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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 ZHETRI( 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*16 A( LDA, * ), WORK( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * ZHETRI 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 * ZHETRF. 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*16 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 ZHETRF. 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 ZHETRF. 00053 * 00054 * WORK (workspace) COMPLEX*16 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 DOUBLE PRECISION ONE 00066 COMPLEX*16 CONE, ZERO 00067 PARAMETER ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ), 00068 $ ZERO = ( 0.0D+0, 0.0D+0 ) ) 00069 * .. 00070 * .. Local Scalars .. 00071 LOGICAL UPPER 00072 INTEGER J, K, KP, KSTEP 00073 DOUBLE PRECISION AK, AKP1, D, T 00074 COMPLEX*16 AKKP1, TEMP 00075 * .. 00076 * .. External Functions .. 00077 LOGICAL LSAME 00078 COMPLEX*16 ZDOTC 00079 EXTERNAL LSAME, ZDOTC 00080 * .. 00081 * .. External Subroutines .. 00082 EXTERNAL XERBLA, ZCOPY, ZHEMV, ZSWAP 00083 * .. 00084 * .. Intrinsic Functions .. 00085 INTRINSIC ABS, DBLE, DCONJG, MAX 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( 'ZHETRI', -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 / DBLE( A( K, K ) ) 00153 * 00154 * Compute column K of the inverse. 00155 * 00156 IF( K.GT.1 ) THEN 00157 CALL ZCOPY( K-1, A( 1, K ), 1, WORK, 1 ) 00158 CALL ZHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO, 00159 $ A( 1, K ), 1 ) 00160 A( K, K ) = A( K, K ) - DBLE( ZDOTC( K-1, WORK, 1, A( 1, 00161 $ K ), 1 ) ) 00162 END IF 00163 KSTEP = 1 00164 ELSE 00165 * 00166 * 2 x 2 diagonal block 00167 * 00168 * Invert the diagonal block. 00169 * 00170 T = ABS( A( K, K+1 ) ) 00171 AK = DBLE( A( K, K ) ) / T 00172 AKP1 = DBLE( A( K+1, K+1 ) ) / T 00173 AKKP1 = A( K, K+1 ) / T 00174 D = T*( AK*AKP1-ONE ) 00175 A( K, K ) = AKP1 / D 00176 A( K+1, K+1 ) = AK / D 00177 A( K, K+1 ) = -AKKP1 / D 00178 * 00179 * Compute columns K and K+1 of the inverse. 00180 * 00181 IF( K.GT.1 ) THEN 00182 CALL ZCOPY( K-1, A( 1, K ), 1, WORK, 1 ) 00183 CALL ZHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO, 00184 $ A( 1, K ), 1 ) 00185 A( K, K ) = A( K, K ) - DBLE( ZDOTC( K-1, WORK, 1, A( 1, 00186 $ K ), 1 ) ) 00187 A( K, K+1 ) = A( K, K+1 ) - 00188 $ ZDOTC( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 ) 00189 CALL ZCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 ) 00190 CALL ZHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO, 00191 $ A( 1, K+1 ), 1 ) 00192 A( K+1, K+1 ) = A( K+1, K+1 ) - 00193 $ DBLE( ZDOTC( K-1, WORK, 1, A( 1, K+1 ), 00194 $ 1 ) ) 00195 END IF 00196 KSTEP = 2 00197 END IF 00198 * 00199 KP = ABS( IPIV( K ) ) 00200 IF( KP.NE.K ) THEN 00201 * 00202 * Interchange rows and columns K and KP in the leading 00203 * submatrix A(1:k+1,1:k+1) 00204 * 00205 CALL ZSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 ) 00206 DO 40 J = KP + 1, K - 1 00207 TEMP = DCONJG( A( J, K ) ) 00208 A( J, K ) = DCONJG( A( KP, J ) ) 00209 A( KP, J ) = TEMP 00210 40 CONTINUE 00211 A( KP, K ) = DCONJG( A( KP, K ) ) 00212 TEMP = A( K, K ) 00213 A( K, K ) = A( KP, KP ) 00214 A( KP, KP ) = TEMP 00215 IF( KSTEP.EQ.2 ) THEN 00216 TEMP = A( K, K+1 ) 00217 A( K, K+1 ) = A( KP, K+1 ) 00218 A( KP, K+1 ) = TEMP 00219 END IF 00220 END IF 00221 * 00222 K = K + KSTEP 00223 GO TO 30 00224 50 CONTINUE 00225 * 00226 ELSE 00227 * 00228 * Compute inv(A) from the factorization A = L*D*L**H. 00229 * 00230 * K is the main loop index, increasing from 1 to N in steps of 00231 * 1 or 2, depending on the size of the diagonal blocks. 00232 * 00233 K = N 00234 60 CONTINUE 00235 * 00236 * If K < 1, exit from loop. 00237 * 00238 IF( K.LT.1 ) 00239 $ GO TO 80 00240 * 00241 IF( IPIV( K ).GT.0 ) THEN 00242 * 00243 * 1 x 1 diagonal block 00244 * 00245 * Invert the diagonal block. 00246 * 00247 A( K, K ) = ONE / DBLE( A( K, K ) ) 00248 * 00249 * Compute column K of the inverse. 00250 * 00251 IF( K.LT.N ) THEN 00252 CALL ZCOPY( N-K, A( K+1, K ), 1, WORK, 1 ) 00253 CALL ZHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK, 00254 $ 1, ZERO, A( K+1, K ), 1 ) 00255 A( K, K ) = A( K, K ) - DBLE( ZDOTC( N-K, WORK, 1, 00256 $ A( K+1, K ), 1 ) ) 00257 END IF 00258 KSTEP = 1 00259 ELSE 00260 * 00261 * 2 x 2 diagonal block 00262 * 00263 * Invert the diagonal block. 00264 * 00265 T = ABS( A( K, K-1 ) ) 00266 AK = DBLE( A( K-1, K-1 ) ) / T 00267 AKP1 = DBLE( A( K, K ) ) / T 00268 AKKP1 = A( K, K-1 ) / T 00269 D = T*( AK*AKP1-ONE ) 00270 A( K-1, K-1 ) = AKP1 / D 00271 A( K, K ) = AK / D 00272 A( K, K-1 ) = -AKKP1 / D 00273 * 00274 * Compute columns K-1 and K of the inverse. 00275 * 00276 IF( K.LT.N ) THEN 00277 CALL ZCOPY( N-K, A( K+1, K ), 1, WORK, 1 ) 00278 CALL ZHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK, 00279 $ 1, ZERO, A( K+1, K ), 1 ) 00280 A( K, K ) = A( K, K ) - DBLE( ZDOTC( N-K, WORK, 1, 00281 $ A( K+1, K ), 1 ) ) 00282 A( K, K-1 ) = A( K, K-1 ) - 00283 $ ZDOTC( N-K, A( K+1, K ), 1, A( K+1, K-1 ), 00284 $ 1 ) 00285 CALL ZCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 ) 00286 CALL ZHEMV( UPLO, N-K, -CONE, A( K+1, K+1 ), LDA, WORK, 00287 $ 1, ZERO, A( K+1, K-1 ), 1 ) 00288 A( K-1, K-1 ) = A( K-1, K-1 ) - 00289 $ DBLE( ZDOTC( N-K, WORK, 1, A( K+1, K-1 ), 00290 $ 1 ) ) 00291 END IF 00292 KSTEP = 2 00293 END IF 00294 * 00295 KP = ABS( IPIV( K ) ) 00296 IF( KP.NE.K ) THEN 00297 * 00298 * Interchange rows and columns K and KP in the trailing 00299 * submatrix A(k-1:n,k-1:n) 00300 * 00301 IF( KP.LT.N ) 00302 $ CALL ZSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 ) 00303 DO 70 J = K + 1, KP - 1 00304 TEMP = DCONJG( A( J, K ) ) 00305 A( J, K ) = DCONJG( A( KP, J ) ) 00306 A( KP, J ) = TEMP 00307 70 CONTINUE 00308 A( KP, K ) = DCONJG( A( KP, K ) ) 00309 TEMP = A( K, K ) 00310 A( K, K ) = A( KP, KP ) 00311 A( KP, KP ) = TEMP 00312 IF( KSTEP.EQ.2 ) THEN 00313 TEMP = A( K, K-1 ) 00314 A( K, K-1 ) = A( KP, K-1 ) 00315 A( KP, K-1 ) = TEMP 00316 END IF 00317 END IF 00318 * 00319 K = K - KSTEP 00320 GO TO 60 00321 80 CONTINUE 00322 END IF 00323 * 00324 RETURN 00325 * 00326 * End of ZHETRI 00327 * 00328 END
1.7.3 
