 |
LAPACK 3.3.1
Linear Algebra PACKage
|
|
LAPACK 3.3.1
Linear Algebra PACKage
|
00001 SUBROUTINE CHPTRI( UPLO, N, AP, 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, N 00011 * .. 00012 * .. Array Arguments .. 00013 INTEGER IPIV( * ) 00014 COMPLEX AP( * ), WORK( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * CHPTRI computes the inverse of a complex Hermitian indefinite matrix 00021 * A in packed storage using the factorization A = U*D*U**H or 00022 * A = L*D*L**H computed by CHPTRF. 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 * AP (input/output) COMPLEX array, dimension (N*(N+1)/2) 00037 * On entry, the block diagonal matrix D and the multipliers 00038 * used to obtain the factor U or L as computed by CHPTRF, 00039 * stored as a packed triangular matrix. 00040 * 00041 * On exit, if INFO = 0, the (Hermitian) inverse of the original 00042 * matrix, stored as a packed triangular matrix. The j-th column 00043 * of inv(A) is stored in the array AP as follows: 00044 * if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; 00045 * if UPLO = 'L', 00046 * AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n. 00047 * 00048 * IPIV (input) INTEGER array, dimension (N) 00049 * Details of the interchanges and the block structure of D 00050 * as determined by CHPTRF. 00051 * 00052 * WORK (workspace) COMPLEX array, dimension (N) 00053 * 00054 * INFO (output) INTEGER 00055 * = 0: successful exit 00056 * < 0: if INFO = -i, the i-th argument had an illegal value 00057 * > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its 00058 * inverse could not be computed. 00059 * 00060 * ===================================================================== 00061 * 00062 * .. Parameters .. 00063 REAL ONE 00064 COMPLEX CONE, ZERO 00065 PARAMETER ( ONE = 1.0E+0, CONE = ( 1.0E+0, 0.0E+0 ), 00066 $ ZERO = ( 0.0E+0, 0.0E+0 ) ) 00067 * .. 00068 * .. Local Scalars .. 00069 LOGICAL UPPER 00070 INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP 00071 REAL AK, AKP1, D, T 00072 COMPLEX AKKP1, TEMP 00073 * .. 00074 * .. External Functions .. 00075 LOGICAL LSAME 00076 COMPLEX CDOTC 00077 EXTERNAL LSAME, CDOTC 00078 * .. 00079 * .. External Subroutines .. 00080 EXTERNAL CCOPY, CHPMV, CSWAP, XERBLA 00081 * .. 00082 * .. Intrinsic Functions .. 00083 INTRINSIC ABS, CONJG, REAL 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 END IF 00096 IF( INFO.NE.0 ) THEN 00097 CALL XERBLA( 'CHPTRI', -INFO ) 00098 RETURN 00099 END IF 00100 * 00101 * Quick return if possible 00102 * 00103 IF( N.EQ.0 ) 00104 $ RETURN 00105 * 00106 * Check that the diagonal matrix D is nonsingular. 00107 * 00108 IF( UPPER ) THEN 00109 * 00110 * Upper triangular storage: examine D from bottom to top 00111 * 00112 KP = N*( N+1 ) / 2 00113 DO 10 INFO = N, 1, -1 00114 IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO ) 00115 $ RETURN 00116 KP = KP - INFO 00117 10 CONTINUE 00118 ELSE 00119 * 00120 * Lower triangular storage: examine D from top to bottom. 00121 * 00122 KP = 1 00123 DO 20 INFO = 1, N 00124 IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO ) 00125 $ RETURN 00126 KP = KP + N - INFO + 1 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 KC = 1 00140 30 CONTINUE 00141 * 00142 * If K > N, exit from loop. 00143 * 00144 IF( K.GT.N ) 00145 $ GO TO 50 00146 * 00147 KCNEXT = KC + K 00148 IF( IPIV( K ).GT.0 ) THEN 00149 * 00150 * 1 x 1 diagonal block 00151 * 00152 * Invert the diagonal block. 00153 * 00154 AP( KC+K-1 ) = ONE / REAL( AP( KC+K-1 ) ) 00155 * 00156 * Compute column K of the inverse. 00157 * 00158 IF( K.GT.1 ) THEN 00159 CALL CCOPY( K-1, AP( KC ), 1, WORK, 1 ) 00160 CALL CHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO, 00161 $ AP( KC ), 1 ) 00162 AP( KC+K-1 ) = AP( KC+K-1 ) - 00163 $ REAL( CDOTC( K-1, WORK, 1, AP( KC ), 1 ) ) 00164 END IF 00165 KSTEP = 1 00166 ELSE 00167 * 00168 * 2 x 2 diagonal block 00169 * 00170 * Invert the diagonal block. 00171 * 00172 T = ABS( AP( KCNEXT+K-1 ) ) 00173 AK = REAL( AP( KC+K-1 ) ) / T 00174 AKP1 = REAL( AP( KCNEXT+K ) ) / T 00175 AKKP1 = AP( KCNEXT+K-1 ) / T 00176 D = T*( AK*AKP1-ONE ) 00177 AP( KC+K-1 ) = AKP1 / D 00178 AP( KCNEXT+K ) = AK / D 00179 AP( KCNEXT+K-1 ) = -AKKP1 / D 00180 * 00181 * Compute columns K and K+1 of the inverse. 00182 * 00183 IF( K.GT.1 ) THEN 00184 CALL CCOPY( K-1, AP( KC ), 1, WORK, 1 ) 00185 CALL CHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO, 00186 $ AP( KC ), 1 ) 00187 AP( KC+K-1 ) = AP( KC+K-1 ) - 00188 $ REAL( CDOTC( K-1, WORK, 1, AP( KC ), 1 ) ) 00189 AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) - 00190 $ CDOTC( K-1, AP( KC ), 1, AP( KCNEXT ), 00191 $ 1 ) 00192 CALL CCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 ) 00193 CALL CHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO, 00194 $ AP( KCNEXT ), 1 ) 00195 AP( KCNEXT+K ) = AP( KCNEXT+K ) - 00196 $ REAL( CDOTC( K-1, WORK, 1, AP( KCNEXT ), $ 1 ) ) 00197 END IF 00198 KSTEP = 2 00199 KCNEXT = KCNEXT + K + 1 00200 END IF 00201 * 00202 KP = ABS( IPIV( K ) ) 00203 IF( KP.NE.K ) THEN 00204 * 00205 * Interchange rows and columns K and KP in the leading 00206 * submatrix A(1:k+1,1:k+1) 00207 * 00208 KPC = ( KP-1 )*KP / 2 + 1 00209 CALL CSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 ) 00210 KX = KPC + KP - 1 00211 DO 40 J = KP + 1, K - 1 00212 KX = KX + J - 1 00213 TEMP = CONJG( AP( KC+J-1 ) ) 00214 AP( KC+J-1 ) = CONJG( AP( KX ) ) 00215 AP( KX ) = TEMP 00216 40 CONTINUE 00217 AP( KC+KP-1 ) = CONJG( AP( KC+KP-1 ) ) 00218 TEMP = AP( KC+K-1 ) 00219 AP( KC+K-1 ) = AP( KPC+KP-1 ) 00220 AP( KPC+KP-1 ) = TEMP 00221 IF( KSTEP.EQ.2 ) THEN 00222 TEMP = AP( KC+K+K-1 ) 00223 AP( KC+K+K-1 ) = AP( KC+K+KP-1 ) 00224 AP( KC+K+KP-1 ) = TEMP 00225 END IF 00226 END IF 00227 * 00228 K = K + KSTEP 00229 KC = KCNEXT 00230 GO TO 30 00231 50 CONTINUE 00232 * 00233 ELSE 00234 * 00235 * Compute inv(A) from the factorization A = L*D*L**H. 00236 * 00237 * K is the main loop index, increasing from 1 to N in steps of 00238 * 1 or 2, depending on the size of the diagonal blocks. 00239 * 00240 NPP = N*( N+1 ) / 2 00241 K = N 00242 KC = NPP 00243 60 CONTINUE 00244 * 00245 * If K < 1, exit from loop. 00246 * 00247 IF( K.LT.1 ) 00248 $ GO TO 80 00249 * 00250 KCNEXT = KC - ( N-K+2 ) 00251 IF( IPIV( K ).GT.0 ) THEN 00252 * 00253 * 1 x 1 diagonal block 00254 * 00255 * Invert the diagonal block. 00256 * 00257 AP( KC ) = ONE / REAL( AP( KC ) ) 00258 * 00259 * Compute column K of the inverse. 00260 * 00261 IF( K.LT.N ) THEN 00262 CALL CCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) 00263 CALL CHPMV( UPLO, N-K, -CONE, AP( KC+N-K+1 ), WORK, 1, 00264 $ ZERO, AP( KC+1 ), 1 ) 00265 AP( KC ) = AP( KC ) - REAL( CDOTC( N-K, WORK, 1, $ AP( KC+1 ), 1 ) ) 00266 END IF 00267 KSTEP = 1 00268 ELSE 00269 * 00270 * 2 x 2 diagonal block 00271 * 00272 * Invert the diagonal block. 00273 * 00274 T = ABS( AP( KCNEXT+1 ) ) 00275 AK = REAL( AP( KCNEXT ) ) / T 00276 AKP1 = REAL( AP( KC ) ) / T 00277 AKKP1 = AP( KCNEXT+1 ) / T 00278 D = T*( AK*AKP1-ONE ) 00279 AP( KCNEXT ) = AKP1 / D 00280 AP( KC ) = AK / D 00281 AP( KCNEXT+1 ) = -AKKP1 / D 00282 * 00283 * Compute columns K-1 and K of the inverse. 00284 * 00285 IF( K.LT.N ) THEN 00286 CALL CCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) 00287 CALL CHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK, 00288 $ 1, ZERO, AP( KC+1 ), 1 ) 00289 AP( KC ) = AP( KC ) - REAL( CDOTC( N-K, WORK, 1, $ AP( KC+1 ), 1 ) ) 00290 AP( KCNEXT+1 ) = AP( KCNEXT+1 ) - 00291 $ CDOTC( N-K, AP( KC+1 ), 1, 00292 $ AP( KCNEXT+2 ), 1 ) 00293 CALL CCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 ) 00294 CALL CHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK, 00295 $ 1, ZERO, AP( KCNEXT+2 ), 1 ) 00296 AP( KCNEXT ) = AP( KCNEXT ) - 00297 $ REAL( CDOTC( N-K, WORK, 1, AP( KCNEXT+2 ), $ 1 ) ) 00298 END IF 00299 KSTEP = 2 00300 KCNEXT = KCNEXT - ( N-K+3 ) 00301 END IF 00302 * 00303 KP = ABS( IPIV( K ) ) 00304 IF( KP.NE.K ) THEN 00305 * 00306 * Interchange rows and columns K and KP in the trailing 00307 * submatrix A(k-1:n,k-1:n) 00308 * 00309 KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1 00310 IF( KP.LT.N ) 00311 $ CALL CSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 ) 00312 KX = KC + KP - K 00313 DO 70 J = K + 1, KP - 1 00314 KX = KX + N - J + 1 00315 TEMP = CONJG( AP( KC+J-K ) ) 00316 AP( KC+J-K ) = CONJG( AP( KX ) ) 00317 AP( KX ) = TEMP 00318 70 CONTINUE 00319 AP( KC+KP-K ) = CONJG( AP( KC+KP-K ) ) 00320 TEMP = AP( KC ) 00321 AP( KC ) = AP( KPC ) 00322 AP( KPC ) = TEMP 00323 IF( KSTEP.EQ.2 ) THEN 00324 TEMP = AP( KC-N+K-1 ) 00325 AP( KC-N+K-1 ) = AP( KC-N+KP-1 ) 00326 AP( KC-N+KP-1 ) = TEMP 00327 END IF 00328 END IF 00329 * 00330 K = K - KSTEP 00331 KC = KCNEXT 00332 GO TO 60 00333 80 CONTINUE 00334 END IF 00335 * 00336 RETURN 00337 * 00338 * End of CHPTRI 00339 * 00340 END 00341
1.7.3 
