Annotation of rpl/lapack/lapack/zhbgv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
! 2: $ LDZ, WORK, 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, KA, KB, LDAB, LDBB, LDZ, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION RWORK( * ), W( * )
! 15: COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
! 16: $ Z( LDZ, * )
! 17: * ..
! 18: *
! 19: * Purpose
! 20: * =======
! 21: *
! 22: * ZHBGV computes all the eigenvalues, and optionally, the eigenvectors
! 23: * of a complex generalized Hermitian-definite banded eigenproblem, of
! 24: * the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
! 25: * and banded, and B is also positive definite.
! 26: *
! 27: * Arguments
! 28: * =========
! 29: *
! 30: * JOBZ (input) CHARACTER*1
! 31: * = 'N': Compute eigenvalues only;
! 32: * = 'V': Compute eigenvalues and eigenvectors.
! 33: *
! 34: * UPLO (input) CHARACTER*1
! 35: * = 'U': Upper triangles of A and B are stored;
! 36: * = 'L': Lower triangles of A and B are stored.
! 37: *
! 38: * N (input) INTEGER
! 39: * The order of the matrices A and B. N >= 0.
! 40: *
! 41: * KA (input) INTEGER
! 42: * The number of superdiagonals of the matrix A if UPLO = 'U',
! 43: * or the number of subdiagonals if UPLO = 'L'. KA >= 0.
! 44: *
! 45: * KB (input) INTEGER
! 46: * The number of superdiagonals of the matrix B if UPLO = 'U',
! 47: * or the number of subdiagonals if UPLO = 'L'. KB >= 0.
! 48: *
! 49: * AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
! 50: * On entry, the upper or lower triangle of the Hermitian band
! 51: * matrix A, stored in the first ka+1 rows of the array. The
! 52: * j-th column of A is stored in the j-th column of the array AB
! 53: * as follows:
! 54: * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
! 55: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
! 56: *
! 57: * On exit, the contents of AB are destroyed.
! 58: *
! 59: * LDAB (input) INTEGER
! 60: * The leading dimension of the array AB. LDAB >= KA+1.
! 61: *
! 62: * BB (input/output) COMPLEX*16 array, dimension (LDBB, N)
! 63: * On entry, the upper or lower triangle of the Hermitian band
! 64: * matrix B, stored in the first kb+1 rows of the array. The
! 65: * j-th column of B is stored in the j-th column of the array BB
! 66: * as follows:
! 67: * if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
! 68: * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
! 69: *
! 70: * On exit, the factor S from the split Cholesky factorization
! 71: * B = S**H*S, as returned by ZPBSTF.
! 72: *
! 73: * LDBB (input) INTEGER
! 74: * The leading dimension of the array BB. LDBB >= KB+1.
! 75: *
! 76: * W (output) DOUBLE PRECISION array, dimension (N)
! 77: * If INFO = 0, the eigenvalues in ascending order.
! 78: *
! 79: * Z (output) COMPLEX*16 array, dimension (LDZ, N)
! 80: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
! 81: * eigenvectors, with the i-th column of Z holding the
! 82: * eigenvector associated with W(i). The eigenvectors are
! 83: * normalized so that Z**H*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 >= N.
! 89: *
! 90: * WORK (workspace) COMPLEX*16 array, dimension (N)
! 91: *
! 92: * RWORK (workspace) DOUBLE PRECISION array, dimension (3*N)
! 93: *
! 94: * INFO (output) INTEGER
! 95: * = 0: successful exit
! 96: * < 0: if INFO = -i, the i-th argument had an illegal value
! 97: * > 0: if INFO = i, and i is:
! 98: * <= N: the algorithm failed to converge:
! 99: * i off-diagonal elements of an intermediate
! 100: * tridiagonal form did not converge to zero;
! 101: * > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
! 102: * returned INFO = i: B is not positive definite.
! 103: * The factorization of B could not be completed and
! 104: * no eigenvalues or eigenvectors were computed.
! 105: *
! 106: * =====================================================================
! 107: *
! 108: * .. Local Scalars ..
! 109: LOGICAL UPPER, WANTZ
! 110: CHARACTER VECT
! 111: INTEGER IINFO, INDE, INDWRK
! 112: * ..
! 113: * .. External Functions ..
! 114: LOGICAL LSAME
! 115: EXTERNAL LSAME
! 116: * ..
! 117: * .. External Subroutines ..
! 118: EXTERNAL DSTERF, XERBLA, ZHBGST, ZHBTRD, ZPBSTF, ZSTEQR
! 119: * ..
! 120: * .. Executable Statements ..
! 121: *
! 122: * Test the input parameters.
! 123: *
! 124: WANTZ = LSAME( JOBZ, 'V' )
! 125: UPPER = LSAME( UPLO, 'U' )
! 126: *
! 127: INFO = 0
! 128: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 129: INFO = -1
! 130: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 131: INFO = -2
! 132: ELSE IF( N.LT.0 ) THEN
! 133: INFO = -3
! 134: ELSE IF( KA.LT.0 ) THEN
! 135: INFO = -4
! 136: ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
! 137: INFO = -5
! 138: ELSE IF( LDAB.LT.KA+1 ) THEN
! 139: INFO = -7
! 140: ELSE IF( LDBB.LT.KB+1 ) THEN
! 141: INFO = -9
! 142: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 143: INFO = -12
! 144: END IF
! 145: IF( INFO.NE.0 ) THEN
! 146: CALL XERBLA( 'ZHBGV ', -INFO )
! 147: RETURN
! 148: END IF
! 149: *
! 150: * Quick return if possible
! 151: *
! 152: IF( N.EQ.0 )
! 153: $ RETURN
! 154: *
! 155: * Form a split Cholesky factorization of B.
! 156: *
! 157: CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO )
! 158: IF( INFO.NE.0 ) THEN
! 159: INFO = N + INFO
! 160: RETURN
! 161: END IF
! 162: *
! 163: * Transform problem to standard eigenvalue problem.
! 164: *
! 165: INDE = 1
! 166: INDWRK = INDE + N
! 167: CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
! 168: $ WORK, RWORK( INDWRK ), IINFO )
! 169: *
! 170: * Reduce to tridiagonal form.
! 171: *
! 172: IF( WANTZ ) THEN
! 173: VECT = 'U'
! 174: ELSE
! 175: VECT = 'N'
! 176: END IF
! 177: CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z,
! 178: $ LDZ, WORK, IINFO )
! 179: *
! 180: * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR.
! 181: *
! 182: IF( .NOT.WANTZ ) THEN
! 183: CALL DSTERF( N, W, RWORK( INDE ), INFO )
! 184: ELSE
! 185: CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
! 186: $ RWORK( INDWRK ), INFO )
! 187: END IF
! 188: RETURN
! 189: *
! 190: * End of ZHBGV
! 191: *
! 192: END
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