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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE CHETRI( UPLO, N, A, LDA, IPIV, WORK, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.3.1) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * -- April 2011 -- 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER UPLO 00010 INTEGER INFO, LDA, N 00011 * .. 00012 * .. Array Arguments .. 00013 INTEGER IPIV( * ) 00014 COMPLEX A( LDA, * ), WORK( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * CHETRI computes the inverse of a complex Hermitian indefinite matrix 00021 * A using the factorization A = U*D*U**H or A = L*D*L**H computed by 00022 * CHETRF. 00023 * 00024 * Arguments 00025 * ========= 00026 * 00027 * UPLO (input) CHARACTER*1 00028 * Specifies whether the details of the factorization are stored 00029 * as an upper or lower triangular matrix. 00030 * = 'U': Upper triangular, form is A = U*D*U**H; 00031 * = 'L': Lower triangular, form is A = L*D*L**H. 00032 * 00033 * N (input) INTEGER 00034 * The order of the matrix A. N >= 0. 00035 * 00036 * A (input/output) COMPLEX array, dimension (LDA,N) 00037 * On entry, the block diagonal matrix D and the multipliers 00038 * used to obtain the factor U or L as computed by CHETRF. 00039 * 00040 * On exit, if INFO = 0, the (Hermitian) inverse of the original 00041 * matrix. If UPLO = 'U', the upper triangular part of the 00042 * inverse is formed and the part of A below the diagonal is not 00043 * referenced; if UPLO = 'L' the lower triangular part of the 00044 * inverse is formed and the part of A above the diagonal is 00045 * not referenced. 00046 * 00047 * LDA (input) INTEGER 00048 * The leading dimension of the array A. LDA >= max(1,N). 00049 * 00050 * IPIV (input) INTEGER array, dimension (N) 00051 * Details of the interchanges and the block structure of D 00052 * as determined by CHETRF. 00053 * 00054 * WORK (workspace) COMPLEX array, dimension (N) 00055 * 00056 * INFO (output) INTEGER 00057 * = 0: successful exit 00058 * < 0: if INFO = -i, the i-th argument had an illegal value 00059 * > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its 00060 * inverse could not be computed. 00061 * 00062 * ===================================================================== 00063 * 00064 * .. Parameters .. 00065 REAL ONE 00066 COMPLEX CONE, ZERO 00067 PARAMETER ( ONE = 1.0E+0, CONE = ( 1.0E+0, 0.0E+0 ), 00068 $ ZERO = ( 0.0E+0, 0.0E+0 ) ) 00069 * .. 00070 * .. Local Scalars .. 00071 LOGICAL UPPER 00072 INTEGER J, K, KP, KSTEP 00073 REAL AK, AKP1, D, T 00074 COMPLEX AKKP1, TEMP 00075 * .. 00076 * .. External Functions .. 00077 LOGICAL LSAME 00078 COMPLEX CDOTC 00079 EXTERNAL LSAME, CDOTC 00080 * .. 00081 * .. External Subroutines .. 00082 EXTERNAL CCOPY, CHEMV, CSWAP, XERBLA 00083 * .. 00084 * .. Intrinsic Functions .. 00085 INTRINSIC ABS, CONJG, MAX, REAL 00086 * .. 00087 * .. Executable Statements .. 00088 * 00089 * Test the input parameters. 00090 * 00091 INFO = 0 00092 UPPER = LSAME( UPLO, 'U' ) 00093 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00094 INFO = -1 00095 ELSE IF( N.LT.0 ) THEN 00096 INFO = -2 00097 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00098 INFO = -4 00099 END IF 00100 IF( INFO.NE.0 ) THEN 00101 CALL XERBLA( 'CHETRI', -INFO ) 00102 RETURN 00103 END IF 00104 * 00105 * Quick return if possible 00106 * 00107 IF( N.EQ.0 ) 00108 $ RETURN 00109 * 00110 * Check that the diagonal matrix D is nonsingular. 00111 * 00112 IF( UPPER ) THEN 00113 * 00114 * Upper triangular storage: examine D from bottom to top 00115 * 00116 DO 10 INFO = N, 1, -1 00117 IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO ) 00118 $ RETURN 00119 10 CONTINUE 00120 ELSE 00121 * 00122 * Lower triangular storage: examine D from top to bottom. 00123 * 00124 DO 20 INFO = 1, N 00125 IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO ) 00126 $ RETURN 00127 20 CONTINUE 00128 END IF 00129 INFO = 0 00130 * 00131 IF( UPPER ) THEN 00132 * 00133 * Compute inv(A) from the factorization A = U*D*U**H. 00134 * 00135 * K is the main loop index, increasing from 1 to N in steps of 00136 * 1 or 2, depending on the size of the diagonal blocks. 00137 * 00138 K = 1 00139 30 CONTINUE 00140 * 00141 * If K > N, exit from loop. 00142 * 00143 IF( K.GT.N ) 00144 $ GO TO 50 00145 * 00146 IF( IPIV( K ).GT.0 ) THEN 00147 * 00148 * 1 x 1 diagonal block 00149 * 00150 * Invert the diagonal block. 00151 * 00152 A( K, K ) = ONE / REAL( A( K, K ) ) 00153 * 00154 * Compute column K of the inverse. 00155 * 00156 IF( K.GT.1 ) THEN 00157 CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 ) 00158 CALL CHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO, 00159 $ A( 1, K ), 1 ) 00160 A( K, K ) = A( K, K ) - REAL( CDOTC( K-1, WORK, 1, A( 1, $ K ), 1 ) ) 00161 END IF 00162 KSTEP = 1 00163 ELSE 00164 * 00165 * 2 x 2 diagonal block 00166 * 00167 * Invert the diagonal block. 00168 * 00169 T = ABS( A( K, K+1 ) ) 00170 AK = REAL( A( K, K ) ) / T 00171 AKP1 = REAL( A( K+1, K+1 ) ) / T 00172 AKKP1 = A( K, K+1 ) / T 00173 D = T*( AK*AKP1-ONE ) 00174 A( K, K ) = AKP1 / D 00175 A( K+1, K+1 ) = AK / D 00176 A( K, K+1 ) = -AKKP1 / D 00177 * 00178 * Compute columns K and K+1 of the inverse. 00179 * 00180 IF( K.GT.1 ) THEN 00181 CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 ) 00182 CALL CHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO, 00183 $ A( 1, K ), 1 ) 00184 A( K, K ) = A( K, K ) - REAL( CDOTC( K-1, WORK, 1, A( 1, $ K ), 1 ) ) 00185 A( K, K+1 ) = A( K, K+1 ) - 00186 $ CDOTC( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 ) 00187 CALL CCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 ) 00188 CALL CHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO, 00189 $ A( 1, K+1 ), 1 ) 00190 A( K+1, K+1 ) = A( K+1, K+1 ) - 00191 $ REAL( CDOTC( K-1, WORK, 1, A( 1, K+1 ), $ 1 ) ) 00192 END IF 00193 KSTEP = 2 00194 END IF 00195 * 00196 KP = ABS( IPIV( K ) ) 00197 IF( KP.NE.K ) THEN 00198 * 00199 * Interchange rows and columns K and KP in the leading 00200 * submatrix A(1:k+1,1:k+1) 00201 * 00202 CALL CSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 ) 00203 DO 40 J = KP + 1, K - 1 00204 TEMP = CONJG( A( J, K ) ) 00205 A( J, K ) = CONJG( A( KP, J ) ) 00206 A( KP, J ) = TEMP 00207 40 CONTINUE 00208 A( KP, K ) = CONJG( A( KP, K ) ) 00209 TEMP = A( K, K ) 00210 A( K, K ) = A( KP, KP ) 00211 A( KP, KP ) = TEMP 00212 IF( KSTEP.EQ.2 ) THEN 00213 TEMP = A( K, K+1 ) 00214 A( K, K+1 ) = A( KP, K+1 ) 00215 A( KP, K+1 ) = TEMP 00216 END IF 00217 END IF 00218 * 00219 K = K + KSTEP 00220 GO TO 30 00221 50 CONTINUE 00222 * 00223 ELSE 00224 * 00225 * Compute inv(A) from the factorization A = L*D*L**H. 00226 * 00227 * K is the main loop index, increasing from 1 to N in steps of 00228 * 1 or 2, depending on the size of the diagonal blocks. 00229 * 00230 K = N 00231 60 CONTINUE 00232 * 00233 * If K < 1, exit from loop. 00234 * 00235 IF( K.LT.1 ) 00236 $ GO TO 80 00237 * 00238 IF( IPIV( K ).GT.0 ) THEN 00239 * 00240 * 1 x 1 diagonal block 00241 * 00242 * Invert the diagonal block. 00243 * 00244 A( K, K ) = ONE / REAL( A( K, K ) ) 00245 * 00246 * Compute column K of the inverse. 00247 * 00248 IF( K.LT.N ) THEN 00249 CALL CCOPY( N-K, A( K+1, K ), 1, WORK, 1 ) 00250 CALL CHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK, 00251 $ 1, ZERO, A( K+1, K ), 1 ) 00252 A( K, K ) = A( K, K ) - REAL( CDOTC( N-K, WORK, 1, $ A( K+1, K ), 1 ) ) 00253 END IF 00254 KSTEP = 1 00255 ELSE 00256 * 00257 * 2 x 2 diagonal block 00258 * 00259 * Invert the diagonal block. 00260 * 00261 T = ABS( A( K, K-1 ) ) 00262 AK = REAL( A( K-1, K-1 ) ) / T 00263 AKP1 = REAL( A( K, K ) ) / T 00264 AKKP1 = A( K, K-1 ) / T 00265 D = T*( AK*AKP1-ONE ) 00266 A( K-1, K-1 ) = AKP1 / D 00267 A( K, K ) = AK / D 00268 A( K, K-1 ) = -AKKP1 / D 00269 * 00270 * Compute columns K-1 and K of the inverse. 00271 * 00272 IF( K.LT.N ) THEN 00273 CALL CCOPY( N-K, A( K+1, K ), 1, WORK, 1 ) 00274 CALL CHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK, 00275 $ 1, ZERO, A( K+1, K ), 1 ) 00276 A( K, K ) = A( K, K ) - REAL( CDOTC( N-K, WORK, 1, $ A( K+1, K ), 1 ) ) 00277 A( K, K-1 ) = A( K, K-1 ) - 00278 $ CDOTC( N-K, A( K+1, K ), 1, A( K+1, K-1 ), 00279 $ 1 ) 00280 CALL CCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 ) 00281 CALL CHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK, 00282 $ 1, ZERO, A( K+1, K-1 ), 1 ) 00283 A( K-1, K-1 ) = A( K-1, K-1 ) - 00284 $ REAL( CDOTC( N-K, WORK, 1, A( K+1, K-1 ), $ 1 ) ) 00285 END IF 00286 KSTEP = 2 00287 END IF 00288 * 00289 KP = ABS( IPIV( K ) ) 00290 IF( KP.NE.K ) THEN 00291 * 00292 * Interchange rows and columns K and KP in the trailing 00293 * submatrix A(k-1:n,k-1:n) 00294 * 00295 IF( KP.LT.N ) 00296 $ CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 ) 00297 DO 70 J = K + 1, KP - 1 00298 TEMP = CONJG( A( J, K ) ) 00299 A( J, K ) = CONJG( A( KP, J ) ) 00300 A( KP, J ) = TEMP 00301 70 CONTINUE 00302 A( KP, K ) = CONJG( A( KP, K ) ) 00303 TEMP = A( K, K ) 00304 A( K, K ) = A( KP, KP ) 00305 A( KP, KP ) = TEMP 00306 IF( KSTEP.EQ.2 ) THEN 00307 TEMP = A( K, K-1 ) 00308 A( K, K-1 ) = A( KP, K-1 ) 00309 A( KP, K-1 ) = TEMP 00310 END IF 00311 END IF 00312 * 00313 K = K - KSTEP 00314 GO TO 60 00315 80 CONTINUE 00316 END IF 00317 * 00318 RETURN 00319 * 00320 * End of CHETRI 00321 * 00322 END 00323
1.7.3 
