
00271       END
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