 |
LAPACK 3.3.1
Linear Algebra PACKage
|
|
LAPACK 3.3.1
Linear Algebra PACKage
|
00001 SUBROUTINE SSPTRI( 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 REAL AP( * ), WORK( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * SSPTRI computes the inverse of a real symmetric indefinite matrix 00021 * A in packed storage using the factorization A = U*D*U**T or 00022 * A = L*D*L**T computed by SSPTRF. 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 * AP (input/output) REAL 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 SSPTRF, 00039 * stored as a packed triangular matrix. 00040 * 00041 * On exit, if INFO = 0, the (symmetric) 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 SSPTRF. 00051 * 00052 * WORK (workspace) REAL 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, ZERO 00064 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00065 * .. 00066 * .. Local Scalars .. 00067 LOGICAL UPPER 00068 INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP 00069 REAL AK, AKKP1, AKP1, D, T, TEMP 00070 * .. 00071 * .. External Functions .. 00072 LOGICAL LSAME 00073 REAL SDOT 00074 EXTERNAL LSAME, SDOT 00075 * .. 00076 * .. External Subroutines .. 00077 EXTERNAL SCOPY, SSPMV, SSWAP, XERBLA 00078 * .. 00079 * .. Intrinsic Functions .. 00080 INTRINSIC ABS 00081 * .. 00082 * .. Executable Statements .. 00083 * 00084 * Test the input parameters. 00085 * 00086 INFO = 0 00087 UPPER = LSAME( UPLO, 'U' ) 00088 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00089 INFO = -1 00090 ELSE IF( N.LT.0 ) THEN 00091 INFO = -2 00092 END IF 00093 IF( INFO.NE.0 ) THEN 00094 CALL XERBLA( 'SSPTRI', -INFO ) 00095 RETURN 00096 END IF 00097 * 00098 * Quick return if possible 00099 * 00100 IF( N.EQ.0 ) 00101 $ RETURN 00102 * 00103 * Check that the diagonal matrix D is nonsingular. 00104 * 00105 IF( UPPER ) THEN 00106 * 00107 * Upper triangular storage: examine D from bottom to top 00108 * 00109 KP = N*( N+1 ) / 2 00110 DO 10 INFO = N, 1, -1 00111 IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO ) 00112 $ RETURN 00113 KP = KP - INFO 00114 10 CONTINUE 00115 ELSE 00116 * 00117 * Lower triangular storage: examine D from top to bottom. 00118 * 00119 KP = 1 00120 DO 20 INFO = 1, N 00121 IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO ) 00122 $ RETURN 00123 KP = KP + N - INFO + 1 00124 20 CONTINUE 00125 END IF 00126 INFO = 0 00127 * 00128 IF( UPPER ) THEN 00129 * 00130 * Compute inv(A) from the factorization A = U*D*U**T. 00131 * 00132 * K is the main loop index, increasing from 1 to N in steps of 00133 * 1 or 2, depending on the size of the diagonal blocks. 00134 * 00135 K = 1 00136 KC = 1 00137 30 CONTINUE 00138 * 00139 * If K > N, exit from loop. 00140 * 00141 IF( K.GT.N ) 00142 $ GO TO 50 00143 * 00144 KCNEXT = KC + K 00145 IF( IPIV( K ).GT.0 ) THEN 00146 * 00147 * 1 x 1 diagonal block 00148 * 00149 * Invert the diagonal block. 00150 * 00151 AP( KC+K-1 ) = ONE / AP( KC+K-1 ) 00152 * 00153 * Compute column K of the inverse. 00154 * 00155 IF( K.GT.1 ) THEN 00156 CALL SCOPY( K-1, AP( KC ), 1, WORK, 1 ) 00157 CALL SSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ), 00158 $ 1 ) 00159 AP( KC+K-1 ) = AP( KC+K-1 ) - 00160 $ SDOT( K-1, WORK, 1, AP( KC ), 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( AP( KCNEXT+K-1 ) ) 00170 AK = AP( KC+K-1 ) / T 00171 AKP1 = AP( KCNEXT+K ) / T 00172 AKKP1 = AP( KCNEXT+K-1 ) / T 00173 D = T*( AK*AKP1-ONE ) 00174 AP( KC+K-1 ) = AKP1 / D 00175 AP( KCNEXT+K ) = AK / D 00176 AP( KCNEXT+K-1 ) = -AKKP1 / D 00177 * 00178 * Compute columns K and K+1 of the inverse. 00179 * 00180 IF( K.GT.1 ) THEN 00181 CALL SCOPY( K-1, AP( KC ), 1, WORK, 1 ) 00182 CALL SSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ), 00183 $ 1 ) 00184 AP( KC+K-1 ) = AP( KC+K-1 ) - 00185 $ SDOT( K-1, WORK, 1, AP( KC ), 1 ) 00186 AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) - 00187 $ SDOT( K-1, AP( KC ), 1, AP( KCNEXT ), 00188 $ 1 ) 00189 CALL SCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 ) 00190 CALL SSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, 00191 $ AP( KCNEXT ), 1 ) 00192 AP( KCNEXT+K ) = AP( KCNEXT+K ) - 00193 $ SDOT( K-1, WORK, 1, AP( KCNEXT ), 1 ) 00194 END IF 00195 KSTEP = 2 00196 KCNEXT = KCNEXT + K + 1 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 KPC = ( KP-1 )*KP / 2 + 1 00206 CALL SSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 ) 00207 KX = KPC + KP - 1 00208 DO 40 J = KP + 1, K - 1 00209 KX = KX + J - 1 00210 TEMP = AP( KC+J-1 ) 00211 AP( KC+J-1 ) = AP( KX ) 00212 AP( KX ) = TEMP 00213 40 CONTINUE 00214 TEMP = AP( KC+K-1 ) 00215 AP( KC+K-1 ) = AP( KPC+KP-1 ) 00216 AP( KPC+KP-1 ) = TEMP 00217 IF( KSTEP.EQ.2 ) THEN 00218 TEMP = AP( KC+K+K-1 ) 00219 AP( KC+K+K-1 ) = AP( KC+K+KP-1 ) 00220 AP( KC+K+KP-1 ) = TEMP 00221 END IF 00222 END IF 00223 * 00224 K = K + KSTEP 00225 KC = KCNEXT 00226 GO TO 30 00227 50 CONTINUE 00228 * 00229 ELSE 00230 * 00231 * Compute inv(A) from the factorization A = L*D*L**T. 00232 * 00233 * K is the main loop index, increasing from 1 to N in steps of 00234 * 1 or 2, depending on the size of the diagonal blocks. 00235 * 00236 NPP = N*( N+1 ) / 2 00237 K = N 00238 KC = NPP 00239 60 CONTINUE 00240 * 00241 * If K < 1, exit from loop. 00242 * 00243 IF( K.LT.1 ) 00244 $ GO TO 80 00245 * 00246 KCNEXT = KC - ( N-K+2 ) 00247 IF( IPIV( K ).GT.0 ) THEN 00248 * 00249 * 1 x 1 diagonal block 00250 * 00251 * Invert the diagonal block. 00252 * 00253 AP( KC ) = ONE / AP( KC ) 00254 * 00255 * Compute column K of the inverse. 00256 * 00257 IF( K.LT.N ) THEN 00258 CALL SCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) 00259 CALL SSPMV( UPLO, N-K, -ONE, AP( KC+N-K+1 ), WORK, 1, 00260 $ ZERO, AP( KC+1 ), 1 ) 00261 AP( KC ) = AP( KC ) - SDOT( N-K, WORK, 1, AP( KC+1 ), 1 ) 00262 END IF 00263 KSTEP = 1 00264 ELSE 00265 * 00266 * 2 x 2 diagonal block 00267 * 00268 * Invert the diagonal block. 00269 * 00270 T = ABS( AP( KCNEXT+1 ) ) 00271 AK = AP( KCNEXT ) / T 00272 AKP1 = AP( KC ) / T 00273 AKKP1 = AP( KCNEXT+1 ) / T 00274 D = T*( AK*AKP1-ONE ) 00275 AP( KCNEXT ) = AKP1 / D 00276 AP( KC ) = AK / D 00277 AP( KCNEXT+1 ) = -AKKP1 / D 00278 * 00279 * Compute columns K-1 and K of the inverse. 00280 * 00281 IF( K.LT.N ) THEN 00282 CALL SCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) 00283 CALL SSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1, 00284 $ ZERO, AP( KC+1 ), 1 ) 00285 AP( KC ) = AP( KC ) - SDOT( N-K, WORK, 1, AP( KC+1 ), 1 ) 00286 AP( KCNEXT+1 ) = AP( KCNEXT+1 ) - 00287 $ SDOT( N-K, AP( KC+1 ), 1, 00288 $ AP( KCNEXT+2 ), 1 ) 00289 CALL SCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 ) 00290 CALL SSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1, 00291 $ ZERO, AP( KCNEXT+2 ), 1 ) 00292 AP( KCNEXT ) = AP( KCNEXT ) - 00293 $ SDOT( N-K, WORK, 1, AP( KCNEXT+2 ), 1 ) 00294 END IF 00295 KSTEP = 2 00296 KCNEXT = KCNEXT - ( N-K+3 ) 00297 END IF 00298 * 00299 KP = ABS( IPIV( K ) ) 00300 IF( KP.NE.K ) THEN 00301 * 00302 * Interchange rows and columns K and KP in the trailing 00303 * submatrix A(k-1:n,k-1:n) 00304 * 00305 KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1 00306 IF( KP.LT.N ) 00307 $ CALL SSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 ) 00308 KX = KC + KP - K 00309 DO 70 J = K + 1, KP - 1 00310 KX = KX + N - J + 1 00311 TEMP = AP( KC+J-K ) 00312 AP( KC+J-K ) = AP( KX ) 00313 AP( KX ) = TEMP 00314 70 CONTINUE 00315 TEMP = AP( KC ) 00316 AP( KC ) = AP( KPC ) 00317 AP( KPC ) = TEMP 00318 IF( KSTEP.EQ.2 ) THEN 00319 TEMP = AP( KC-N+K-1 ) 00320 AP( KC-N+K-1 ) = AP( KC-N+KP-1 ) 00321 AP( KC-N+KP-1 ) = TEMP 00322 END IF 00323 END IF 00324 * 00325 K = K - KSTEP 00326 KC = KCNEXT 00327 GO TO 60 00328 80 CONTINUE 00329 END IF 00330 * 00331 RETURN 00332 * 00333 * End of SSPTRI 00334 * 00335 END
1.7.3 
