LAPACK 3.3.0
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00001 SUBROUTINE CSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 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 * CSYTRI computes the inverse of a complex symmetric indefinite matrix 00021 * A using the factorization A = U*D*U**T or A = L*D*L**T computed by 00022 * CSYTRF. 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**T; 00031 * = 'L': Lower triangular, form is A = L*D*L**T. 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 CSYTRF. 00039 * 00040 * On exit, if INFO = 0, the (symmetric) 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 CSYTRF. 00053 * 00054 * WORK (workspace) COMPLEX array, dimension (2*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 COMPLEX ONE, ZERO 00066 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), 00067 $ ZERO = ( 0.0E+0, 0.0E+0 ) ) 00068 * .. 00069 * .. Local Scalars .. 00070 LOGICAL UPPER 00071 INTEGER K, KP, KSTEP 00072 COMPLEX AK, AKKP1, AKP1, D, T, TEMP 00073 * .. 00074 * .. External Functions .. 00075 LOGICAL LSAME 00076 COMPLEX CDOTU 00077 EXTERNAL LSAME, CDOTU 00078 * .. 00079 * .. External Subroutines .. 00080 EXTERNAL CCOPY, CSWAP, CSYMV, XERBLA 00081 * .. 00082 * .. Intrinsic Functions .. 00083 INTRINSIC ABS, MAX 00084 * .. 00085 * .. Executable Statements .. 00086 * 00087 * Test the input parameters. 00088 * 00089 INFO = 0 00090 UPPER = LSAME( UPLO, 'U' ) 00091 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00092 INFO = -1 00093 ELSE IF( N.LT.0 ) THEN 00094 INFO = -2 00095 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00096 INFO = -4 00097 END IF 00098 IF( INFO.NE.0 ) THEN 00099 CALL XERBLA( 'CSYTRI', -INFO ) 00100 RETURN 00101 END IF 00102 * 00103 * Quick return if possible 00104 * 00105 IF( N.EQ.0 ) 00106 $ RETURN 00107 * 00108 * Check that the diagonal matrix D is nonsingular. 00109 * 00110 IF( UPPER ) THEN 00111 * 00112 * Upper triangular storage: examine D from bottom to top 00113 * 00114 DO 10 INFO = N, 1, -1 00115 IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO ) 00116 $ RETURN 00117 10 CONTINUE 00118 ELSE 00119 * 00120 * Lower triangular storage: examine D from top to bottom. 00121 * 00122 DO 20 INFO = 1, N 00123 IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO ) 00124 $ RETURN 00125 20 CONTINUE 00126 END IF 00127 INFO = 0 00128 * 00129 IF( UPPER ) THEN 00130 * 00131 * Compute inv(A) from the factorization A = U*D*U'. 00132 * 00133 * K is the main loop index, increasing from 1 to N in steps of 00134 * 1 or 2, depending on the size of the diagonal blocks. 00135 * 00136 K = 1 00137 30 CONTINUE 00138 * 00139 * If K > N, exit from loop. 00140 * 00141 IF( K.GT.N ) 00142 $ GO TO 40 00143 * 00144 IF( IPIV( K ).GT.0 ) THEN 00145 * 00146 * 1 x 1 diagonal block 00147 * 00148 * Invert the diagonal block. 00149 * 00150 A( K, K ) = ONE / A( K, K ) 00151 * 00152 * Compute column K of the inverse. 00153 * 00154 IF( K.GT.1 ) THEN 00155 CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 ) 00156 CALL CSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO, 00157 $ A( 1, K ), 1 ) 00158 A( K, K ) = A( K, K ) - CDOTU( K-1, WORK, 1, A( 1, K ), 00159 $ 1 ) 00160 END IF 00161 KSTEP = 1 00162 ELSE 00163 * 00164 * 2 x 2 diagonal block 00165 * 00166 * Invert the diagonal block. 00167 * 00168 T = A( K, K+1 ) 00169 AK = A( K, K ) / T 00170 AKP1 = A( K+1, K+1 ) / T 00171 AKKP1 = A( K, K+1 ) / T 00172 D = T*( AK*AKP1-ONE ) 00173 A( K, K ) = AKP1 / D 00174 A( K+1, K+1 ) = AK / D 00175 A( K, K+1 ) = -AKKP1 / D 00176 * 00177 * Compute columns K and K+1 of the inverse. 00178 * 00179 IF( K.GT.1 ) THEN 00180 CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 ) 00181 CALL CSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO, 00182 $ A( 1, K ), 1 ) 00183 A( K, K ) = A( K, K ) - CDOTU( K-1, WORK, 1, A( 1, K ), 00184 $ 1 ) 00185 A( K, K+1 ) = A( K, K+1 ) - 00186 $ CDOTU( 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 CSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO, 00189 $ A( 1, K+1 ), 1 ) 00190 A( K+1, K+1 ) = A( K+1, K+1 ) - 00191 $ CDOTU( 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 CALL CSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA ) 00204 TEMP = A( K, K ) 00205 A( K, K ) = A( KP, KP ) 00206 A( KP, KP ) = TEMP 00207 IF( KSTEP.EQ.2 ) THEN 00208 TEMP = A( K, K+1 ) 00209 A( K, K+1 ) = A( KP, K+1 ) 00210 A( KP, K+1 ) = TEMP 00211 END IF 00212 END IF 00213 * 00214 K = K + KSTEP 00215 GO TO 30 00216 40 CONTINUE 00217 * 00218 ELSE 00219 * 00220 * Compute inv(A) from the factorization A = L*D*L'. 00221 * 00222 * K is the main loop index, increasing from 1 to N in steps of 00223 * 1 or 2, depending on the size of the diagonal blocks. 00224 * 00225 K = N 00226 50 CONTINUE 00227 * 00228 * If K < 1, exit from loop. 00229 * 00230 IF( K.LT.1 ) 00231 $ GO TO 60 00232 * 00233 IF( IPIV( K ).GT.0 ) THEN 00234 * 00235 * 1 x 1 diagonal block 00236 * 00237 * Invert the diagonal block. 00238 * 00239 A( K, K ) = ONE / A( K, K ) 00240 * 00241 * Compute column K of the inverse. 00242 * 00243 IF( K.LT.N ) THEN 00244 CALL CCOPY( N-K, A( K+1, K ), 1, WORK, 1 ) 00245 CALL CSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1, 00246 $ ZERO, A( K+1, K ), 1 ) 00247 A( K, K ) = A( K, K ) - CDOTU( N-K, WORK, 1, A( K+1, K ), 00248 $ 1 ) 00249 END IF 00250 KSTEP = 1 00251 ELSE 00252 * 00253 * 2 x 2 diagonal block 00254 * 00255 * Invert the diagonal block. 00256 * 00257 T = A( K, K-1 ) 00258 AK = A( K-1, K-1 ) / T 00259 AKP1 = A( K, K ) / T 00260 AKKP1 = A( K, K-1 ) / T 00261 D = T*( AK*AKP1-ONE ) 00262 A( K-1, K-1 ) = AKP1 / D 00263 A( K, K ) = AK / D 00264 A( K, K-1 ) = -AKKP1 / D 00265 * 00266 * Compute columns K-1 and K of the inverse. 00267 * 00268 IF( K.LT.N ) THEN 00269 CALL CCOPY( N-K, A( K+1, K ), 1, WORK, 1 ) 00270 CALL CSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1, 00271 $ ZERO, A( K+1, K ), 1 ) 00272 A( K, K ) = A( K, K ) - CDOTU( N-K, WORK, 1, A( K+1, K ), 00273 $ 1 ) 00274 A( K, K-1 ) = A( K, K-1 ) - 00275 $ CDOTU( N-K, A( K+1, K ), 1, A( K+1, K-1 ), 00276 $ 1 ) 00277 CALL CCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 ) 00278 CALL CSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1, 00279 $ ZERO, A( K+1, K-1 ), 1 ) 00280 A( K-1, K-1 ) = A( K-1, K-1 ) - 00281 $ CDOTU( N-K, WORK, 1, A( K+1, K-1 ), 1 ) 00282 END IF 00283 KSTEP = 2 00284 END IF 00285 * 00286 KP = ABS( IPIV( K ) ) 00287 IF( KP.NE.K ) THEN 00288 * 00289 * Interchange rows and columns K and KP in the trailing 00290 * submatrix A(k-1:n,k-1:n) 00291 * 00292 IF( KP.LT.N ) 00293 $ CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 ) 00294 CALL CSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA ) 00295 TEMP = A( K, K ) 00296 A( K, K ) = A( KP, KP ) 00297 A( KP, KP ) = TEMP 00298 IF( KSTEP.EQ.2 ) THEN 00299 TEMP = A( K, K-1 ) 00300 A( K, K-1 ) = A( KP, K-1 ) 00301 A( KP, K-1 ) = TEMP 00302 END IF 00303 END IF 00304 * 00305 K = K - KSTEP 00306 GO TO 50 00307 60 CONTINUE 00308 END IF 00309 * 00310 RETURN 00311 * 00312 * End of CSYTRI 00313 * 00314 END