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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO ) 2: * 3: * -- LAPACK routine (version 3.2) -- 4: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 6: * November 2006 7: * 8: * .. Scalar Arguments .. 9: CHARACTER UPLO 10: INTEGER INFO, LDA, N 11: * .. 12: * .. Array Arguments .. 13: INTEGER IPIV( * ) 14: DOUBLE PRECISION A( LDA, * ), WORK( * ) 15: * .. 16: * 17: * Purpose 18: * ======= 19: * 20: * DSYTRI computes the inverse of a real symmetric indefinite matrix 21: * A using the factorization A = U*D*U**T or A = L*D*L**T computed by 22: * DSYTRF. 23: * 24: * Arguments 25: * ========= 26: * 27: * UPLO (input) CHARACTER*1 28: * Specifies whether the details of the factorization are stored 29: * as an upper or lower triangular matrix. 30: * = 'U': Upper triangular, form is A = U*D*U**T; 31: * = 'L': Lower triangular, form is A = L*D*L**T. 32: * 33: * N (input) INTEGER 34: * The order of the matrix A. N >= 0. 35: * 36: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) 37: * On entry, the block diagonal matrix D and the multipliers 38: * used to obtain the factor U or L as computed by DSYTRF. 39: * 40: * On exit, if INFO = 0, the (symmetric) inverse of the original 41: * matrix. If UPLO = 'U', the upper triangular part of the 42: * inverse is formed and the part of A below the diagonal is not 43: * referenced; if UPLO = 'L' the lower triangular part of the 44: * inverse is formed and the part of A above the diagonal is 45: * not referenced. 46: * 47: * LDA (input) INTEGER 48: * The leading dimension of the array A. LDA >= max(1,N). 49: * 50: * IPIV (input) INTEGER array, dimension (N) 51: * Details of the interchanges and the block structure of D 52: * as determined by DSYTRF. 53: * 54: * WORK (workspace) DOUBLE PRECISION array, dimension (N) 55: * 56: * INFO (output) INTEGER 57: * = 0: successful exit 58: * < 0: if INFO = -i, the i-th argument had an illegal value 59: * > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its 60: * inverse could not be computed. 61: * 62: * ===================================================================== 63: * 64: * .. Parameters .. 65: DOUBLE PRECISION ONE, ZERO 66: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 67: * .. 68: * .. Local Scalars .. 69: LOGICAL UPPER 70: INTEGER K, KP, KSTEP 71: DOUBLE PRECISION AK, AKKP1, AKP1, D, T, TEMP 72: * .. 73: * .. External Functions .. 74: LOGICAL LSAME 75: DOUBLE PRECISION DDOT 76: EXTERNAL LSAME, DDOT 77: * .. 78: * .. External Subroutines .. 79: EXTERNAL DCOPY, DSWAP, DSYMV, XERBLA 80: * .. 81: * .. Intrinsic Functions .. 82: INTRINSIC ABS, MAX 83: * .. 84: * .. Executable Statements .. 85: * 86: * Test the input parameters. 87: * 88: INFO = 0 89: UPPER = LSAME( UPLO, 'U' ) 90: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 91: INFO = -1 92: ELSE IF( N.LT.0 ) THEN 93: INFO = -2 94: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 95: INFO = -4 96: END IF 97: IF( INFO.NE.0 ) THEN 98: CALL XERBLA( 'DSYTRI', -INFO ) 99: RETURN 100: END IF 101: * 102: * Quick return if possible 103: * 104: IF( N.EQ.0 ) 105: $ RETURN 106: * 107: * Check that the diagonal matrix D is nonsingular. 108: * 109: IF( UPPER ) THEN 110: * 111: * Upper triangular storage: examine D from bottom to top 112: * 113: DO 10 INFO = N, 1, -1 114: IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO ) 115: $ RETURN 116: 10 CONTINUE 117: ELSE 118: * 119: * Lower triangular storage: examine D from top to bottom. 120: * 121: DO 20 INFO = 1, N 122: IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO ) 123: $ RETURN 124: 20 CONTINUE 125: END IF 126: INFO = 0 127: * 128: IF( UPPER ) THEN 129: * 130: * Compute inv(A) from the factorization A = U*D*U'. 131: * 132: * K is the main loop index, increasing from 1 to N in steps of 133: * 1 or 2, depending on the size of the diagonal blocks. 134: * 135: K = 1 136: 30 CONTINUE 137: * 138: * If K > N, exit from loop. 139: * 140: IF( K.GT.N ) 141: $ GO TO 40 142: * 143: IF( IPIV( K ).GT.0 ) THEN 144: * 145: * 1 x 1 diagonal block 146: * 147: * Invert the diagonal block. 148: * 149: A( K, K ) = ONE / A( K, K ) 150: * 151: * Compute column K of the inverse. 152: * 153: IF( K.GT.1 ) THEN 154: CALL DCOPY( K-1, A( 1, K ), 1, WORK, 1 ) 155: CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO, 156: $ A( 1, K ), 1 ) 157: A( K, K ) = A( K, K ) - DDOT( K-1, WORK, 1, A( 1, K ), 158: $ 1 ) 159: END IF 160: KSTEP = 1 161: ELSE 162: * 163: * 2 x 2 diagonal block 164: * 165: * Invert the diagonal block. 166: * 167: T = ABS( A( K, K+1 ) ) 168: AK = A( K, K ) / T 169: AKP1 = A( K+1, K+1 ) / T 170: AKKP1 = A( K, K+1 ) / T 171: D = T*( AK*AKP1-ONE ) 172: A( K, K ) = AKP1 / D 173: A( K+1, K+1 ) = AK / D 174: A( K, K+1 ) = -AKKP1 / D 175: * 176: * Compute columns K and K+1 of the inverse. 177: * 178: IF( K.GT.1 ) THEN 179: CALL DCOPY( K-1, A( 1, K ), 1, WORK, 1 ) 180: CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO, 181: $ A( 1, K ), 1 ) 182: A( K, K ) = A( K, K ) - DDOT( K-1, WORK, 1, A( 1, K ), 183: $ 1 ) 184: A( K, K+1 ) = A( K, K+1 ) - 185: $ DDOT( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 ) 186: CALL DCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 ) 187: CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO, 188: $ A( 1, K+1 ), 1 ) 189: A( K+1, K+1 ) = A( K+1, K+1 ) - 190: $ DDOT( K-1, WORK, 1, A( 1, K+1 ), 1 ) 191: END IF 192: KSTEP = 2 193: END IF 194: * 195: KP = ABS( IPIV( K ) ) 196: IF( KP.NE.K ) THEN 197: * 198: * Interchange rows and columns K and KP in the leading 199: * submatrix A(1:k+1,1:k+1) 200: * 201: CALL DSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 ) 202: CALL DSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA ) 203: TEMP = A( K, K ) 204: A( K, K ) = A( KP, KP ) 205: A( KP, KP ) = TEMP 206: IF( KSTEP.EQ.2 ) THEN 207: TEMP = A( K, K+1 ) 208: A( K, K+1 ) = A( KP, K+1 ) 209: A( KP, K+1 ) = TEMP 210: END IF 211: END IF 212: * 213: K = K + KSTEP 214: GO TO 30 215: 40 CONTINUE 216: * 217: ELSE 218: * 219: * Compute inv(A) from the factorization A = L*D*L'. 220: * 221: * K is the main loop index, increasing from 1 to N in steps of 222: * 1 or 2, depending on the size of the diagonal blocks. 223: * 224: K = N 225: 50 CONTINUE 226: * 227: * If K < 1, exit from loop. 228: * 229: IF( K.LT.1 ) 230: $ GO TO 60 231: * 232: IF( IPIV( K ).GT.0 ) THEN 233: * 234: * 1 x 1 diagonal block 235: * 236: * Invert the diagonal block. 237: * 238: A( K, K ) = ONE / A( K, K ) 239: * 240: * Compute column K of the inverse. 241: * 242: IF( K.LT.N ) THEN 243: CALL DCOPY( N-K, A( K+1, K ), 1, WORK, 1 ) 244: CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1, 245: $ ZERO, A( K+1, K ), 1 ) 246: A( K, K ) = A( K, K ) - DDOT( N-K, WORK, 1, A( K+1, K ), 247: $ 1 ) 248: END IF 249: KSTEP = 1 250: ELSE 251: * 252: * 2 x 2 diagonal block 253: * 254: * Invert the diagonal block. 255: * 256: T = ABS( A( K, K-1 ) ) 257: AK = A( K-1, K-1 ) / T 258: AKP1 = A( K, K ) / T 259: AKKP1 = A( K, K-1 ) / T 260: D = T*( AK*AKP1-ONE ) 261: A( K-1, K-1 ) = AKP1 / D 262: A( K, K ) = AK / D 263: A( K, K-1 ) = -AKKP1 / D 264: * 265: * Compute columns K-1 and K of the inverse. 266: * 267: IF( K.LT.N ) THEN 268: CALL DCOPY( N-K, A( K+1, K ), 1, WORK, 1 ) 269: CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1, 270: $ ZERO, A( K+1, K ), 1 ) 271: A( K, K ) = A( K, K ) - DDOT( N-K, WORK, 1, A( K+1, K ), 272: $ 1 ) 273: A( K, K-1 ) = A( K, K-1 ) - 274: $ DDOT( N-K, A( K+1, K ), 1, A( K+1, K-1 ), 275: $ 1 ) 276: CALL DCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 ) 277: CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1, 278: $ ZERO, A( K+1, K-1 ), 1 ) 279: A( K-1, K-1 ) = A( K-1, K-1 ) - 280: $ DDOT( N-K, WORK, 1, A( K+1, K-1 ), 1 ) 281: END IF 282: KSTEP = 2 283: END IF 284: * 285: KP = ABS( IPIV( K ) ) 286: IF( KP.NE.K ) THEN 287: * 288: * Interchange rows and columns K and KP in the trailing 289: * submatrix A(k-1:n,k-1:n) 290: * 291: IF( KP.LT.N ) 292: $ CALL DSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 ) 293: CALL DSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA ) 294: TEMP = A( K, K ) 295: A( K, K ) = A( KP, KP ) 296: A( KP, KP ) = TEMP 297: IF( KSTEP.EQ.2 ) THEN 298: TEMP = A( K, K-1 ) 299: A( K, K-1 ) = A( KP, K-1 ) 300: A( KP, K-1 ) = TEMP 301: END IF 302: END IF 303: * 304: K = K - KSTEP 305: GO TO 50 306: 60 CONTINUE 307: END IF 308: * 309: RETURN 310: * 311: * End of DSYTRI 312: * 313: END