Annotation of rpl/lapack/lapack/dsbgvd.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
! 2: $ Z, LDZ, WORK, 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, KA, KB, LDAB, LDBB, LDZ, LIWORK, LWORK, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: INTEGER IWORK( * )
! 15: DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
! 16: $ WORK( * ), Z( LDZ, * )
! 17: * ..
! 18: *
! 19: * Purpose
! 20: * =======
! 21: *
! 22: * DSBGVD computes all the eigenvalues, and optionally, the eigenvectors
! 23: * of a real generalized symmetric-definite banded eigenproblem, of the
! 24: * form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and
! 25: * banded, and B is also positive definite. If eigenvectors are
! 26: * desired, it uses a divide and conquer algorithm.
! 27: *
! 28: * The divide and conquer algorithm makes very mild assumptions about
! 29: * floating point arithmetic. It will work on machines with a guard
! 30: * digit in add/subtract, or on those binary machines without guard
! 31: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 32: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 33: * without guard digits, but we know of none.
! 34: *
! 35: * Arguments
! 36: * =========
! 37: *
! 38: * JOBZ (input) CHARACTER*1
! 39: * = 'N': Compute eigenvalues only;
! 40: * = 'V': Compute eigenvalues and eigenvectors.
! 41: *
! 42: * UPLO (input) CHARACTER*1
! 43: * = 'U': Upper triangles of A and B are stored;
! 44: * = 'L': Lower triangles of A and B are stored.
! 45: *
! 46: * N (input) INTEGER
! 47: * The order of the matrices A and B. N >= 0.
! 48: *
! 49: * KA (input) INTEGER
! 50: * The number of superdiagonals of the matrix A if UPLO = 'U',
! 51: * or the number of subdiagonals if UPLO = 'L'. KA >= 0.
! 52: *
! 53: * KB (input) INTEGER
! 54: * The number of superdiagonals of the matrix B if UPLO = 'U',
! 55: * or the number of subdiagonals if UPLO = 'L'. KB >= 0.
! 56: *
! 57: * AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
! 58: * On entry, the upper or lower triangle of the symmetric band
! 59: * matrix A, stored in the first ka+1 rows of the array. The
! 60: * j-th column of A is stored in the j-th column of the array AB
! 61: * as follows:
! 62: * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
! 63: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
! 64: *
! 65: * On exit, the contents of AB are destroyed.
! 66: *
! 67: * LDAB (input) INTEGER
! 68: * The leading dimension of the array AB. LDAB >= KA+1.
! 69: *
! 70: * BB (input/output) DOUBLE PRECISION array, dimension (LDBB, N)
! 71: * On entry, the upper or lower triangle of the symmetric band
! 72: * matrix B, stored in the first kb+1 rows of the array. The
! 73: * j-th column of B is stored in the j-th column of the array BB
! 74: * as follows:
! 75: * if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
! 76: * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
! 77: *
! 78: * On exit, the factor S from the split Cholesky factorization
! 79: * B = S**T*S, as returned by DPBSTF.
! 80: *
! 81: * LDBB (input) INTEGER
! 82: * The leading dimension of the array BB. LDBB >= KB+1.
! 83: *
! 84: * W (output) DOUBLE PRECISION array, dimension (N)
! 85: * If INFO = 0, the eigenvalues in ascending order.
! 86: *
! 87: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
! 88: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
! 89: * eigenvectors, with the i-th column of Z holding the
! 90: * eigenvector associated with W(i). The eigenvectors are
! 91: * normalized so Z**T*B*Z = I.
! 92: * If JOBZ = 'N', then Z is not referenced.
! 93: *
! 94: * LDZ (input) INTEGER
! 95: * The leading dimension of the array Z. LDZ >= 1, and if
! 96: * JOBZ = 'V', LDZ >= max(1,N).
! 97: *
! 98: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 99: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 100: *
! 101: * LWORK (input) INTEGER
! 102: * The dimension of the array WORK.
! 103: * If N <= 1, LWORK >= 1.
! 104: * If JOBZ = 'N' and N > 1, LWORK >= 3*N.
! 105: * If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2.
! 106: *
! 107: * If LWORK = -1, then a workspace query is assumed; the routine
! 108: * only calculates the optimal sizes of the WORK and IWORK
! 109: * arrays, returns these values as the first entries of the WORK
! 110: * and IWORK arrays, and no error message related to LWORK or
! 111: * LIWORK is issued by XERBLA.
! 112: *
! 113: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
! 114: * On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
! 115: *
! 116: * LIWORK (input) INTEGER
! 117: * The dimension of the array IWORK.
! 118: * If JOBZ = 'N' or N <= 1, LIWORK >= 1.
! 119: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
! 120: *
! 121: * If LIWORK = -1, then a workspace query is assumed; the
! 122: * routine only calculates the optimal sizes of the WORK and
! 123: * IWORK arrays, returns these values as the first entries of
! 124: * the WORK and IWORK arrays, and no error message related to
! 125: * LWORK or LIWORK is issued by XERBLA.
! 126: *
! 127: * INFO (output) INTEGER
! 128: * = 0: successful exit
! 129: * < 0: if INFO = -i, the i-th argument had an illegal value
! 130: * > 0: if INFO = i, and i is:
! 131: * <= N: the algorithm failed to converge:
! 132: * i off-diagonal elements of an intermediate
! 133: * tridiagonal form did not converge to zero;
! 134: * > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF
! 135: * returned INFO = i: B is not positive definite.
! 136: * The factorization of B could not be completed and
! 137: * no eigenvalues or eigenvectors were computed.
! 138: *
! 139: * Further Details
! 140: * ===============
! 141: *
! 142: * Based on contributions by
! 143: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
! 144: *
! 145: * =====================================================================
! 146: *
! 147: * .. Parameters ..
! 148: DOUBLE PRECISION ONE, ZERO
! 149: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 150: * ..
! 151: * .. Local Scalars ..
! 152: LOGICAL LQUERY, UPPER, WANTZ
! 153: CHARACTER VECT
! 154: INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLWRK2,
! 155: $ LWMIN
! 156: * ..
! 157: * .. External Functions ..
! 158: LOGICAL LSAME
! 159: EXTERNAL LSAME
! 160: * ..
! 161: * .. External Subroutines ..
! 162: EXTERNAL DGEMM, DLACPY, DPBSTF, DSBGST, DSBTRD, DSTEDC,
! 163: $ DSTERF, XERBLA
! 164: * ..
! 165: * .. Executable Statements ..
! 166: *
! 167: * Test the input parameters.
! 168: *
! 169: WANTZ = LSAME( JOBZ, 'V' )
! 170: UPPER = LSAME( UPLO, 'U' )
! 171: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 172: *
! 173: INFO = 0
! 174: IF( N.LE.1 ) THEN
! 175: LIWMIN = 1
! 176: LWMIN = 1
! 177: ELSE IF( WANTZ ) THEN
! 178: LIWMIN = 3 + 5*N
! 179: LWMIN = 1 + 5*N + 2*N**2
! 180: ELSE
! 181: LIWMIN = 1
! 182: LWMIN = 2*N
! 183: END IF
! 184: *
! 185: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 186: INFO = -1
! 187: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 188: INFO = -2
! 189: ELSE IF( N.LT.0 ) THEN
! 190: INFO = -3
! 191: ELSE IF( KA.LT.0 ) THEN
! 192: INFO = -4
! 193: ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
! 194: INFO = -5
! 195: ELSE IF( LDAB.LT.KA+1 ) THEN
! 196: INFO = -7
! 197: ELSE IF( LDBB.LT.KB+1 ) THEN
! 198: INFO = -9
! 199: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 200: INFO = -12
! 201: END IF
! 202: *
! 203: IF( INFO.EQ.0 ) THEN
! 204: WORK( 1 ) = LWMIN
! 205: IWORK( 1 ) = LIWMIN
! 206: *
! 207: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 208: INFO = -14
! 209: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 210: INFO = -16
! 211: END IF
! 212: END IF
! 213: *
! 214: IF( INFO.NE.0 ) THEN
! 215: CALL XERBLA( 'DSBGVD', -INFO )
! 216: RETURN
! 217: ELSE IF( LQUERY ) THEN
! 218: RETURN
! 219: END IF
! 220: *
! 221: * Quick return if possible
! 222: *
! 223: IF( N.EQ.0 )
! 224: $ RETURN
! 225: *
! 226: * Form a split Cholesky factorization of B.
! 227: *
! 228: CALL DPBSTF( UPLO, N, KB, BB, LDBB, INFO )
! 229: IF( INFO.NE.0 ) THEN
! 230: INFO = N + INFO
! 231: RETURN
! 232: END IF
! 233: *
! 234: * Transform problem to standard eigenvalue problem.
! 235: *
! 236: INDE = 1
! 237: INDWRK = INDE + N
! 238: INDWK2 = INDWRK + N*N
! 239: LLWRK2 = LWORK - INDWK2 + 1
! 240: CALL DSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
! 241: $ WORK( INDWRK ), IINFO )
! 242: *
! 243: * Reduce to tridiagonal form.
! 244: *
! 245: IF( WANTZ ) THEN
! 246: VECT = 'U'
! 247: ELSE
! 248: VECT = 'N'
! 249: END IF
! 250: CALL DSBTRD( VECT, UPLO, N, KA, AB, LDAB, W, WORK( INDE ), Z, LDZ,
! 251: $ WORK( INDWRK ), IINFO )
! 252: *
! 253: * For eigenvalues only, call DSTERF. For eigenvectors, call SSTEDC.
! 254: *
! 255: IF( .NOT.WANTZ ) THEN
! 256: CALL DSTERF( N, W, WORK( INDE ), INFO )
! 257: ELSE
! 258: CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,
! 259: $ WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO )
! 260: CALL DGEMM( 'N', 'N', N, N, N, ONE, Z, LDZ, WORK( INDWRK ), N,
! 261: $ ZERO, WORK( INDWK2 ), N )
! 262: CALL DLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
! 263: END IF
! 264: *
! 265: WORK( 1 ) = LWMIN
! 266: IWORK( 1 ) = LIWMIN
! 267: *
! 268: RETURN
! 269: *
! 270: * End of DSBGVD
! 271: *
! 272: END
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