Annotation of rpl/lapack/lapack/zhpgvx.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU,
! 2: $ IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
! 3: $ IWORK, IFAIL, INFO )
! 4: *
! 5: * -- LAPACK driver routine (version 3.2) --
! 6: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 7: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 8: * November 2006
! 9: *
! 10: * .. Scalar Arguments ..
! 11: CHARACTER JOBZ, RANGE, UPLO
! 12: INTEGER IL, INFO, ITYPE, IU, LDZ, M, N
! 13: DOUBLE PRECISION ABSTOL, VL, VU
! 14: * ..
! 15: * .. Array Arguments ..
! 16: INTEGER IFAIL( * ), IWORK( * )
! 17: DOUBLE PRECISION RWORK( * ), W( * )
! 18: COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * ZHPGVX computes selected eigenvalues and, optionally, eigenvectors
! 25: * of a complex generalized Hermitian-definite eigenproblem, of the form
! 26: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
! 27: * B are assumed to be Hermitian, stored in packed format, and B is also
! 28: * positive definite. Eigenvalues and eigenvectors can be selected by
! 29: * specifying either a range of values or a range of indices for the
! 30: * desired eigenvalues.
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * ITYPE (input) INTEGER
! 36: * Specifies the problem type to be solved:
! 37: * = 1: A*x = (lambda)*B*x
! 38: * = 2: A*B*x = (lambda)*x
! 39: * = 3: B*A*x = (lambda)*x
! 40: *
! 41: * JOBZ (input) CHARACTER*1
! 42: * = 'N': Compute eigenvalues only;
! 43: * = 'V': Compute eigenvalues and eigenvectors.
! 44: *
! 45: * RANGE (input) CHARACTER*1
! 46: * = 'A': all eigenvalues will be found;
! 47: * = 'V': all eigenvalues in the half-open interval (VL,VU]
! 48: * will be found;
! 49: * = 'I': the IL-th through IU-th eigenvalues will be found.
! 50: *
! 51: * UPLO (input) CHARACTER*1
! 52: * = 'U': Upper triangles of A and B are stored;
! 53: * = 'L': Lower triangles of A and B are stored.
! 54: *
! 55: * N (input) INTEGER
! 56: * The order of the matrices A and B. N >= 0.
! 57: *
! 58: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
! 59: * On entry, the upper or lower triangle of the Hermitian matrix
! 60: * A, packed columnwise in a linear array. The j-th column of A
! 61: * is stored in the array AP as follows:
! 62: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 63: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
! 64: *
! 65: * On exit, the contents of AP are destroyed.
! 66: *
! 67: * BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
! 68: * On entry, the upper or lower triangle of the Hermitian matrix
! 69: * B, packed columnwise in a linear array. The j-th column of B
! 70: * is stored in the array BP as follows:
! 71: * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
! 72: * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
! 73: *
! 74: * On exit, the triangular factor U or L from the Cholesky
! 75: * factorization B = U**H*U or B = L*L**H, in the same storage
! 76: * format as B.
! 77: *
! 78: * VL (input) DOUBLE PRECISION
! 79: * VU (input) DOUBLE PRECISION
! 80: * If RANGE='V', the lower and upper bounds of the interval to
! 81: * be searched for eigenvalues. VL < VU.
! 82: * Not referenced if RANGE = 'A' or 'I'.
! 83: *
! 84: * IL (input) INTEGER
! 85: * IU (input) INTEGER
! 86: * If RANGE='I', the indices (in ascending order) of the
! 87: * smallest and largest eigenvalues to be returned.
! 88: * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
! 89: * Not referenced if RANGE = 'A' or 'V'.
! 90: *
! 91: * ABSTOL (input) DOUBLE PRECISION
! 92: * The absolute error tolerance for the eigenvalues.
! 93: * An approximate eigenvalue is accepted as converged
! 94: * when it is determined to lie in an interval [a,b]
! 95: * of width less than or equal to
! 96: *
! 97: * ABSTOL + EPS * max( |a|,|b| ) ,
! 98: *
! 99: * where EPS is the machine precision. If ABSTOL is less than
! 100: * or equal to zero, then EPS*|T| will be used in its place,
! 101: * where |T| is the 1-norm of the tridiagonal matrix obtained
! 102: * by reducing AP to tridiagonal form.
! 103: *
! 104: * Eigenvalues will be computed most accurately when ABSTOL is
! 105: * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
! 106: * If this routine returns with INFO>0, indicating that some
! 107: * eigenvectors did not converge, try setting ABSTOL to
! 108: * 2*DLAMCH('S').
! 109: *
! 110: * M (output) INTEGER
! 111: * The total number of eigenvalues found. 0 <= M <= N.
! 112: * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
! 113: *
! 114: * W (output) DOUBLE PRECISION array, dimension (N)
! 115: * On normal exit, the first M elements contain the selected
! 116: * eigenvalues in ascending order.
! 117: *
! 118: * Z (output) COMPLEX*16 array, dimension (LDZ, N)
! 119: * If JOBZ = 'N', then Z is not referenced.
! 120: * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
! 121: * contain the orthonormal eigenvectors of the matrix A
! 122: * corresponding to the selected eigenvalues, with the i-th
! 123: * column of Z holding the eigenvector associated with W(i).
! 124: * The eigenvectors are normalized as follows:
! 125: * if ITYPE = 1 or 2, Z**H*B*Z = I;
! 126: * if ITYPE = 3, Z**H*inv(B)*Z = I.
! 127: *
! 128: * If an eigenvector fails to converge, then that column of Z
! 129: * contains the latest approximation to the eigenvector, and the
! 130: * index of the eigenvector is returned in IFAIL.
! 131: * Note: the user must ensure that at least max(1,M) columns are
! 132: * supplied in the array Z; if RANGE = 'V', the exact value of M
! 133: * is not known in advance and an upper bound must be used.
! 134: *
! 135: * LDZ (input) INTEGER
! 136: * The leading dimension of the array Z. LDZ >= 1, and if
! 137: * JOBZ = 'V', LDZ >= max(1,N).
! 138: *
! 139: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
! 140: *
! 141: * RWORK (workspace) DOUBLE PRECISION array, dimension (7*N)
! 142: *
! 143: * IWORK (workspace) INTEGER array, dimension (5*N)
! 144: *
! 145: * IFAIL (output) INTEGER array, dimension (N)
! 146: * If JOBZ = 'V', then if INFO = 0, the first M elements of
! 147: * IFAIL are zero. If INFO > 0, then IFAIL contains the
! 148: * indices of the eigenvectors that failed to converge.
! 149: * If JOBZ = 'N', then IFAIL is not referenced.
! 150: *
! 151: * INFO (output) INTEGER
! 152: * = 0: successful exit
! 153: * < 0: if INFO = -i, the i-th argument had an illegal value
! 154: * > 0: ZPPTRF or ZHPEVX returned an error code:
! 155: * <= N: if INFO = i, ZHPEVX failed to converge;
! 156: * i eigenvectors failed to converge. Their indices
! 157: * are stored in array IFAIL.
! 158: * > N: if INFO = N + i, for 1 <= i <= n, then the leading
! 159: * minor of order i of B is not positive definite.
! 160: * The factorization of B could not be completed and
! 161: * no eigenvalues or eigenvectors were computed.
! 162: *
! 163: * Further Details
! 164: * ===============
! 165: *
! 166: * Based on contributions by
! 167: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
! 168: *
! 169: * =====================================================================
! 170: *
! 171: * .. Local Scalars ..
! 172: LOGICAL ALLEIG, INDEIG, UPPER, VALEIG, WANTZ
! 173: CHARACTER TRANS
! 174: INTEGER J
! 175: * ..
! 176: * .. External Functions ..
! 177: LOGICAL LSAME
! 178: EXTERNAL LSAME
! 179: * ..
! 180: * .. External Subroutines ..
! 181: EXTERNAL XERBLA, ZHPEVX, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
! 182: * ..
! 183: * .. Intrinsic Functions ..
! 184: INTRINSIC MIN
! 185: * ..
! 186: * .. Executable Statements ..
! 187: *
! 188: * Test the input parameters.
! 189: *
! 190: WANTZ = LSAME( JOBZ, 'V' )
! 191: UPPER = LSAME( UPLO, 'U' )
! 192: ALLEIG = LSAME( RANGE, 'A' )
! 193: VALEIG = LSAME( RANGE, 'V' )
! 194: INDEIG = LSAME( RANGE, 'I' )
! 195: *
! 196: INFO = 0
! 197: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
! 198: INFO = -1
! 199: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 200: INFO = -2
! 201: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
! 202: INFO = -3
! 203: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 204: INFO = -4
! 205: ELSE IF( N.LT.0 ) THEN
! 206: INFO = -5
! 207: ELSE
! 208: IF( VALEIG ) THEN
! 209: IF( N.GT.0 .AND. VU.LE.VL ) THEN
! 210: INFO = -9
! 211: END IF
! 212: ELSE IF( INDEIG ) THEN
! 213: IF( IL.LT.1 ) THEN
! 214: INFO = -10
! 215: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
! 216: INFO = -11
! 217: END IF
! 218: END IF
! 219: END IF
! 220: IF( INFO.EQ.0 ) THEN
! 221: IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 222: INFO = -16
! 223: END IF
! 224: END IF
! 225: *
! 226: IF( INFO.NE.0 ) THEN
! 227: CALL XERBLA( 'ZHPGVX', -INFO )
! 228: RETURN
! 229: END IF
! 230: *
! 231: * Quick return if possible
! 232: *
! 233: IF( N.EQ.0 )
! 234: $ RETURN
! 235: *
! 236: * Form a Cholesky factorization of B.
! 237: *
! 238: CALL ZPPTRF( UPLO, N, BP, INFO )
! 239: IF( INFO.NE.0 ) THEN
! 240: INFO = N + INFO
! 241: RETURN
! 242: END IF
! 243: *
! 244: * Transform problem to standard eigenvalue problem and solve.
! 245: *
! 246: CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
! 247: CALL ZHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABSTOL, M,
! 248: $ W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO )
! 249: *
! 250: IF( WANTZ ) THEN
! 251: *
! 252: * Backtransform eigenvectors to the original problem.
! 253: *
! 254: IF( INFO.GT.0 )
! 255: $ M = INFO - 1
! 256: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
! 257: *
! 258: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
! 259: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
! 260: *
! 261: IF( UPPER ) THEN
! 262: TRANS = 'N'
! 263: ELSE
! 264: TRANS = 'C'
! 265: END IF
! 266: *
! 267: DO 10 J = 1, M
! 268: CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
! 269: $ 1 )
! 270: 10 CONTINUE
! 271: *
! 272: ELSE IF( ITYPE.EQ.3 ) THEN
! 273: *
! 274: * For B*A*x=(lambda)*x;
! 275: * backtransform eigenvectors: x = L*y or U'*y
! 276: *
! 277: IF( UPPER ) THEN
! 278: TRANS = 'C'
! 279: ELSE
! 280: TRANS = 'N'
! 281: END IF
! 282: *
! 283: DO 20 J = 1, M
! 284: CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
! 285: $ 1 )
! 286: 20 CONTINUE
! 287: END IF
! 288: END IF
! 289: *
! 290: RETURN
! 291: *
! 292: * End of ZHPGVX
! 293: *
! 294: END
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