Annotation of rpl/lapack/lapack/dspevx.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU,
! 2: $ ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL,
! 3: $ 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, IU, LDZ, M, N
! 13: DOUBLE PRECISION ABSTOL, VL, VU
! 14: * ..
! 15: * .. Array Arguments ..
! 16: INTEGER IFAIL( * ), IWORK( * )
! 17: DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
! 18: * ..
! 19: *
! 20: * Purpose
! 21: * =======
! 22: *
! 23: * DSPEVX computes selected eigenvalues and, optionally, eigenvectors
! 24: * of a real symmetric matrix A in packed storage. Eigenvalues/vectors
! 25: * can be selected by specifying either a range of values or a range of
! 26: * indices for the desired eigenvalues.
! 27: *
! 28: * Arguments
! 29: * =========
! 30: *
! 31: * JOBZ (input) CHARACTER*1
! 32: * = 'N': Compute eigenvalues only;
! 33: * = 'V': Compute eigenvalues and eigenvectors.
! 34: *
! 35: * RANGE (input) CHARACTER*1
! 36: * = 'A': all eigenvalues will be found;
! 37: * = 'V': all eigenvalues in the half-open interval (VL,VU]
! 38: * will be found;
! 39: * = 'I': the IL-th through IU-th eigenvalues will be found.
! 40: *
! 41: * UPLO (input) CHARACTER*1
! 42: * = 'U': Upper triangle of A is stored;
! 43: * = 'L': Lower triangle of A is stored.
! 44: *
! 45: * N (input) INTEGER
! 46: * The order of the matrix A. N >= 0.
! 47: *
! 48: * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 49: * On entry, the upper or lower triangle of the symmetric matrix
! 50: * A, packed columnwise in a linear array. The j-th column of A
! 51: * is stored in the array AP as follows:
! 52: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 53: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
! 54: *
! 55: * On exit, AP is overwritten by values generated during the
! 56: * reduction to tridiagonal form. If UPLO = 'U', the diagonal
! 57: * and first superdiagonal of the tridiagonal matrix T overwrite
! 58: * the corresponding elements of A, and if UPLO = 'L', the
! 59: * diagonal and first subdiagonal of T overwrite the
! 60: * corresponding elements of A.
! 61: *
! 62: * VL (input) DOUBLE PRECISION
! 63: * VU (input) DOUBLE PRECISION
! 64: * If RANGE='V', the lower and upper bounds of the interval to
! 65: * be searched for eigenvalues. VL < VU.
! 66: * Not referenced if RANGE = 'A' or 'I'.
! 67: *
! 68: * IL (input) INTEGER
! 69: * IU (input) INTEGER
! 70: * If RANGE='I', the indices (in ascending order) of the
! 71: * smallest and largest eigenvalues to be returned.
! 72: * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
! 73: * Not referenced if RANGE = 'A' or 'V'.
! 74: *
! 75: * ABSTOL (input) DOUBLE PRECISION
! 76: * The absolute error tolerance for the eigenvalues.
! 77: * An approximate eigenvalue is accepted as converged
! 78: * when it is determined to lie in an interval [a,b]
! 79: * of width less than or equal to
! 80: *
! 81: * ABSTOL + EPS * max( |a|,|b| ) ,
! 82: *
! 83: * where EPS is the machine precision. If ABSTOL is less than
! 84: * or equal to zero, then EPS*|T| will be used in its place,
! 85: * where |T| is the 1-norm of the tridiagonal matrix obtained
! 86: * by reducing AP to tridiagonal form.
! 87: *
! 88: * Eigenvalues will be computed most accurately when ABSTOL is
! 89: * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
! 90: * If this routine returns with INFO>0, indicating that some
! 91: * eigenvectors did not converge, try setting ABSTOL to
! 92: * 2*DLAMCH('S').
! 93: *
! 94: * See "Computing Small Singular Values of Bidiagonal Matrices
! 95: * with Guaranteed High Relative Accuracy," by Demmel and
! 96: * Kahan, LAPACK Working Note #3.
! 97: *
! 98: * M (output) INTEGER
! 99: * The total number of eigenvalues found. 0 <= M <= N.
! 100: * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
! 101: *
! 102: * W (output) DOUBLE PRECISION array, dimension (N)
! 103: * If INFO = 0, the selected eigenvalues in ascending order.
! 104: *
! 105: * Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
! 106: * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
! 107: * contain the orthonormal eigenvectors of the matrix A
! 108: * corresponding to the selected eigenvalues, with the i-th
! 109: * column of Z holding the eigenvector associated with W(i).
! 110: * If an eigenvector fails to converge, then that column of Z
! 111: * contains the latest approximation to the eigenvector, and the
! 112: * index of the eigenvector is returned in IFAIL.
! 113: * If JOBZ = 'N', then Z is not referenced.
! 114: * Note: the user must ensure that at least max(1,M) columns are
! 115: * supplied in the array Z; if RANGE = 'V', the exact value of M
! 116: * is not known in advance and an upper bound must be used.
! 117: *
! 118: * LDZ (input) INTEGER
! 119: * The leading dimension of the array Z. LDZ >= 1, and if
! 120: * JOBZ = 'V', LDZ >= max(1,N).
! 121: *
! 122: * WORK (workspace) DOUBLE PRECISION array, dimension (8*N)
! 123: *
! 124: * IWORK (workspace) INTEGER array, dimension (5*N)
! 125: *
! 126: * IFAIL (output) INTEGER array, dimension (N)
! 127: * If JOBZ = 'V', then if INFO = 0, the first M elements of
! 128: * IFAIL are zero. If INFO > 0, then IFAIL contains the
! 129: * indices of the eigenvectors that failed to converge.
! 130: * If JOBZ = 'N', then IFAIL is not referenced.
! 131: *
! 132: * INFO (output) INTEGER
! 133: * = 0: successful exit
! 134: * < 0: if INFO = -i, the i-th argument had an illegal value
! 135: * > 0: if INFO = i, then i eigenvectors failed to converge.
! 136: * Their indices are stored in array IFAIL.
! 137: *
! 138: * =====================================================================
! 139: *
! 140: * .. Parameters ..
! 141: DOUBLE PRECISION ZERO, ONE
! 142: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 143: * ..
! 144: * .. Local Scalars ..
! 145: LOGICAL ALLEIG, INDEIG, TEST, VALEIG, WANTZ
! 146: CHARACTER ORDER
! 147: INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
! 148: $ INDISP, INDIWO, INDTAU, INDWRK, ISCALE, ITMP1,
! 149: $ J, JJ, NSPLIT
! 150: DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
! 151: $ SIGMA, SMLNUM, TMP1, VLL, VUU
! 152: * ..
! 153: * .. External Functions ..
! 154: LOGICAL LSAME
! 155: DOUBLE PRECISION DLAMCH, DLANSP
! 156: EXTERNAL LSAME, DLAMCH, DLANSP
! 157: * ..
! 158: * .. External Subroutines ..
! 159: EXTERNAL DCOPY, DOPGTR, DOPMTR, DSCAL, DSPTRD, DSTEBZ,
! 160: $ DSTEIN, DSTEQR, DSTERF, DSWAP, XERBLA
! 161: * ..
! 162: * .. Intrinsic Functions ..
! 163: INTRINSIC MAX, MIN, SQRT
! 164: * ..
! 165: * .. Executable Statements ..
! 166: *
! 167: * Test the input parameters.
! 168: *
! 169: WANTZ = LSAME( JOBZ, 'V' )
! 170: ALLEIG = LSAME( RANGE, 'A' )
! 171: VALEIG = LSAME( RANGE, 'V' )
! 172: INDEIG = LSAME( RANGE, 'I' )
! 173: *
! 174: INFO = 0
! 175: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 176: INFO = -1
! 177: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
! 178: INFO = -2
! 179: ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) )
! 180: $ THEN
! 181: INFO = -3
! 182: ELSE IF( N.LT.0 ) THEN
! 183: INFO = -4
! 184: ELSE
! 185: IF( VALEIG ) THEN
! 186: IF( N.GT.0 .AND. VU.LE.VL )
! 187: $ INFO = -7
! 188: ELSE IF( INDEIG ) THEN
! 189: IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
! 190: INFO = -8
! 191: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
! 192: INFO = -9
! 193: END IF
! 194: END IF
! 195: END IF
! 196: IF( INFO.EQ.0 ) THEN
! 197: IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) )
! 198: $ INFO = -14
! 199: END IF
! 200: *
! 201: IF( INFO.NE.0 ) THEN
! 202: CALL XERBLA( 'DSPEVX', -INFO )
! 203: RETURN
! 204: END IF
! 205: *
! 206: * Quick return if possible
! 207: *
! 208: M = 0
! 209: IF( N.EQ.0 )
! 210: $ RETURN
! 211: *
! 212: IF( N.EQ.1 ) THEN
! 213: IF( ALLEIG .OR. INDEIG ) THEN
! 214: M = 1
! 215: W( 1 ) = AP( 1 )
! 216: ELSE
! 217: IF( VL.LT.AP( 1 ) .AND. VU.GE.AP( 1 ) ) THEN
! 218: M = 1
! 219: W( 1 ) = AP( 1 )
! 220: END IF
! 221: END IF
! 222: IF( WANTZ )
! 223: $ Z( 1, 1 ) = ONE
! 224: RETURN
! 225: END IF
! 226: *
! 227: * Get machine constants.
! 228: *
! 229: SAFMIN = DLAMCH( 'Safe minimum' )
! 230: EPS = DLAMCH( 'Precision' )
! 231: SMLNUM = SAFMIN / EPS
! 232: BIGNUM = ONE / SMLNUM
! 233: RMIN = SQRT( SMLNUM )
! 234: RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
! 235: *
! 236: * Scale matrix to allowable range, if necessary.
! 237: *
! 238: ISCALE = 0
! 239: ABSTLL = ABSTOL
! 240: IF( VALEIG ) THEN
! 241: VLL = VL
! 242: VUU = VU
! 243: ELSE
! 244: VLL = ZERO
! 245: VUU = ZERO
! 246: END IF
! 247: ANRM = DLANSP( 'M', UPLO, N, AP, WORK )
! 248: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 249: ISCALE = 1
! 250: SIGMA = RMIN / ANRM
! 251: ELSE IF( ANRM.GT.RMAX ) THEN
! 252: ISCALE = 1
! 253: SIGMA = RMAX / ANRM
! 254: END IF
! 255: IF( ISCALE.EQ.1 ) THEN
! 256: CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
! 257: IF( ABSTOL.GT.0 )
! 258: $ ABSTLL = ABSTOL*SIGMA
! 259: IF( VALEIG ) THEN
! 260: VLL = VL*SIGMA
! 261: VUU = VU*SIGMA
! 262: END IF
! 263: END IF
! 264: *
! 265: * Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
! 266: *
! 267: INDTAU = 1
! 268: INDE = INDTAU + N
! 269: INDD = INDE + N
! 270: INDWRK = INDD + N
! 271: CALL DSPTRD( UPLO, N, AP, WORK( INDD ), WORK( INDE ),
! 272: $ WORK( INDTAU ), IINFO )
! 273: *
! 274: * If all eigenvalues are desired and ABSTOL is less than or equal
! 275: * to zero, then call DSTERF or DOPGTR and SSTEQR. If this fails
! 276: * for some eigenvalue, then try DSTEBZ.
! 277: *
! 278: TEST = .FALSE.
! 279: IF (INDEIG) THEN
! 280: IF (IL.EQ.1 .AND. IU.EQ.N) THEN
! 281: TEST = .TRUE.
! 282: END IF
! 283: END IF
! 284: IF ((ALLEIG .OR. TEST) .AND. (ABSTOL.LE.ZERO)) THEN
! 285: CALL DCOPY( N, WORK( INDD ), 1, W, 1 )
! 286: INDEE = INDWRK + 2*N
! 287: IF( .NOT.WANTZ ) THEN
! 288: CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
! 289: CALL DSTERF( N, W, WORK( INDEE ), INFO )
! 290: ELSE
! 291: CALL DOPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ,
! 292: $ WORK( INDWRK ), IINFO )
! 293: CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
! 294: CALL DSTEQR( JOBZ, N, W, WORK( INDEE ), Z, LDZ,
! 295: $ WORK( INDWRK ), INFO )
! 296: IF( INFO.EQ.0 ) THEN
! 297: DO 10 I = 1, N
! 298: IFAIL( I ) = 0
! 299: 10 CONTINUE
! 300: END IF
! 301: END IF
! 302: IF( INFO.EQ.0 ) THEN
! 303: M = N
! 304: GO TO 20
! 305: END IF
! 306: INFO = 0
! 307: END IF
! 308: *
! 309: * Otherwise, call DSTEBZ and, if eigenvectors are desired, SSTEIN.
! 310: *
! 311: IF( WANTZ ) THEN
! 312: ORDER = 'B'
! 313: ELSE
! 314: ORDER = 'E'
! 315: END IF
! 316: INDIBL = 1
! 317: INDISP = INDIBL + N
! 318: INDIWO = INDISP + N
! 319: CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
! 320: $ WORK( INDD ), WORK( INDE ), M, NSPLIT, W,
! 321: $ IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWRK ),
! 322: $ IWORK( INDIWO ), INFO )
! 323: *
! 324: IF( WANTZ ) THEN
! 325: CALL DSTEIN( N, WORK( INDD ), WORK( INDE ), M, W,
! 326: $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
! 327: $ WORK( INDWRK ), IWORK( INDIWO ), IFAIL, INFO )
! 328: *
! 329: * Apply orthogonal matrix used in reduction to tridiagonal
! 330: * form to eigenvectors returned by DSTEIN.
! 331: *
! 332: CALL DOPMTR( 'L', UPLO, 'N', N, M, AP, WORK( INDTAU ), Z, LDZ,
! 333: $ WORK( INDWRK ), IINFO )
! 334: END IF
! 335: *
! 336: * If matrix was scaled, then rescale eigenvalues appropriately.
! 337: *
! 338: 20 CONTINUE
! 339: IF( ISCALE.EQ.1 ) THEN
! 340: IF( INFO.EQ.0 ) THEN
! 341: IMAX = M
! 342: ELSE
! 343: IMAX = INFO - 1
! 344: END IF
! 345: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 346: END IF
! 347: *
! 348: * If eigenvalues are not in order, then sort them, along with
! 349: * eigenvectors.
! 350: *
! 351: IF( WANTZ ) THEN
! 352: DO 40 J = 1, M - 1
! 353: I = 0
! 354: TMP1 = W( J )
! 355: DO 30 JJ = J + 1, M
! 356: IF( W( JJ ).LT.TMP1 ) THEN
! 357: I = JJ
! 358: TMP1 = W( JJ )
! 359: END IF
! 360: 30 CONTINUE
! 361: *
! 362: IF( I.NE.0 ) THEN
! 363: ITMP1 = IWORK( INDIBL+I-1 )
! 364: W( I ) = W( J )
! 365: IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
! 366: W( J ) = TMP1
! 367: IWORK( INDIBL+J-1 ) = ITMP1
! 368: CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
! 369: IF( INFO.NE.0 ) THEN
! 370: ITMP1 = IFAIL( I )
! 371: IFAIL( I ) = IFAIL( J )
! 372: IFAIL( J ) = ITMP1
! 373: END IF
! 374: END IF
! 375: 40 CONTINUE
! 376: END IF
! 377: *
! 378: RETURN
! 379: *
! 380: * End of DSPEVX
! 381: *
! 382: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dspevx.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack