Annotation of rpl/lapack/lapack/zhbgvd.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
! 2: $ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
! 3: $ LIWORK, 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, UPLO
! 12: INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK,
! 13: $ LWORK, N
! 14: * ..
! 15: * .. Array Arguments ..
! 16: INTEGER IWORK( * )
! 17: DOUBLE PRECISION RWORK( * ), W( * )
! 18: COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
! 19: $ Z( LDZ, * )
! 20: * ..
! 21: *
! 22: * Purpose
! 23: * =======
! 24: *
! 25: * ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors
! 26: * of a complex generalized Hermitian-definite banded eigenproblem, of
! 27: * the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
! 28: * and banded, and B is also positive definite. If eigenvectors are
! 29: * desired, it uses a divide and conquer algorithm.
! 30: *
! 31: * The divide and conquer algorithm makes very mild assumptions about
! 32: * floating point arithmetic. It will work on machines with a guard
! 33: * digit in add/subtract, or on those binary machines without guard
! 34: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 35: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 36: * without guard digits, but we know of none.
! 37: *
! 38: * Arguments
! 39: * =========
! 40: *
! 41: * JOBZ (input) CHARACTER*1
! 42: * = 'N': Compute eigenvalues only;
! 43: * = 'V': Compute eigenvalues and eigenvectors.
! 44: *
! 45: * UPLO (input) CHARACTER*1
! 46: * = 'U': Upper triangles of A and B are stored;
! 47: * = 'L': Lower triangles of A and B are stored.
! 48: *
! 49: * N (input) INTEGER
! 50: * The order of the matrices A and B. N >= 0.
! 51: *
! 52: * KA (input) INTEGER
! 53: * The number of superdiagonals of the matrix A if UPLO = 'U',
! 54: * or the number of subdiagonals if UPLO = 'L'. KA >= 0.
! 55: *
! 56: * KB (input) INTEGER
! 57: * The number of superdiagonals of the matrix B if UPLO = 'U',
! 58: * or the number of subdiagonals if UPLO = 'L'. KB >= 0.
! 59: *
! 60: * AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
! 61: * On entry, the upper or lower triangle of the Hermitian band
! 62: * matrix A, stored in the first ka+1 rows of the array. The
! 63: * j-th column of A is stored in the j-th column of the array AB
! 64: * as follows:
! 65: * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
! 66: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
! 67: *
! 68: * On exit, the contents of AB are destroyed.
! 69: *
! 70: * LDAB (input) INTEGER
! 71: * The leading dimension of the array AB. LDAB >= KA+1.
! 72: *
! 73: * BB (input/output) COMPLEX*16 array, dimension (LDBB, N)
! 74: * On entry, the upper or lower triangle of the Hermitian band
! 75: * matrix B, stored in the first kb+1 rows of the array. The
! 76: * j-th column of B is stored in the j-th column of the array BB
! 77: * as follows:
! 78: * if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
! 79: * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
! 80: *
! 81: * On exit, the factor S from the split Cholesky factorization
! 82: * B = S**H*S, as returned by ZPBSTF.
! 83: *
! 84: * LDBB (input) INTEGER
! 85: * The leading dimension of the array BB. LDBB >= KB+1.
! 86: *
! 87: * W (output) DOUBLE PRECISION array, dimension (N)
! 88: * If INFO = 0, the eigenvalues in ascending order.
! 89: *
! 90: * Z (output) COMPLEX*16 array, dimension (LDZ, N)
! 91: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
! 92: * eigenvectors, with the i-th column of Z holding the
! 93: * eigenvector associated with W(i). The eigenvectors are
! 94: * normalized so that Z**H*B*Z = I.
! 95: * If JOBZ = 'N', then Z is not referenced.
! 96: *
! 97: * LDZ (input) INTEGER
! 98: * The leading dimension of the array Z. LDZ >= 1, and if
! 99: * JOBZ = 'V', LDZ >= N.
! 100: *
! 101: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 102: * On exit, if INFO=0, WORK(1) returns the optimal LWORK.
! 103: *
! 104: * LWORK (input) INTEGER
! 105: * The dimension of the array WORK.
! 106: * If N <= 1, LWORK >= 1.
! 107: * If JOBZ = 'N' and N > 1, LWORK >= N.
! 108: * If JOBZ = 'V' and N > 1, LWORK >= 2*N**2.
! 109: *
! 110: * If LWORK = -1, then a workspace query is assumed; the routine
! 111: * only calculates the optimal sizes of the WORK, RWORK and
! 112: * IWORK arrays, returns these values as the first entries of
! 113: * the WORK, RWORK and IWORK arrays, and no error message
! 114: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 115: *
! 116: * RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
! 117: * On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.
! 118: *
! 119: * LRWORK (input) INTEGER
! 120: * The dimension of array RWORK.
! 121: * If N <= 1, LRWORK >= 1.
! 122: * If JOBZ = 'N' and N > 1, LRWORK >= N.
! 123: * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
! 124: *
! 125: * If LRWORK = -1, then a workspace query is assumed; the
! 126: * routine only calculates the optimal sizes of the WORK, RWORK
! 127: * and IWORK arrays, returns these values as the first entries
! 128: * of the WORK, RWORK and IWORK arrays, and no error message
! 129: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 130: *
! 131: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
! 132: * On exit, if INFO=0, IWORK(1) returns the optimal LIWORK.
! 133: *
! 134: * LIWORK (input) INTEGER
! 135: * The dimension of array IWORK.
! 136: * If JOBZ = 'N' or N <= 1, LIWORK >= 1.
! 137: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
! 138: *
! 139: * If LIWORK = -1, then a workspace query is assumed; the
! 140: * routine only calculates the optimal sizes of the WORK, RWORK
! 141: * and IWORK arrays, returns these values as the first entries
! 142: * of the WORK, RWORK and IWORK arrays, and no error message
! 143: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 144: *
! 145: * INFO (output) INTEGER
! 146: * = 0: successful exit
! 147: * < 0: if INFO = -i, the i-th argument had an illegal value
! 148: * > 0: if INFO = i, and i is:
! 149: * <= N: the algorithm failed to converge:
! 150: * i off-diagonal elements of an intermediate
! 151: * tridiagonal form did not converge to zero;
! 152: * > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
! 153: * returned INFO = i: B is not positive definite.
! 154: * The factorization of B could not be completed and
! 155: * no eigenvalues or eigenvectors were computed.
! 156: *
! 157: * Further Details
! 158: * ===============
! 159: *
! 160: * Based on contributions by
! 161: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
! 162: *
! 163: * =====================================================================
! 164: *
! 165: * .. Parameters ..
! 166: COMPLEX*16 CONE, CZERO
! 167: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
! 168: $ CZERO = ( 0.0D+0, 0.0D+0 ) )
! 169: * ..
! 170: * .. Local Scalars ..
! 171: LOGICAL LQUERY, UPPER, WANTZ
! 172: CHARACTER VECT
! 173: INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLRWK,
! 174: $ LLWK2, LRWMIN, LWMIN
! 175: * ..
! 176: * .. External Functions ..
! 177: LOGICAL LSAME
! 178: EXTERNAL LSAME
! 179: * ..
! 180: * .. External Subroutines ..
! 181: EXTERNAL DSTERF, XERBLA, ZGEMM, ZHBGST, ZHBTRD, ZLACPY,
! 182: $ ZPBSTF, ZSTEDC
! 183: * ..
! 184: * .. Executable Statements ..
! 185: *
! 186: * Test the input parameters.
! 187: *
! 188: WANTZ = LSAME( JOBZ, 'V' )
! 189: UPPER = LSAME( UPLO, 'U' )
! 190: LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 191: *
! 192: INFO = 0
! 193: IF( N.LE.1 ) THEN
! 194: LWMIN = 1
! 195: LRWMIN = 1
! 196: LIWMIN = 1
! 197: ELSE IF( WANTZ ) THEN
! 198: LWMIN = 2*N**2
! 199: LRWMIN = 1 + 5*N + 2*N**2
! 200: LIWMIN = 3 + 5*N
! 201: ELSE
! 202: LWMIN = N
! 203: LRWMIN = N
! 204: LIWMIN = 1
! 205: END IF
! 206: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 207: INFO = -1
! 208: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 209: INFO = -2
! 210: ELSE IF( N.LT.0 ) THEN
! 211: INFO = -3
! 212: ELSE IF( KA.LT.0 ) THEN
! 213: INFO = -4
! 214: ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
! 215: INFO = -5
! 216: ELSE IF( LDAB.LT.KA+1 ) THEN
! 217: INFO = -7
! 218: ELSE IF( LDBB.LT.KB+1 ) THEN
! 219: INFO = -9
! 220: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 221: INFO = -12
! 222: END IF
! 223: *
! 224: IF( INFO.EQ.0 ) THEN
! 225: WORK( 1 ) = LWMIN
! 226: RWORK( 1 ) = LRWMIN
! 227: IWORK( 1 ) = LIWMIN
! 228: *
! 229: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 230: INFO = -14
! 231: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
! 232: INFO = -16
! 233: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 234: INFO = -18
! 235: END IF
! 236: END IF
! 237: *
! 238: IF( INFO.NE.0 ) THEN
! 239: CALL XERBLA( 'ZHBGVD', -INFO )
! 240: RETURN
! 241: ELSE IF( LQUERY ) THEN
! 242: RETURN
! 243: END IF
! 244: *
! 245: * Quick return if possible
! 246: *
! 247: IF( N.EQ.0 )
! 248: $ RETURN
! 249: *
! 250: * Form a split Cholesky factorization of B.
! 251: *
! 252: CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO )
! 253: IF( INFO.NE.0 ) THEN
! 254: INFO = N + INFO
! 255: RETURN
! 256: END IF
! 257: *
! 258: * Transform problem to standard eigenvalue problem.
! 259: *
! 260: INDE = 1
! 261: INDWRK = INDE + N
! 262: INDWK2 = 1 + N*N
! 263: LLWK2 = LWORK - INDWK2 + 2
! 264: LLRWK = LRWORK - INDWRK + 2
! 265: CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
! 266: $ WORK, RWORK( INDWRK ), IINFO )
! 267: *
! 268: * Reduce Hermitian band matrix to tridiagonal form.
! 269: *
! 270: IF( WANTZ ) THEN
! 271: VECT = 'U'
! 272: ELSE
! 273: VECT = 'N'
! 274: END IF
! 275: CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z,
! 276: $ LDZ, WORK, IINFO )
! 277: *
! 278: * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEDC.
! 279: *
! 280: IF( .NOT.WANTZ ) THEN
! 281: CALL DSTERF( N, W, RWORK( INDE ), INFO )
! 282: ELSE
! 283: CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ),
! 284: $ LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK,
! 285: $ INFO )
! 286: CALL ZGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO,
! 287: $ WORK( INDWK2 ), N )
! 288: CALL ZLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
! 289: END IF
! 290: *
! 291: WORK( 1 ) = LWMIN
! 292: RWORK( 1 ) = LRWMIN
! 293: IWORK( 1 ) = LIWMIN
! 294: RETURN
! 295: *
! 296: * End of ZHBGVD
! 297: *
! 298: END
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