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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 ZSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, 00002 $ WORK, INFO ) 00003 * 00004 * -- LAPACK PROTOTYPE routine (version 3.3.1) -- 00005 * 00006 * -- Written by Julie Langou of the Univ. of TN -- 00007 * -- April 2011 -- 00008 * 00009 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00010 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00011 * 00012 * .. Scalar Arguments .. 00013 CHARACTER UPLO 00014 INTEGER INFO, LDA, LDB, N, NRHS 00015 * .. 00016 * .. Array Arguments .. 00017 INTEGER IPIV( * ) 00018 DOUBLE COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) 00019 * .. 00020 * 00021 * Purpose 00022 * ======= 00023 * 00024 * ZSYTRS2 solves a system of linear equations A*X = B with a real 00025 * symmetric matrix A using the factorization A = U*D*U**T or 00026 * A = L*D*L**T computed by ZSYTRF and converted by ZSYCONV. 00027 * 00028 * Arguments 00029 * ========= 00030 * 00031 * UPLO (input) CHARACTER*1 00032 * Specifies whether the details of the factorization are stored 00033 * as an upper or lower triangular matrix. 00034 * = 'U': Upper triangular, form is A = U*D*U**T; 00035 * = 'L': Lower triangular, form is A = L*D*L**T. 00036 * 00037 * N (input) INTEGER 00038 * The order of the matrix A. N >= 0. 00039 * 00040 * NRHS (input) INTEGER 00041 * The number of right hand sides, i.e., the number of columns 00042 * of the matrix B. NRHS >= 0. 00043 * 00044 * A (input) DOUBLE COMPLEX array, dimension (LDA,N) 00045 * The block diagonal matrix D and the multipliers used to 00046 * obtain the factor U or L as computed by ZSYTRF. 00047 * 00048 * LDA (input) INTEGER 00049 * The leading dimension of the array A. LDA >= max(1,N). 00050 * 00051 * IPIV (input) INTEGER array, dimension (N) 00052 * Details of the interchanges and the block structure of D 00053 * as determined by ZSYTRF. 00054 * 00055 * B (input/output) DOUBLE COMPLEX array, dimension (LDB,NRHS) 00056 * On entry, the right hand side matrix B. 00057 * On exit, the solution matrix X. 00058 * 00059 * LDB (input) INTEGER 00060 * The leading dimension of the array B. LDB >= max(1,N). 00061 * 00062 * WORK (workspace) REAL array, dimension (N) 00063 * 00064 * INFO (output) INTEGER 00065 * = 0: successful exit 00066 * < 0: if INFO = -i, the i-th argument had an illegal value 00067 * 00068 * ===================================================================== 00069 * 00070 * .. Parameters .. 00071 DOUBLE COMPLEX ONE 00072 PARAMETER ( ONE = (1.0D+0,0.0D+0) ) 00073 * .. 00074 * .. Local Scalars .. 00075 LOGICAL UPPER 00076 INTEGER I, IINFO, J, K, KP 00077 DOUBLE COMPLEX AK, AKM1, AKM1K, BK, BKM1, DENOM 00078 * .. 00079 * .. External Functions .. 00080 LOGICAL LSAME 00081 EXTERNAL LSAME 00082 * .. 00083 * .. External Subroutines .. 00084 EXTERNAL ZSCAL, ZSYCONV, ZSWAP, ZTRSM, XERBLA 00085 * .. 00086 * .. Intrinsic Functions .. 00087 INTRINSIC MAX 00088 * .. 00089 * .. Executable Statements .. 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( NRHS.LT.0 ) THEN 00098 INFO = -3 00099 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00100 INFO = -5 00101 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00102 INFO = -8 00103 END IF 00104 IF( INFO.NE.0 ) THEN 00105 CALL XERBLA( 'ZSYTRS2', -INFO ) 00106 RETURN 00107 END IF 00108 * 00109 * Quick return if possible 00110 * 00111 IF( N.EQ.0 .OR. NRHS.EQ.0 ) 00112 $ RETURN 00113 * 00114 * Convert A 00115 * 00116 CALL ZSYCONV( UPLO, 'C', N, A, LDA, IPIV, WORK, IINFO ) 00117 * 00118 IF( UPPER ) THEN 00119 * 00120 * Solve A*X = B, where A = U*D*U**T. 00121 * 00122 * P**T * B 00123 K=N 00124 DO WHILE ( K .GE. 1 ) 00125 IF( IPIV( K ).GT.0 ) THEN 00126 * 1 x 1 diagonal block 00127 * Interchange rows K and IPIV(K). 00128 KP = IPIV( K ) 00129 IF( KP.NE.K ) 00130 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00131 K=K-1 00132 ELSE 00133 * 2 x 2 diagonal block 00134 * Interchange rows K-1 and -IPIV(K). 00135 KP = -IPIV( K ) 00136 IF( KP.EQ.-IPIV( K-1 ) ) 00137 $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB ) 00138 K=K-2 00139 END IF 00140 END DO 00141 * 00142 * Compute (U \P**T * B) -> B [ (U \P**T * B) ] 00143 * 00144 CALL ZTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB) 00145 * 00146 * Compute D \ B -> B [ D \ (U \P**T * B) ] 00147 * 00148 I=N 00149 DO WHILE ( I .GE. 1 ) 00150 IF( IPIV(I) .GT. 0 ) THEN 00151 CALL ZSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB ) 00152 ELSEIF ( I .GT. 1) THEN 00153 IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN 00154 AKM1K = WORK(I) 00155 AKM1 = A( I-1, I-1 ) / AKM1K 00156 AK = A( I, I ) / AKM1K 00157 DENOM = AKM1*AK - ONE 00158 DO 15 J = 1, NRHS 00159 BKM1 = B( I-1, J ) / AKM1K 00160 BK = B( I, J ) / AKM1K 00161 B( I-1, J ) = ( AK*BKM1-BK ) / DENOM 00162 B( I, J ) = ( AKM1*BK-BKM1 ) / DENOM 00163 15 CONTINUE 00164 I = I - 1 00165 ENDIF 00166 ENDIF 00167 I = I - 1 00168 END DO 00169 * 00170 * Compute (U**T \ B) -> B [ U**T \ (D \ (U \P**T * B) ) ] 00171 * 00172 CALL ZTRSM('L','U','T','U',N,NRHS,ONE,A,LDA,B,LDB) 00173 * 00174 * P * B [ P * (U**T \ (D \ (U \P**T * B) )) ] 00175 * 00176 K=1 00177 DO WHILE ( K .LE. N ) 00178 IF( IPIV( K ).GT.0 ) THEN 00179 * 1 x 1 diagonal block 00180 * Interchange rows K and IPIV(K). 00181 KP = IPIV( K ) 00182 IF( KP.NE.K ) 00183 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00184 K=K+1 00185 ELSE 00186 * 2 x 2 diagonal block 00187 * Interchange rows K-1 and -IPIV(K). 00188 KP = -IPIV( K ) 00189 IF( K .LT. N .AND. KP.EQ.-IPIV( K+1 ) ) 00190 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00191 K=K+2 00192 ENDIF 00193 END DO 00194 * 00195 ELSE 00196 * 00197 * Solve A*X = B, where A = L*D*L**T. 00198 * 00199 * P**T * B 00200 K=1 00201 DO WHILE ( K .LE. N ) 00202 IF( IPIV( K ).GT.0 ) THEN 00203 * 1 x 1 diagonal block 00204 * Interchange rows K and IPIV(K). 00205 KP = IPIV( K ) 00206 IF( KP.NE.K ) 00207 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00208 K=K+1 00209 ELSE 00210 * 2 x 2 diagonal block 00211 * Interchange rows K and -IPIV(K+1). 00212 KP = -IPIV( K+1 ) 00213 IF( KP.EQ.-IPIV( K ) ) 00214 $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB ) 00215 K=K+2 00216 ENDIF 00217 END DO 00218 * 00219 * Compute (L \P**T * B) -> B [ (L \P**T * B) ] 00220 * 00221 CALL ZTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB) 00222 * 00223 * Compute D \ B -> B [ D \ (L \P**T * B) ] 00224 * 00225 I=1 00226 DO WHILE ( I .LE. N ) 00227 IF( IPIV(I) .GT. 0 ) THEN 00228 CALL ZSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB ) 00229 ELSE 00230 AKM1K = WORK(I) 00231 AKM1 = A( I, I ) / AKM1K 00232 AK = A( I+1, I+1 ) / AKM1K 00233 DENOM = AKM1*AK - ONE 00234 DO 25 J = 1, NRHS 00235 BKM1 = B( I, J ) / AKM1K 00236 BK = B( I+1, J ) / AKM1K 00237 B( I, J ) = ( AK*BKM1-BK ) / DENOM 00238 B( I+1, J ) = ( AKM1*BK-BKM1 ) / DENOM 00239 25 CONTINUE 00240 I = I + 1 00241 ENDIF 00242 I = I + 1 00243 END DO 00244 * 00245 * Compute (L**T \ B) -> B [ L**T \ (D \ (L \P**T * B) ) ] 00246 * 00247 CALL ZTRSM('L','L','T','U',N,NRHS,ONE,A,LDA,B,LDB) 00248 * 00249 * P * B [ P * (L**T \ (D \ (L \P**T * B) )) ] 00250 * 00251 K=N 00252 DO WHILE ( K .GE. 1 ) 00253 IF( IPIV( K ).GT.0 ) THEN 00254 * 1 x 1 diagonal block 00255 * Interchange rows K and IPIV(K). 00256 KP = IPIV( K ) 00257 IF( KP.NE.K ) 00258 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00259 K=K-1 00260 ELSE 00261 * 2 x 2 diagonal block 00262 * Interchange rows K-1 and -IPIV(K). 00263 KP = -IPIV( K ) 00264 IF( K.GT.1 .AND. KP.EQ.-IPIV( K-1 ) ) 00265 $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) 00266 K=K-2 00267 ENDIF 00268 END DO 00269 * 00270 END IF 00271 * 00272 * Revert A 00273 * 00274 CALL ZSYCONV( UPLO, 'R', N, A, LDA, IPIV, WORK, IINFO ) 00275 * 00276 RETURN 00277 * 00278 * End of ZSYTRS2 00279 * 00280 END
1.7.3 
