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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 ZHPTRI( 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*16 AP( * ), WORK( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * ZHPTRI 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 ZHPTRF. 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*16 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 ZHPTRF, 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 ZHPTRF. 00051 * 00052 * WORK (workspace) COMPLEX*16 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 DOUBLE PRECISION ONE 00064 COMPLEX*16 CONE, ZERO 00065 PARAMETER ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ), 00066 $ ZERO = ( 0.0D+0, 0.0D+0 ) ) 00067 * .. 00068 * .. Local Scalars .. 00069 LOGICAL UPPER 00070 INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP 00071 DOUBLE PRECISION AK, AKP1, D, T 00072 COMPLEX*16 AKKP1, TEMP 00073 * .. 00074 * .. External Functions .. 00075 LOGICAL LSAME 00076 COMPLEX*16 ZDOTC 00077 EXTERNAL LSAME, ZDOTC 00078 * .. 00079 * .. External Subroutines .. 00080 EXTERNAL XERBLA, ZCOPY, ZHPMV, ZSWAP 00081 * .. 00082 * .. Intrinsic Functions .. 00083 INTRINSIC ABS, DBLE, DCONJG 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( 'ZHPTRI', -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 / DBLE( AP( KC+K-1 ) ) 00155 * 00156 * Compute column K of the inverse. 00157 * 00158 IF( K.GT.1 ) THEN 00159 CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 ) 00160 CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO, 00161 $ AP( KC ), 1 ) 00162 AP( KC+K-1 ) = AP( KC+K-1 ) - 00163 $ DBLE( ZDOTC( 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 = DBLE( AP( KC+K-1 ) ) / T 00174 AKP1 = DBLE( 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 ZCOPY( K-1, AP( KC ), 1, WORK, 1 ) 00185 CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO, 00186 $ AP( KC ), 1 ) 00187 AP( KC+K-1 ) = AP( KC+K-1 ) - 00188 $ DBLE( ZDOTC( K-1, WORK, 1, AP( KC ), 1 ) ) 00189 AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) - 00190 $ ZDOTC( K-1, AP( KC ), 1, AP( KCNEXT ), 00191 $ 1 ) 00192 CALL ZCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 ) 00193 CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO, 00194 $ AP( KCNEXT ), 1 ) 00195 AP( KCNEXT+K ) = AP( KCNEXT+K ) - 00196 $ DBLE( ZDOTC( K-1, WORK, 1, AP( KCNEXT ), 00197 $ 1 ) ) 00198 END IF 00199 KSTEP = 2 00200 KCNEXT = KCNEXT + K + 1 00201 END IF 00202 * 00203 KP = ABS( IPIV( K ) ) 00204 IF( KP.NE.K ) THEN 00205 * 00206 * Interchange rows and columns K and KP in the leading 00207 * submatrix A(1:k+1,1:k+1) 00208 * 00209 KPC = ( KP-1 )*KP / 2 + 1 00210 CALL ZSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 ) 00211 KX = KPC + KP - 1 00212 DO 40 J = KP + 1, K - 1 00213 KX = KX + J - 1 00214 TEMP = DCONJG( AP( KC+J-1 ) ) 00215 AP( KC+J-1 ) = DCONJG( AP( KX ) ) 00216 AP( KX ) = TEMP 00217 40 CONTINUE 00218 AP( KC+KP-1 ) = DCONJG( AP( KC+KP-1 ) ) 00219 TEMP = AP( KC+K-1 ) 00220 AP( KC+K-1 ) = AP( KPC+KP-1 ) 00221 AP( KPC+KP-1 ) = TEMP 00222 IF( KSTEP.EQ.2 ) THEN 00223 TEMP = AP( KC+K+K-1 ) 00224 AP( KC+K+K-1 ) = AP( KC+K+KP-1 ) 00225 AP( KC+K+KP-1 ) = TEMP 00226 END IF 00227 END IF 00228 * 00229 K = K + KSTEP 00230 KC = KCNEXT 00231 GO TO 30 00232 50 CONTINUE 00233 * 00234 ELSE 00235 * 00236 * Compute inv(A) from the factorization A = L*D*L**H. 00237 * 00238 * K is the main loop index, increasing from 1 to N in steps of 00239 * 1 or 2, depending on the size of the diagonal blocks. 00240 * 00241 NPP = N*( N+1 ) / 2 00242 K = N 00243 KC = NPP 00244 60 CONTINUE 00245 * 00246 * If K < 1, exit from loop. 00247 * 00248 IF( K.LT.1 ) 00249 $ GO TO 80 00250 * 00251 KCNEXT = KC - ( N-K+2 ) 00252 IF( IPIV( K ).GT.0 ) THEN 00253 * 00254 * 1 x 1 diagonal block 00255 * 00256 * Invert the diagonal block. 00257 * 00258 AP( KC ) = ONE / DBLE( AP( KC ) ) 00259 * 00260 * Compute column K of the inverse. 00261 * 00262 IF( K.LT.N ) THEN 00263 CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) 00264 CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+N-K+1 ), WORK, 1, 00265 $ ZERO, AP( KC+1 ), 1 ) 00266 AP( KC ) = AP( KC ) - DBLE( ZDOTC( N-K, WORK, 1, 00267 $ AP( KC+1 ), 1 ) ) 00268 END IF 00269 KSTEP = 1 00270 ELSE 00271 * 00272 * 2 x 2 diagonal block 00273 * 00274 * Invert the diagonal block. 00275 * 00276 T = ABS( AP( KCNEXT+1 ) ) 00277 AK = DBLE( AP( KCNEXT ) ) / T 00278 AKP1 = DBLE( AP( KC ) ) / T 00279 AKKP1 = AP( KCNEXT+1 ) / T 00280 D = T*( AK*AKP1-ONE ) 00281 AP( KCNEXT ) = AKP1 / D 00282 AP( KC ) = AK / D 00283 AP( KCNEXT+1 ) = -AKKP1 / D 00284 * 00285 * Compute columns K-1 and K of the inverse. 00286 * 00287 IF( K.LT.N ) THEN 00288 CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) 00289 CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK, 00290 $ 1, ZERO, AP( KC+1 ), 1 ) 00291 AP( KC ) = AP( KC ) - DBLE( ZDOTC( N-K, WORK, 1, 00292 $ AP( KC+1 ), 1 ) ) 00293 AP( KCNEXT+1 ) = AP( KCNEXT+1 ) - 00294 $ ZDOTC( N-K, AP( KC+1 ), 1, 00295 $ AP( KCNEXT+2 ), 1 ) 00296 CALL ZCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 ) 00297 CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK, 00298 $ 1, ZERO, AP( KCNEXT+2 ), 1 ) 00299 AP( KCNEXT ) = AP( KCNEXT ) - 00300 $ DBLE( ZDOTC( N-K, WORK, 1, AP( KCNEXT+2 ), 00301 $ 1 ) ) 00302 END IF 00303 KSTEP = 2 00304 KCNEXT = KCNEXT - ( N-K+3 ) 00305 END IF 00306 * 00307 KP = ABS( IPIV( K ) ) 00308 IF( KP.NE.K ) THEN 00309 * 00310 * Interchange rows and columns K and KP in the trailing 00311 * submatrix A(k-1:n,k-1:n) 00312 * 00313 KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1 00314 IF( KP.LT.N ) 00315 $ CALL ZSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 ) 00316 KX = KC + KP - K 00317 DO 70 J = K + 1, KP - 1 00318 KX = KX + N - J + 1 00319 TEMP = DCONJG( AP( KC+J-K ) ) 00320 AP( KC+J-K ) = DCONJG( AP( KX ) ) 00321 AP( KX ) = TEMP 00322 70 CONTINUE 00323 AP( KC+KP-K ) = DCONJG( AP( KC+KP-K ) ) 00324 TEMP = AP( KC ) 00325 AP( KC ) = AP( KPC ) 00326 AP( KPC ) = TEMP 00327 IF( KSTEP.EQ.2 ) THEN 00328 TEMP = AP( KC-N+K-1 ) 00329 AP( KC-N+K-1 ) = AP( KC-N+KP-1 ) 00330 AP( KC-N+KP-1 ) = TEMP 00331 END IF 00332 END IF 00333 * 00334 K = K - KSTEP 00335 KC = KCNEXT 00336 GO TO 60 00337 80 CONTINUE 00338 END IF 00339 * 00340 RETURN 00341 * 00342 * End of ZHPTRI 00343 * 00344 END
1.7.3 
