00001 SUBROUTINE ZHET22( ITYPE, UPLO, N, M, KBAND, A, LDA, D, E, U, LDU, 00002 $ V, LDV, TAU, WORK, RWORK, RESULT ) 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 UPLO 00010 INTEGER ITYPE, KBAND, LDA, LDU, LDV, M, N 00011 * .. 00012 * .. Array Arguments .. 00013 DOUBLE PRECISION D( * ), E( * ), RESULT( 2 ), RWORK( * ) 00014 COMPLEX*16 A( LDA, * ), TAU( * ), U( LDU, * ), 00015 $ V( LDV, * ), WORK( * ) 00016 * .. 00017 * 00018 * Purpose 00019 * ======= 00020 * 00021 * ZHET22 generally checks a decomposition of the form 00022 * 00023 * A U = U S 00024 * 00025 * where A is complex Hermitian, the columns of U are orthonormal, 00026 * and S is diagonal (if KBAND=0) or symmetric tridiagonal (if 00027 * KBAND=1). If ITYPE=1, then U is represented as a dense matrix, 00028 * otherwise the U is expressed as a product of Householder 00029 * transformations, whose vectors are stored in the array "V" and 00030 * whose scaling constants are in "TAU"; we shall use the letter 00031 * "V" to refer to the product of Householder transformations 00032 * (which should be equal to U). 00033 * 00034 * Specifically, if ITYPE=1, then: 00035 * 00036 * RESULT(1) = | U' A U - S | / ( |A| m ulp ) *and* 00037 * RESULT(2) = | I - U'U | / ( m ulp ) 00038 * 00039 * Arguments 00040 * ========= 00041 * 00042 * ITYPE INTEGER 00043 * Specifies the type of tests to be performed. 00044 * 1: U expressed as a dense orthogonal matrix: 00045 * RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and* 00046 * RESULT(2) = | I - UU' | / ( n ulp ) 00047 * 00048 * UPLO CHARACTER 00049 * If UPLO='U', the upper triangle of A will be used and the 00050 * (strictly) lower triangle will not be referenced. If 00051 * UPLO='L', the lower triangle of A will be used and the 00052 * (strictly) upper triangle will not be referenced. 00053 * Not modified. 00054 * 00055 * N INTEGER 00056 * The size of the matrix. If it is zero, ZHET22 does nothing. 00057 * It must be at least zero. 00058 * Not modified. 00059 * 00060 * M INTEGER 00061 * The number of columns of U. If it is zero, ZHET22 does 00062 * nothing. It must be at least zero. 00063 * Not modified. 00064 * 00065 * KBAND INTEGER 00066 * The bandwidth of the matrix. It may only be zero or one. 00067 * If zero, then S is diagonal, and E is not referenced. If 00068 * one, then S is symmetric tri-diagonal. 00069 * Not modified. 00070 * 00071 * A COMPLEX*16 array, dimension (LDA , N) 00072 * The original (unfactored) matrix. It is assumed to be 00073 * symmetric, and only the upper (UPLO='U') or only the lower 00074 * (UPLO='L') will be referenced. 00075 * Not modified. 00076 * 00077 * LDA INTEGER 00078 * The leading dimension of A. It must be at least 1 00079 * and at least N. 00080 * Not modified. 00081 * 00082 * D DOUBLE PRECISION array, dimension (N) 00083 * The diagonal of the (symmetric tri-) diagonal matrix. 00084 * Not modified. 00085 * 00086 * E DOUBLE PRECISION array, dimension (N) 00087 * The off-diagonal of the (symmetric tri-) diagonal matrix. 00088 * E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. 00089 * Not referenced if KBAND=0. 00090 * Not modified. 00091 * 00092 * U COMPLEX*16 array, dimension (LDU, N) 00093 * If ITYPE=1, this contains the orthogonal matrix in 00094 * the decomposition, expressed as a dense matrix. 00095 * Not modified. 00096 * 00097 * LDU INTEGER 00098 * The leading dimension of U. LDU must be at least N and 00099 * at least 1. 00100 * Not modified. 00101 * 00102 * V COMPLEX*16 array, dimension (LDV, N) 00103 * If ITYPE=2 or 3, the lower triangle of this array contains 00104 * the Householder vectors used to describe the orthogonal 00105 * matrix in the decomposition. If ITYPE=1, then it is not 00106 * referenced. 00107 * Not modified. 00108 * 00109 * LDV INTEGER 00110 * The leading dimension of V. LDV must be at least N and 00111 * at least 1. 00112 * Not modified. 00113 * 00114 * TAU COMPLEX*16 array, dimension (N) 00115 * If ITYPE >= 2, then TAU(j) is the scalar factor of 00116 * v(j) v(j)' in the Householder transformation H(j) of 00117 * the product U = H(1)...H(n-2) 00118 * If ITYPE < 2, then TAU is not referenced. 00119 * Not modified. 00120 * 00121 * WORK COMPLEX*16 array, dimension (2*N**2) 00122 * Workspace. 00123 * Modified. 00124 * 00125 * RWORK DOUBLE PRECISION array, dimension (N) 00126 * Workspace. 00127 * Modified. 00128 * 00129 * RESULT DOUBLE PRECISION array, dimension (2) 00130 * The values computed by the two tests described above. The 00131 * values are currently limited to 1/ulp, to avoid overflow. 00132 * RESULT(1) is always modified. RESULT(2) is modified only 00133 * if LDU is at least N. 00134 * Modified. 00135 * 00136 * ===================================================================== 00137 * 00138 * .. Parameters .. 00139 DOUBLE PRECISION ZERO, ONE 00140 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) 00141 COMPLEX*16 CZERO, CONE 00142 PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ), 00143 $ CONE = ( 1.0D0, 0.0D0 ) ) 00144 * .. 00145 * .. Local Scalars .. 00146 INTEGER J, JJ, JJ1, JJ2, NN, NNP1 00147 DOUBLE PRECISION ANORM, ULP, UNFL, WNORM 00148 * .. 00149 * .. External Functions .. 00150 DOUBLE PRECISION DLAMCH, ZLANHE 00151 EXTERNAL DLAMCH, ZLANHE 00152 * .. 00153 * .. External Subroutines .. 00154 EXTERNAL ZGEMM, ZHEMM, ZUNT01 00155 * .. 00156 * .. Intrinsic Functions .. 00157 INTRINSIC DBLE, MAX, MIN 00158 * .. 00159 * .. Executable Statements .. 00160 * 00161 RESULT( 1 ) = ZERO 00162 RESULT( 2 ) = ZERO 00163 IF( N.LE.0 .OR. M.LE.0 ) 00164 $ RETURN 00165 * 00166 UNFL = DLAMCH( 'Safe minimum' ) 00167 ULP = DLAMCH( 'Precision' ) 00168 * 00169 * Do Test 1 00170 * 00171 * Norm of A: 00172 * 00173 ANORM = MAX( ZLANHE( '1', UPLO, N, A, LDA, RWORK ), UNFL ) 00174 * 00175 * Compute error matrix: 00176 * 00177 * ITYPE=1: error = U' A U - S 00178 * 00179 CALL ZHEMM( 'L', UPLO, N, M, CONE, A, LDA, U, LDU, CZERO, WORK, 00180 $ N ) 00181 NN = N*N 00182 NNP1 = NN + 1 00183 CALL ZGEMM( 'C', 'N', M, M, N, CONE, U, LDU, WORK, N, CZERO, 00184 $ WORK( NNP1 ), N ) 00185 DO 10 J = 1, M 00186 JJ = NN + ( J-1 )*N + J 00187 WORK( JJ ) = WORK( JJ ) - D( J ) 00188 10 CONTINUE 00189 IF( KBAND.EQ.1 .AND. N.GT.1 ) THEN 00190 DO 20 J = 2, M 00191 JJ1 = NN + ( J-1 )*N + J - 1 00192 JJ2 = NN + ( J-2 )*N + J 00193 WORK( JJ1 ) = WORK( JJ1 ) - E( J-1 ) 00194 WORK( JJ2 ) = WORK( JJ2 ) - E( J-1 ) 00195 20 CONTINUE 00196 END IF 00197 WNORM = ZLANHE( '1', UPLO, M, WORK( NNP1 ), N, RWORK ) 00198 * 00199 IF( ANORM.GT.WNORM ) THEN 00200 RESULT( 1 ) = ( WNORM / ANORM ) / ( M*ULP ) 00201 ELSE 00202 IF( ANORM.LT.ONE ) THEN 00203 RESULT( 1 ) = ( MIN( WNORM, M*ANORM ) / ANORM ) / ( M*ULP ) 00204 ELSE 00205 RESULT( 1 ) = MIN( WNORM / ANORM, DBLE( M ) ) / ( M*ULP ) 00206 END IF 00207 END IF 00208 * 00209 * Do Test 2 00210 * 00211 * Compute U'U - I 00212 * 00213 IF( ITYPE.EQ.1 ) 00214 $ CALL ZUNT01( 'Columns', N, M, U, LDU, WORK, 2*N*N, RWORK, 00215 $ RESULT( 2 ) ) 00216 * 00217 RETURN 00218 * 00219 * End of ZHET22 00220 * 00221 END
1.7.2