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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, 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, LWORK, N 11: * .. 12: * .. Array Arguments .. 13: INTEGER IPIV( * ) 14: COMPLEX*16 A( LDA, * ), WORK( * ) 15: * .. 16: * 17: * Purpose 18: * ======= 19: * 20: * ZSYTRF computes the factorization of a complex symmetric matrix A 21: * using the Bunch-Kaufman diagonal pivoting method. The form of the 22: * factorization is 23: * 24: * A = U*D*U**T or A = L*D*L**T 25: * 26: * where U (or L) is a product of permutation and unit upper (lower) 27: * triangular matrices, and D is symmetric and block diagonal with 28: * with 1-by-1 and 2-by-2 diagonal blocks. 29: * 30: * This is the blocked version of the algorithm, calling Level 3 BLAS. 31: * 32: * Arguments 33: * ========= 34: * 35: * UPLO (input) CHARACTER*1 36: * = 'U': Upper triangle of A is stored; 37: * = 'L': Lower triangle of A is stored. 38: * 39: * N (input) INTEGER 40: * The order of the matrix A. N >= 0. 41: * 42: * A (input/output) COMPLEX*16 array, dimension (LDA,N) 43: * On entry, the symmetric matrix A. If UPLO = 'U', the leading 44: * N-by-N upper triangular part of A contains the upper 45: * triangular part of the matrix A, and the strictly lower 46: * triangular part of A is not referenced. If UPLO = 'L', the 47: * leading N-by-N lower triangular part of A contains the lower 48: * triangular part of the matrix A, and the strictly upper 49: * triangular part of A is not referenced. 50: * 51: * On exit, the block diagonal matrix D and the multipliers used 52: * to obtain the factor U or L (see below for further details). 53: * 54: * LDA (input) INTEGER 55: * The leading dimension of the array A. LDA >= max(1,N). 56: * 57: * IPIV (output) INTEGER array, dimension (N) 58: * Details of the interchanges and the block structure of D. 59: * If IPIV(k) > 0, then rows and columns k and IPIV(k) were 60: * interchanged and D(k,k) is a 1-by-1 diagonal block. 61: * If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and 62: * columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) 63: * is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = 64: * IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were 65: * interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. 66: * 67: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 68: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 69: * 70: * LWORK (input) INTEGER 71: * The length of WORK. LWORK >=1. For best performance 72: * LWORK >= N*NB, where NB is the block size returned by ILAENV. 73: * 74: * If LWORK = -1, then a workspace query is assumed; the routine 75: * only calculates the optimal size of the WORK array, returns 76: * this value as the first entry of the WORK array, and no error 77: * message related to LWORK is issued by XERBLA. 78: * 79: * INFO (output) INTEGER 80: * = 0: successful exit 81: * < 0: if INFO = -i, the i-th argument had an illegal value 82: * > 0: if INFO = i, D(i,i) is exactly zero. The factorization 83: * has been completed, but the block diagonal matrix D is 84: * exactly singular, and division by zero will occur if it 85: * is used to solve a system of equations. 86: * 87: * Further Details 88: * =============== 89: * 90: * If UPLO = 'U', then A = U*D*U', where 91: * U = P(n)*U(n)* ... *P(k)U(k)* ..., 92: * i.e., U is a product of terms P(k)*U(k), where k decreases from n to 93: * 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 94: * and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as 95: * defined by IPIV(k), and U(k) is a unit upper triangular matrix, such 96: * that if the diagonal block D(k) is of order s (s = 1 or 2), then 97: * 98: * ( I v 0 ) k-s 99: * U(k) = ( 0 I 0 ) s 100: * ( 0 0 I ) n-k 101: * k-s s n-k 102: * 103: * If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). 104: * If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), 105: * and A(k,k), and v overwrites A(1:k-2,k-1:k). 106: * 107: * If UPLO = 'L', then A = L*D*L', where 108: * L = P(1)*L(1)* ... *P(k)*L(k)* ..., 109: * i.e., L is a product of terms P(k)*L(k), where k increases from 1 to 110: * n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 111: * and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as 112: * defined by IPIV(k), and L(k) is a unit lower triangular matrix, such 113: * that if the diagonal block D(k) is of order s (s = 1 or 2), then 114: * 115: * ( I 0 0 ) k-1 116: * L(k) = ( 0 I 0 ) s 117: * ( 0 v I ) n-k-s+1 118: * k-1 s n-k-s+1 119: * 120: * If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). 121: * If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), 122: * and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). 123: * 124: * ===================================================================== 125: * 126: * .. Local Scalars .. 127: LOGICAL LQUERY, UPPER 128: INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN 129: * .. 130: * .. External Functions .. 131: LOGICAL LSAME 132: INTEGER ILAENV 133: EXTERNAL LSAME, ILAENV 134: * .. 135: * .. External Subroutines .. 136: EXTERNAL XERBLA, ZLASYF, ZSYTF2 137: * .. 138: * .. Intrinsic Functions .. 139: INTRINSIC MAX 140: * .. 141: * .. Executable Statements .. 142: * 143: * Test the input parameters. 144: * 145: INFO = 0 146: UPPER = LSAME( UPLO, 'U' ) 147: LQUERY = ( LWORK.EQ.-1 ) 148: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 149: INFO = -1 150: ELSE IF( N.LT.0 ) THEN 151: INFO = -2 152: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 153: INFO = -4 154: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN 155: INFO = -7 156: END IF 157: * 158: IF( INFO.EQ.0 ) THEN 159: * 160: * Determine the block size 161: * 162: NB = ILAENV( 1, 'ZSYTRF', UPLO, N, -1, -1, -1 ) 163: LWKOPT = N*NB 164: WORK( 1 ) = LWKOPT 165: END IF 166: * 167: IF( INFO.NE.0 ) THEN 168: CALL XERBLA( 'ZSYTRF', -INFO ) 169: RETURN 170: ELSE IF( LQUERY ) THEN 171: RETURN 172: END IF 173: * 174: NBMIN = 2 175: LDWORK = N 176: IF( NB.GT.1 .AND. NB.LT.N ) THEN 177: IWS = LDWORK*NB 178: IF( LWORK.LT.IWS ) THEN 179: NB = MAX( LWORK / LDWORK, 1 ) 180: NBMIN = MAX( 2, ILAENV( 2, 'ZSYTRF', UPLO, N, -1, -1, -1 ) ) 181: END IF 182: ELSE 183: IWS = 1 184: END IF 185: IF( NB.LT.NBMIN ) 186: $ NB = N 187: * 188: IF( UPPER ) THEN 189: * 190: * Factorize A as U*D*U' using the upper triangle of A 191: * 192: * K is the main loop index, decreasing from N to 1 in steps of 193: * KB, where KB is the number of columns factorized by ZLASYF; 194: * KB is either NB or NB-1, or K for the last block 195: * 196: K = N 197: 10 CONTINUE 198: * 199: * If K < 1, exit from loop 200: * 201: IF( K.LT.1 ) 202: $ GO TO 40 203: * 204: IF( K.GT.NB ) THEN 205: * 206: * Factorize columns k-kb+1:k of A and use blocked code to 207: * update columns 1:k-kb 208: * 209: CALL ZLASYF( UPLO, K, NB, KB, A, LDA, IPIV, WORK, N, IINFO ) 210: ELSE 211: * 212: * Use unblocked code to factorize columns 1:k of A 213: * 214: CALL ZSYTF2( UPLO, K, A, LDA, IPIV, IINFO ) 215: KB = K 216: END IF 217: * 218: * Set INFO on the first occurrence of a zero pivot 219: * 220: IF( INFO.EQ.0 .AND. IINFO.GT.0 ) 221: $ INFO = IINFO 222: * 223: * Decrease K and return to the start of the main loop 224: * 225: K = K - KB 226: GO TO 10 227: * 228: ELSE 229: * 230: * Factorize A as L*D*L' using the lower triangle of A 231: * 232: * K is the main loop index, increasing from 1 to N in steps of 233: * KB, where KB is the number of columns factorized by ZLASYF; 234: * KB is either NB or NB-1, or N-K+1 for the last block 235: * 236: K = 1 237: 20 CONTINUE 238: * 239: * If K > N, exit from loop 240: * 241: IF( K.GT.N ) 242: $ GO TO 40 243: * 244: IF( K.LE.N-NB ) THEN 245: * 246: * Factorize columns k:k+kb-1 of A and use blocked code to 247: * update columns k+kb:n 248: * 249: CALL ZLASYF( UPLO, N-K+1, NB, KB, A( K, K ), LDA, IPIV( K ), 250: $ WORK, N, IINFO ) 251: ELSE 252: * 253: * Use unblocked code to factorize columns k:n of A 254: * 255: CALL ZSYTF2( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ), IINFO ) 256: KB = N - K + 1 257: END IF 258: * 259: * Set INFO on the first occurrence of a zero pivot 260: * 261: IF( INFO.EQ.0 .AND. IINFO.GT.0 ) 262: $ INFO = IINFO + K - 1 263: * 264: * Adjust IPIV 265: * 266: DO 30 J = K, K + KB - 1 267: IF( IPIV( J ).GT.0 ) THEN 268: IPIV( J ) = IPIV( J ) + K - 1 269: ELSE 270: IPIV( J ) = IPIV( J ) - K + 1 271: END IF 272: 30 CONTINUE 273: * 274: * Increase K and return to the start of the main loop 275: * 276: K = K + KB 277: GO TO 20 278: * 279: END IF 280: * 281: 40 CONTINUE 282: WORK( 1 ) = LWKOPT 283: RETURN 284: * 285: * End of ZSYTRF 286: * 287: END