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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZSPTRI( UPLO, N, AP, 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, N 11: * .. 12: * .. Array Arguments .. 13: INTEGER IPIV( * ) 14: COMPLEX*16 AP( * ), WORK( * ) 15: * .. 16: * 17: * Purpose 18: * ======= 19: * 20: * ZSPTRI computes the inverse of a complex symmetric indefinite matrix 21: * A in packed storage using the factorization A = U*D*U**T or 22: * A = L*D*L**T computed by ZSPTRF. 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: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) 37: * On entry, the block diagonal matrix D and the multipliers 38: * used to obtain the factor U or L as computed by ZSPTRF, 39: * stored as a packed triangular matrix. 40: * 41: * On exit, if INFO = 0, the (symmetric) inverse of the original 42: * matrix, stored as a packed triangular matrix. The j-th column 43: * of inv(A) is stored in the array AP as follows: 44: * if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; 45: * if UPLO = 'L', 46: * AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n. 47: * 48: * IPIV (input) INTEGER array, dimension (N) 49: * Details of the interchanges and the block structure of D 50: * as determined by ZSPTRF. 51: * 52: * WORK (workspace) COMPLEX*16 array, dimension (N) 53: * 54: * INFO (output) INTEGER 55: * = 0: successful exit 56: * < 0: if INFO = -i, the i-th argument had an illegal value 57: * > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its 58: * inverse could not be computed. 59: * 60: * ===================================================================== 61: * 62: * .. Parameters .. 63: COMPLEX*16 ONE, ZERO 64: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), 65: $ ZERO = ( 0.0D+0, 0.0D+0 ) ) 66: * .. 67: * .. Local Scalars .. 68: LOGICAL UPPER 69: INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP 70: COMPLEX*16 AK, AKKP1, AKP1, D, T, TEMP 71: * .. 72: * .. External Functions .. 73: LOGICAL LSAME 74: COMPLEX*16 ZDOTU 75: EXTERNAL LSAME, ZDOTU 76: * .. 77: * .. External Subroutines .. 78: EXTERNAL XERBLA, ZCOPY, ZSPMV, ZSWAP 79: * .. 80: * .. Intrinsic Functions .. 81: INTRINSIC ABS 82: * .. 83: * .. Executable Statements .. 84: * 85: * Test the input parameters. 86: * 87: INFO = 0 88: UPPER = LSAME( UPLO, 'U' ) 89: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 90: INFO = -1 91: ELSE IF( N.LT.0 ) THEN 92: INFO = -2 93: END IF 94: IF( INFO.NE.0 ) THEN 95: CALL XERBLA( 'ZSPTRI', -INFO ) 96: RETURN 97: END IF 98: * 99: * Quick return if possible 100: * 101: IF( N.EQ.0 ) 102: $ RETURN 103: * 104: * Check that the diagonal matrix D is nonsingular. 105: * 106: IF( UPPER ) THEN 107: * 108: * Upper triangular storage: examine D from bottom to top 109: * 110: KP = N*( N+1 ) / 2 111: DO 10 INFO = N, 1, -1 112: IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO ) 113: $ RETURN 114: KP = KP - INFO 115: 10 CONTINUE 116: ELSE 117: * 118: * Lower triangular storage: examine D from top to bottom. 119: * 120: KP = 1 121: DO 20 INFO = 1, N 122: IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO ) 123: $ RETURN 124: KP = KP + N - INFO + 1 125: 20 CONTINUE 126: END IF 127: INFO = 0 128: * 129: IF( UPPER ) THEN 130: * 131: * Compute inv(A) from the factorization A = U*D*U'. 132: * 133: * K is the main loop index, increasing from 1 to N in steps of 134: * 1 or 2, depending on the size of the diagonal blocks. 135: * 136: K = 1 137: KC = 1 138: 30 CONTINUE 139: * 140: * If K > N, exit from loop. 141: * 142: IF( K.GT.N ) 143: $ GO TO 50 144: * 145: KCNEXT = KC + K 146: IF( IPIV( K ).GT.0 ) THEN 147: * 148: * 1 x 1 diagonal block 149: * 150: * Invert the diagonal block. 151: * 152: AP( KC+K-1 ) = ONE / AP( KC+K-1 ) 153: * 154: * Compute column K of the inverse. 155: * 156: IF( K.GT.1 ) THEN 157: CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 ) 158: CALL ZSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ), 159: $ 1 ) 160: AP( KC+K-1 ) = AP( KC+K-1 ) - 161: $ ZDOTU( K-1, WORK, 1, AP( KC ), 1 ) 162: END IF 163: KSTEP = 1 164: ELSE 165: * 166: * 2 x 2 diagonal block 167: * 168: * Invert the diagonal block. 169: * 170: T = AP( KCNEXT+K-1 ) 171: AK = AP( KC+K-1 ) / T 172: AKP1 = AP( KCNEXT+K ) / T 173: AKKP1 = AP( KCNEXT+K-1 ) / T 174: D = T*( AK*AKP1-ONE ) 175: AP( KC+K-1 ) = AKP1 / D 176: AP( KCNEXT+K ) = AK / D 177: AP( KCNEXT+K-1 ) = -AKKP1 / D 178: * 179: * Compute columns K and K+1 of the inverse. 180: * 181: IF( K.GT.1 ) THEN 182: CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 ) 183: CALL ZSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ), 184: $ 1 ) 185: AP( KC+K-1 ) = AP( KC+K-1 ) - 186: $ ZDOTU( K-1, WORK, 1, AP( KC ), 1 ) 187: AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) - 188: $ ZDOTU( K-1, AP( KC ), 1, AP( KCNEXT ), 189: $ 1 ) 190: CALL ZCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 ) 191: CALL ZSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, 192: $ AP( KCNEXT ), 1 ) 193: AP( KCNEXT+K ) = AP( KCNEXT+K ) - 194: $ ZDOTU( K-1, WORK, 1, AP( KCNEXT ), 1 ) 195: END IF 196: KSTEP = 2 197: KCNEXT = KCNEXT + K + 1 198: END IF 199: * 200: KP = ABS( IPIV( K ) ) 201: IF( KP.NE.K ) THEN 202: * 203: * Interchange rows and columns K and KP in the leading 204: * submatrix A(1:k+1,1:k+1) 205: * 206: KPC = ( KP-1 )*KP / 2 + 1 207: CALL ZSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 ) 208: KX = KPC + KP - 1 209: DO 40 J = KP + 1, K - 1 210: KX = KX + J - 1 211: TEMP = AP( KC+J-1 ) 212: AP( KC+J-1 ) = AP( KX ) 213: AP( KX ) = TEMP 214: 40 CONTINUE 215: TEMP = AP( KC+K-1 ) 216: AP( KC+K-1 ) = AP( KPC+KP-1 ) 217: AP( KPC+KP-1 ) = TEMP 218: IF( KSTEP.EQ.2 ) THEN 219: TEMP = AP( KC+K+K-1 ) 220: AP( KC+K+K-1 ) = AP( KC+K+KP-1 ) 221: AP( KC+K+KP-1 ) = TEMP 222: END IF 223: END IF 224: * 225: K = K + KSTEP 226: KC = KCNEXT 227: GO TO 30 228: 50 CONTINUE 229: * 230: ELSE 231: * 232: * Compute inv(A) from the factorization A = L*D*L'. 233: * 234: * K is the main loop index, increasing from 1 to N in steps of 235: * 1 or 2, depending on the size of the diagonal blocks. 236: * 237: NPP = N*( N+1 ) / 2 238: K = N 239: KC = NPP 240: 60 CONTINUE 241: * 242: * If K < 1, exit from loop. 243: * 244: IF( K.LT.1 ) 245: $ GO TO 80 246: * 247: KCNEXT = KC - ( N-K+2 ) 248: IF( IPIV( K ).GT.0 ) THEN 249: * 250: * 1 x 1 diagonal block 251: * 252: * Invert the diagonal block. 253: * 254: AP( KC ) = ONE / AP( KC ) 255: * 256: * Compute column K of the inverse. 257: * 258: IF( K.LT.N ) THEN 259: CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) 260: CALL ZSPMV( UPLO, N-K, -ONE, AP( KC+N-K+1 ), WORK, 1, 261: $ ZERO, AP( KC+1 ), 1 ) 262: AP( KC ) = AP( KC ) - ZDOTU( N-K, WORK, 1, AP( KC+1 ), 263: $ 1 ) 264: END IF 265: KSTEP = 1 266: ELSE 267: * 268: * 2 x 2 diagonal block 269: * 270: * Invert the diagonal block. 271: * 272: T = AP( KCNEXT+1 ) 273: AK = AP( KCNEXT ) / T 274: AKP1 = AP( KC ) / T 275: AKKP1 = AP( KCNEXT+1 ) / T 276: D = T*( AK*AKP1-ONE ) 277: AP( KCNEXT ) = AKP1 / D 278: AP( KC ) = AK / D 279: AP( KCNEXT+1 ) = -AKKP1 / D 280: * 281: * Compute columns K-1 and K of the inverse. 282: * 283: IF( K.LT.N ) THEN 284: CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 ) 285: CALL ZSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1, 286: $ ZERO, AP( KC+1 ), 1 ) 287: AP( KC ) = AP( KC ) - ZDOTU( N-K, WORK, 1, AP( KC+1 ), 288: $ 1 ) 289: AP( KCNEXT+1 ) = AP( KCNEXT+1 ) - 290: $ ZDOTU( N-K, AP( KC+1 ), 1, 291: $ AP( KCNEXT+2 ), 1 ) 292: CALL ZCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 ) 293: CALL ZSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1, 294: $ ZERO, AP( KCNEXT+2 ), 1 ) 295: AP( KCNEXT ) = AP( KCNEXT ) - 296: $ ZDOTU( N-K, WORK, 1, AP( KCNEXT+2 ), 1 ) 297: END IF 298: KSTEP = 2 299: KCNEXT = KCNEXT - ( N-K+3 ) 300: END IF 301: * 302: KP = ABS( IPIV( K ) ) 303: IF( KP.NE.K ) THEN 304: * 305: * Interchange rows and columns K and KP in the trailing 306: * submatrix A(k-1:n,k-1:n) 307: * 308: KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1 309: IF( KP.LT.N ) 310: $ CALL ZSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 ) 311: KX = KC + KP - K 312: DO 70 J = K + 1, KP - 1 313: KX = KX + N - J + 1 314: TEMP = AP( KC+J-K ) 315: AP( KC+J-K ) = AP( KX ) 316: AP( KX ) = TEMP 317: 70 CONTINUE 318: TEMP = AP( KC ) 319: AP( KC ) = AP( KPC ) 320: AP( KPC ) = TEMP 321: IF( KSTEP.EQ.2 ) THEN 322: TEMP = AP( KC-N+K-1 ) 323: AP( KC-N+K-1 ) = AP( KC-N+KP-1 ) 324: AP( KC-N+KP-1 ) = TEMP 325: END IF 326: END IF 327: * 328: K = K - KSTEP 329: KC = KCNEXT 330: GO TO 60 331: 80 CONTINUE 332: END IF 333: * 334: RETURN 335: * 336: * End of ZSPTRI 337: * 338: END