![]() ![]() | ![]() |
Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, 2: $ RWORK, 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, N 12: * .. 13: * .. Array Arguments .. 14: DOUBLE PRECISION RWORK( * ), W( * ) 15: COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) 16: * .. 17: * 18: * Purpose 19: * ======= 20: * 21: * ZHPGV computes all the eigenvalues and, optionally, the eigenvectors 22: * of a complex generalized Hermitian-definite eigenproblem, of the form 23: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. 24: * Here A and B are assumed to be Hermitian, stored in packed format, 25: * and B is also positive definite. 26: * 27: * Arguments 28: * ========= 29: * 30: * ITYPE (input) INTEGER 31: * Specifies the problem type to be solved: 32: * = 1: A*x = (lambda)*B*x 33: * = 2: A*B*x = (lambda)*x 34: * = 3: B*A*x = (lambda)*x 35: * 36: * JOBZ (input) CHARACTER*1 37: * = 'N': Compute eigenvalues only; 38: * = 'V': Compute eigenvalues and eigenvectors. 39: * 40: * UPLO (input) CHARACTER*1 41: * = 'U': Upper triangles of A and B are stored; 42: * = 'L': Lower triangles of A and B are stored. 43: * 44: * N (input) INTEGER 45: * The order of the matrices A and B. N >= 0. 46: * 47: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) 48: * On entry, the upper or lower triangle of the Hermitian matrix 49: * A, packed columnwise in a linear array. The j-th column of A 50: * is stored in the array AP as follows: 51: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 52: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. 53: * 54: * On exit, the contents of AP are destroyed. 55: * 56: * BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) 57: * On entry, the upper or lower triangle of the Hermitian matrix 58: * B, packed columnwise in a linear array. The j-th column of B 59: * is stored in the array BP as follows: 60: * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; 61: * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. 62: * 63: * On exit, the triangular factor U or L from the Cholesky 64: * factorization B = U**H*U or B = L*L**H, in the same storage 65: * format as B. 66: * 67: * W (output) DOUBLE PRECISION array, dimension (N) 68: * If INFO = 0, the eigenvalues in ascending order. 69: * 70: * Z (output) COMPLEX*16 array, dimension (LDZ, N) 71: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of 72: * eigenvectors. The eigenvectors are normalized as follows: 73: * if ITYPE = 1 or 2, Z**H*B*Z = I; 74: * if ITYPE = 3, Z**H*inv(B)*Z = I. 75: * If JOBZ = 'N', then Z is not referenced. 76: * 77: * LDZ (input) INTEGER 78: * The leading dimension of the array Z. LDZ >= 1, and if 79: * JOBZ = 'V', LDZ >= max(1,N). 80: * 81: * WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1)) 82: * 83: * RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2)) 84: * 85: * INFO (output) INTEGER 86: * = 0: successful exit 87: * < 0: if INFO = -i, the i-th argument had an illegal value 88: * > 0: ZPPTRF or ZHPEV returned an error code: 89: * <= N: if INFO = i, ZHPEV failed to converge; 90: * i off-diagonal elements of an intermediate 91: * tridiagonal form did not convergeto zero; 92: * > N: if INFO = N + i, for 1 <= i <= n, then the leading 93: * minor of order i of B is not positive definite. 94: * The factorization of B could not be completed and 95: * no eigenvalues or eigenvectors were computed. 96: * 97: * ===================================================================== 98: * 99: * .. Local Scalars .. 100: LOGICAL UPPER, WANTZ 101: CHARACTER TRANS 102: INTEGER J, NEIG 103: * .. 104: * .. External Functions .. 105: LOGICAL LSAME 106: EXTERNAL LSAME 107: * .. 108: * .. External Subroutines .. 109: EXTERNAL XERBLA, ZHPEV, ZHPGST, ZPPTRF, ZTPMV, ZTPSV 110: * .. 111: * .. Executable Statements .. 112: * 113: * Test the input parameters. 114: * 115: WANTZ = LSAME( JOBZ, 'V' ) 116: UPPER = LSAME( UPLO, 'U' ) 117: * 118: INFO = 0 119: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 120: INFO = -1 121: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 122: INFO = -2 123: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 124: INFO = -3 125: ELSE IF( N.LT.0 ) THEN 126: INFO = -4 127: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 128: INFO = -9 129: END IF 130: IF( INFO.NE.0 ) THEN 131: CALL XERBLA( 'ZHPGV ', -INFO ) 132: RETURN 133: END IF 134: * 135: * Quick return if possible 136: * 137: IF( N.EQ.0 ) 138: $ RETURN 139: * 140: * Form a Cholesky factorization of B. 141: * 142: CALL ZPPTRF( UPLO, N, BP, INFO ) 143: IF( INFO.NE.0 ) THEN 144: INFO = N + INFO 145: RETURN 146: END IF 147: * 148: * Transform problem to standard eigenvalue problem and solve. 149: * 150: CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO ) 151: CALL ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO ) 152: * 153: IF( WANTZ ) THEN 154: * 155: * Backtransform eigenvectors to the original problem. 156: * 157: NEIG = N 158: IF( INFO.GT.0 ) 159: $ NEIG = INFO - 1 160: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 161: * 162: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 163: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y 164: * 165: IF( UPPER ) THEN 166: TRANS = 'N' 167: ELSE 168: TRANS = 'C' 169: END IF 170: * 171: DO 10 J = 1, NEIG 172: CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 173: $ 1 ) 174: 10 CONTINUE 175: * 176: ELSE IF( ITYPE.EQ.3 ) THEN 177: * 178: * For B*A*x=(lambda)*x; 179: * backtransform eigenvectors: x = L*y or U'*y 180: * 181: IF( UPPER ) THEN 182: TRANS = 'C' 183: ELSE 184: TRANS = 'N' 185: END IF 186: * 187: DO 20 J = 1, NEIG 188: CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 189: $ 1 ) 190: 20 CONTINUE 191: END IF 192: END IF 193: RETURN 194: * 195: * End of ZHPGV 196: * 197: END