Annotation of rpl/lapack/lapack/dsbevd.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
! 2: $ 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, KD, LDAB, LDZ, LIWORK, LWORK, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: INTEGER IWORK( * )
! 15: DOUBLE PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * DSBEVD computes all the eigenvalues and, optionally, eigenvectors of
! 22: * a real symmetric band matrix A. If eigenvectors are desired, it uses
! 23: * a divide and conquer algorithm.
! 24: *
! 25: * The divide and conquer algorithm makes very mild assumptions about
! 26: * floating point arithmetic. It will work on machines with a guard
! 27: * digit in add/subtract, or on those binary machines without guard
! 28: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 29: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 30: * without guard digits, but we know of none.
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * JOBZ (input) CHARACTER*1
! 36: * = 'N': Compute eigenvalues only;
! 37: * = 'V': Compute eigenvalues and eigenvectors.
! 38: *
! 39: * UPLO (input) CHARACTER*1
! 40: * = 'U': Upper triangle of A is stored;
! 41: * = 'L': Lower triangle of A is stored.
! 42: *
! 43: * N (input) INTEGER
! 44: * The order of the matrix A. N >= 0.
! 45: *
! 46: * KD (input) INTEGER
! 47: * The number of superdiagonals of the matrix A if UPLO = 'U',
! 48: * or the number of subdiagonals if UPLO = 'L'. KD >= 0.
! 49: *
! 50: * AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
! 51: * On entry, the upper or lower triangle of the symmetric band
! 52: * matrix A, stored in the first KD+1 rows of the array. The
! 53: * j-th column of A is stored in the j-th column of the array AB
! 54: * as follows:
! 55: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 56: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 57: *
! 58: * On exit, AB is overwritten by values generated during the
! 59: * reduction to tridiagonal form. If UPLO = 'U', the first
! 60: * superdiagonal and the diagonal of the tridiagonal matrix T
! 61: * are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
! 62: * the diagonal and first subdiagonal of T are returned in the
! 63: * first two rows of AB.
! 64: *
! 65: * LDAB (input) INTEGER
! 66: * The leading dimension of the array AB. LDAB >= KD + 1.
! 67: *
! 68: * W (output) DOUBLE PRECISION array, dimension (N)
! 69: * If INFO = 0, the eigenvalues in ascending order.
! 70: *
! 71: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
! 72: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
! 73: * eigenvectors of the matrix A, with the i-th column of Z
! 74: * holding the eigenvector associated with W(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/output) DOUBLE PRECISION array,
! 82: * dimension (LWORK)
! 83: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 84: *
! 85: * LWORK (input) INTEGER
! 86: * The dimension of the array WORK.
! 87: * IF N <= 1, LWORK must be at least 1.
! 88: * If JOBZ = 'N' and N > 2, LWORK must be at least 2*N.
! 89: * If JOBZ = 'V' and N > 2, LWORK must be at least
! 90: * ( 1 + 5*N + 2*N**2 ).
! 91: *
! 92: * If LWORK = -1, then a workspace query is assumed; the routine
! 93: * only calculates the optimal sizes of the WORK and IWORK
! 94: * arrays, returns these values as the first entries of the WORK
! 95: * and IWORK arrays, and no error message related to LWORK or
! 96: * LIWORK is issued by XERBLA.
! 97: *
! 98: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
! 99: * On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
! 100: *
! 101: * LIWORK (input) INTEGER
! 102: * The dimension of the array LIWORK.
! 103: * If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
! 104: * If JOBZ = 'V' and N > 2, LIWORK must be at least 3 + 5*N.
! 105: *
! 106: * If LIWORK = -1, then a workspace query is assumed; the
! 107: * routine only calculates the optimal sizes of the WORK and
! 108: * IWORK arrays, returns these values as the first entries of
! 109: * the WORK and IWORK arrays, and no error message related to
! 110: * LWORK or LIWORK is issued by XERBLA.
! 111: *
! 112: * INFO (output) INTEGER
! 113: * = 0: successful exit
! 114: * < 0: if INFO = -i, the i-th argument had an illegal value
! 115: * > 0: if INFO = i, the algorithm failed to converge; i
! 116: * off-diagonal elements of an intermediate tridiagonal
! 117: * form did not converge to zero.
! 118: *
! 119: * =====================================================================
! 120: *
! 121: * .. Parameters ..
! 122: DOUBLE PRECISION ZERO, ONE
! 123: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 124: * ..
! 125: * .. Local Scalars ..
! 126: LOGICAL LOWER, LQUERY, WANTZ
! 127: INTEGER IINFO, INDE, INDWK2, INDWRK, ISCALE, LIWMIN,
! 128: $ LLWRK2, LWMIN
! 129: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 130: $ SMLNUM
! 131: * ..
! 132: * .. External Functions ..
! 133: LOGICAL LSAME
! 134: DOUBLE PRECISION DLAMCH, DLANSB
! 135: EXTERNAL LSAME, DLAMCH, DLANSB
! 136: * ..
! 137: * .. External Subroutines ..
! 138: EXTERNAL DGEMM, DLACPY, DLASCL, DSBTRD, DSCAL, DSTEDC,
! 139: $ DSTERF, XERBLA
! 140: * ..
! 141: * .. Intrinsic Functions ..
! 142: INTRINSIC SQRT
! 143: * ..
! 144: * .. Executable Statements ..
! 145: *
! 146: * Test the input parameters.
! 147: *
! 148: WANTZ = LSAME( JOBZ, 'V' )
! 149: LOWER = LSAME( UPLO, 'L' )
! 150: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 151: *
! 152: INFO = 0
! 153: IF( N.LE.1 ) THEN
! 154: LIWMIN = 1
! 155: LWMIN = 1
! 156: ELSE
! 157: IF( WANTZ ) THEN
! 158: LIWMIN = 3 + 5*N
! 159: LWMIN = 1 + 5*N + 2*N**2
! 160: ELSE
! 161: LIWMIN = 1
! 162: LWMIN = 2*N
! 163: END IF
! 164: END IF
! 165: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 166: INFO = -1
! 167: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 168: INFO = -2
! 169: ELSE IF( N.LT.0 ) THEN
! 170: INFO = -3
! 171: ELSE IF( KD.LT.0 ) THEN
! 172: INFO = -4
! 173: ELSE IF( LDAB.LT.KD+1 ) THEN
! 174: INFO = -6
! 175: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 176: INFO = -9
! 177: END IF
! 178: *
! 179: IF( INFO.EQ.0 ) THEN
! 180: WORK( 1 ) = LWMIN
! 181: IWORK( 1 ) = LIWMIN
! 182: *
! 183: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 184: INFO = -11
! 185: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 186: INFO = -13
! 187: END IF
! 188: END IF
! 189: *
! 190: IF( INFO.NE.0 ) THEN
! 191: CALL XERBLA( 'DSBEVD', -INFO )
! 192: RETURN
! 193: ELSE IF( LQUERY ) THEN
! 194: RETURN
! 195: END IF
! 196: *
! 197: * Quick return if possible
! 198: *
! 199: IF( N.EQ.0 )
! 200: $ RETURN
! 201: *
! 202: IF( N.EQ.1 ) THEN
! 203: W( 1 ) = AB( 1, 1 )
! 204: IF( WANTZ )
! 205: $ Z( 1, 1 ) = ONE
! 206: RETURN
! 207: END IF
! 208: *
! 209: * Get machine constants.
! 210: *
! 211: SAFMIN = DLAMCH( 'Safe minimum' )
! 212: EPS = DLAMCH( 'Precision' )
! 213: SMLNUM = SAFMIN / EPS
! 214: BIGNUM = ONE / SMLNUM
! 215: RMIN = SQRT( SMLNUM )
! 216: RMAX = SQRT( BIGNUM )
! 217: *
! 218: * Scale matrix to allowable range, if necessary.
! 219: *
! 220: ANRM = DLANSB( 'M', UPLO, N, KD, AB, LDAB, WORK )
! 221: ISCALE = 0
! 222: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 223: ISCALE = 1
! 224: SIGMA = RMIN / ANRM
! 225: ELSE IF( ANRM.GT.RMAX ) THEN
! 226: ISCALE = 1
! 227: SIGMA = RMAX / ANRM
! 228: END IF
! 229: IF( ISCALE.EQ.1 ) THEN
! 230: IF( LOWER ) THEN
! 231: CALL DLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 232: ELSE
! 233: CALL DLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 234: END IF
! 235: END IF
! 236: *
! 237: * Call DSBTRD to reduce symmetric band matrix to tridiagonal form.
! 238: *
! 239: INDE = 1
! 240: INDWRK = INDE + N
! 241: INDWK2 = INDWRK + N*N
! 242: LLWRK2 = LWORK - INDWK2 + 1
! 243: CALL DSBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, WORK( INDE ), Z, LDZ,
! 244: $ WORK( INDWRK ), IINFO )
! 245: *
! 246: * For eigenvalues only, call DSTERF. For eigenvectors, call SSTEDC.
! 247: *
! 248: IF( .NOT.WANTZ ) THEN
! 249: CALL DSTERF( N, W, WORK( INDE ), INFO )
! 250: ELSE
! 251: CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,
! 252: $ WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO )
! 253: CALL DGEMM( 'N', 'N', N, N, N, ONE, Z, LDZ, WORK( INDWRK ), N,
! 254: $ ZERO, WORK( INDWK2 ), N )
! 255: CALL DLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
! 256: END IF
! 257: *
! 258: * If matrix was scaled, then rescale eigenvalues appropriately.
! 259: *
! 260: IF( ISCALE.EQ.1 )
! 261: $ CALL DSCAL( N, ONE / SIGMA, W, 1 )
! 262: *
! 263: WORK( 1 ) = LWMIN
! 264: IWORK( 1 ) = LIWMIN
! 265: RETURN
! 266: *
! 267: * End of DSBEVD
! 268: *
! 269: END
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