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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, 2: $ LWORK, IWORK, LIWORK, INFO ) 3: * 4: * -- LAPACK driver routine (version 3.2) -- 5: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 7: * November 2006 8: * 9: * .. Scalar Arguments .. 10: CHARACTER JOBZ, UPLO 11: INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N 12: * .. 13: * .. Array Arguments .. 14: INTEGER IWORK( * ) 15: DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ), 16: $ Z( LDZ, * ) 17: * .. 18: * 19: * Purpose 20: * ======= 21: * 22: * DSPGVD computes all the eigenvalues, and optionally, the eigenvectors 23: * of a real generalized symmetric-definite eigenproblem, of the form 24: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and 25: * B are assumed to be symmetric, stored in packed format, and B is also 26: * positive definite. 27: * If eigenvectors are desired, it uses a divide and conquer algorithm. 28: * 29: * The divide and conquer algorithm makes very mild assumptions about 30: * floating point arithmetic. It will work on machines with a guard 31: * digit in add/subtract, or on those binary machines without guard 32: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or 33: * Cray-2. It could conceivably fail on hexadecimal or decimal machines 34: * without guard digits, but we know of none. 35: * 36: * Arguments 37: * ========= 38: * 39: * ITYPE (input) INTEGER 40: * Specifies the problem type to be solved: 41: * = 1: A*x = (lambda)*B*x 42: * = 2: A*B*x = (lambda)*x 43: * = 3: B*A*x = (lambda)*x 44: * 45: * JOBZ (input) CHARACTER*1 46: * = 'N': Compute eigenvalues only; 47: * = 'V': Compute eigenvalues and eigenvectors. 48: * 49: * UPLO (input) CHARACTER*1 50: * = 'U': Upper triangles of A and B are stored; 51: * = 'L': Lower triangles of A and B are stored. 52: * 53: * N (input) INTEGER 54: * The order of the matrices A and B. N >= 0. 55: * 56: * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) 57: * On entry, the upper or lower triangle of the symmetric matrix 58: * A, packed columnwise in a linear array. The j-th column of A 59: * is stored in the array AP as follows: 60: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 61: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. 62: * 63: * On exit, the contents of AP are destroyed. 64: * 65: * BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) 66: * On entry, the upper or lower triangle of the symmetric matrix 67: * B, packed columnwise in a linear array. The j-th column of B 68: * is stored in the array BP as follows: 69: * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; 70: * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. 71: * 72: * On exit, the triangular factor U or L from the Cholesky 73: * factorization B = U**T*U or B = L*L**T, in the same storage 74: * format as B. 75: * 76: * W (output) DOUBLE PRECISION array, dimension (N) 77: * If INFO = 0, the eigenvalues in ascending order. 78: * 79: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N) 80: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of 81: * eigenvectors. The eigenvectors are normalized as follows: 82: * if ITYPE = 1 or 2, Z**T*B*Z = I; 83: * if ITYPE = 3, Z**T*inv(B)*Z = I. 84: * If JOBZ = 'N', then Z is not referenced. 85: * 86: * LDZ (input) INTEGER 87: * The leading dimension of the array Z. LDZ >= 1, and if 88: * JOBZ = 'V', LDZ >= max(1,N). 89: * 90: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 91: * On exit, if INFO = 0, WORK(1) returns the required LWORK. 92: * 93: * LWORK (input) INTEGER 94: * The dimension of the array WORK. 95: * If N <= 1, LWORK >= 1. 96: * If JOBZ = 'N' and N > 1, LWORK >= 2*N. 97: * If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. 98: * 99: * If LWORK = -1, then a workspace query is assumed; the routine 100: * only calculates the required sizes of the WORK and IWORK 101: * arrays, returns these values as the first entries of the WORK 102: * and IWORK arrays, and no error message related to LWORK or 103: * LIWORK is issued by XERBLA. 104: * 105: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) 106: * On exit, if INFO = 0, IWORK(1) returns the required LIWORK. 107: * 108: * LIWORK (input) INTEGER 109: * The dimension of the array IWORK. 110: * If JOBZ = 'N' or N <= 1, LIWORK >= 1. 111: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. 112: * 113: * If LIWORK = -1, then a workspace query is assumed; the 114: * routine only calculates the required sizes of the WORK and 115: * IWORK arrays, returns these values as the first entries of 116: * the WORK and IWORK arrays, and no error message related to 117: * LWORK or LIWORK is issued by XERBLA. 118: * 119: * INFO (output) INTEGER 120: * = 0: successful exit 121: * < 0: if INFO = -i, the i-th argument had an illegal value 122: * > 0: DPPTRF or DSPEVD returned an error code: 123: * <= N: if INFO = i, DSPEVD failed to converge; 124: * i off-diagonal elements of an intermediate 125: * tridiagonal form did not converge to zero; 126: * > N: if INFO = N + i, for 1 <= i <= N, then the leading 127: * minor of order i of B is not positive definite. 128: * The factorization of B could not be completed and 129: * no eigenvalues or eigenvectors were computed. 130: * 131: * Further Details 132: * =============== 133: * 134: * Based on contributions by 135: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 136: * 137: * ===================================================================== 138: * 139: * .. Parameters .. 140: DOUBLE PRECISION TWO 141: PARAMETER ( TWO = 2.0D+0 ) 142: * .. 143: * .. Local Scalars .. 144: LOGICAL LQUERY, UPPER, WANTZ 145: CHARACTER TRANS 146: INTEGER J, LIWMIN, LWMIN, NEIG 147: * .. 148: * .. External Functions .. 149: LOGICAL LSAME 150: EXTERNAL LSAME 151: * .. 152: * .. External Subroutines .. 153: EXTERNAL DPPTRF, DSPEVD, DSPGST, DTPMV, DTPSV, XERBLA 154: * .. 155: * .. Intrinsic Functions .. 156: INTRINSIC DBLE, MAX 157: * .. 158: * .. Executable Statements .. 159: * 160: * Test the input parameters. 161: * 162: WANTZ = LSAME( JOBZ, 'V' ) 163: UPPER = LSAME( UPLO, 'U' ) 164: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) 165: * 166: INFO = 0 167: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 168: INFO = -1 169: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 170: INFO = -2 171: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 172: INFO = -3 173: ELSE IF( N.LT.0 ) THEN 174: INFO = -4 175: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 176: INFO = -9 177: END IF 178: * 179: IF( INFO.EQ.0 ) THEN 180: IF( N.LE.1 ) THEN 181: LIWMIN = 1 182: LWMIN = 1 183: ELSE 184: IF( WANTZ ) THEN 185: LIWMIN = 3 + 5*N 186: LWMIN = 1 + 6*N + 2*N**2 187: ELSE 188: LIWMIN = 1 189: LWMIN = 2*N 190: END IF 191: END IF 192: WORK( 1 ) = LWMIN 193: IWORK( 1 ) = LIWMIN 194: * 195: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 196: INFO = -11 197: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 198: INFO = -13 199: END IF 200: END IF 201: * 202: IF( INFO.NE.0 ) THEN 203: CALL XERBLA( 'DSPGVD', -INFO ) 204: RETURN 205: ELSE IF( LQUERY ) THEN 206: RETURN 207: END IF 208: * 209: * Quick return if possible 210: * 211: IF( N.EQ.0 ) 212: $ RETURN 213: * 214: * Form a Cholesky factorization of BP. 215: * 216: CALL DPPTRF( UPLO, N, BP, INFO ) 217: IF( INFO.NE.0 ) THEN 218: INFO = N + INFO 219: RETURN 220: END IF 221: * 222: * Transform problem to standard eigenvalue problem and solve. 223: * 224: CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO ) 225: CALL DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK, 226: $ LIWORK, INFO ) 227: LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) ) 228: LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) ) 229: * 230: IF( WANTZ ) THEN 231: * 232: * Backtransform eigenvectors to the original problem. 233: * 234: NEIG = N 235: IF( INFO.GT.0 ) 236: $ NEIG = INFO - 1 237: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 238: * 239: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 240: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y 241: * 242: IF( UPPER ) THEN 243: TRANS = 'N' 244: ELSE 245: TRANS = 'T' 246: END IF 247: * 248: DO 10 J = 1, NEIG 249: CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 250: $ 1 ) 251: 10 CONTINUE 252: * 253: ELSE IF( ITYPE.EQ.3 ) THEN 254: * 255: * For B*A*x=(lambda)*x; 256: * backtransform eigenvectors: x = L*y or U'*y 257: * 258: IF( UPPER ) THEN 259: TRANS = 'T' 260: ELSE 261: TRANS = 'N' 262: END IF 263: * 264: DO 20 J = 1, NEIG 265: CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 266: $ 1 ) 267: 20 CONTINUE 268: END IF 269: END IF 270: * 271: WORK( 1 ) = LWMIN 272: IWORK( 1 ) = LIWMIN 273: * 274: RETURN 275: * 276: * End of DSPGVD 277: * 278: END