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author | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
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committer | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
commit | baba851215b44ac3b60b9248eb02bcce7eb76247 (patch) | |
tree | 8c0f5c006875532a30d4409f5e94b0f310ff00a7 /SRC/dspevx.f | |
download | lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.gz lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.bz2 lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.zip |
Move LAPACK trunk into position.
Diffstat (limited to 'SRC/dspevx.f')
-rw-r--r-- | SRC/dspevx.f | 381 |
1 files changed, 381 insertions, 0 deletions
diff --git a/SRC/dspevx.f b/SRC/dspevx.f new file mode 100644 index 00000000..68611699 --- /dev/null +++ b/SRC/dspevx.f @@ -0,0 +1,381 @@ + SUBROUTINE DSPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, + $ ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, + $ INFO ) +* +* -- LAPACK driver routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER JOBZ, RANGE, UPLO + INTEGER IL, INFO, IU, LDZ, M, N + DOUBLE PRECISION ABSTOL, VL, VU +* .. +* .. Array Arguments .. + INTEGER IFAIL( * ), IWORK( * ) + DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +* DSPEVX computes selected eigenvalues and, optionally, eigenvectors +* of a real symmetric matrix A in packed storage. Eigenvalues/vectors +* can be selected by specifying either a range of values or a range of +* indices for the desired eigenvalues. +* +* Arguments +* ========= +* +* JOBZ (input) CHARACTER*1 +* = 'N': Compute eigenvalues only; +* = 'V': Compute eigenvalues and eigenvectors. +* +* RANGE (input) CHARACTER*1 +* = 'A': all eigenvalues will be found; +* = 'V': all eigenvalues in the half-open interval (VL,VU] +* will be found; +* = 'I': the IL-th through IU-th eigenvalues will be found. +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangle of A is stored; +* = 'L': Lower triangle of A is stored. +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) +* On entry, the upper or lower triangle of the symmetric matrix +* A, packed columnwise in a linear array. The j-th column of A +* is stored in the array AP as follows: +* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; +* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. +* +* On exit, AP is overwritten by values generated during the +* reduction to tridiagonal form. If UPLO = 'U', the diagonal +* and first superdiagonal of the tridiagonal matrix T overwrite +* the corresponding elements of A, and if UPLO = 'L', the +* diagonal and first subdiagonal of T overwrite the +* corresponding elements of A. +* +* VL (input) DOUBLE PRECISION +* VU (input) DOUBLE PRECISION +* If RANGE='V', the lower and upper bounds of the interval to +* be searched for eigenvalues. VL < VU. +* Not referenced if RANGE = 'A' or 'I'. +* +* IL (input) INTEGER +* IU (input) INTEGER +* If RANGE='I', the indices (in ascending order) of the +* smallest and largest eigenvalues to be returned. +* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. +* Not referenced if RANGE = 'A' or 'V'. +* +* ABSTOL (input) DOUBLE PRECISION +* The absolute error tolerance for the eigenvalues. +* An approximate eigenvalue is accepted as converged +* when it is determined to lie in an interval [a,b] +* of width less than or equal to +* +* ABSTOL + EPS * max( |a|,|b| ) , +* +* where EPS is the machine precision. If ABSTOL is less than +* or equal to zero, then EPS*|T| will be used in its place, +* where |T| is the 1-norm of the tridiagonal matrix obtained +* by reducing AP to tridiagonal form. +* +* Eigenvalues will be computed most accurately when ABSTOL is +* set to twice the underflow threshold 2*DLAMCH('S'), not zero. +* If this routine returns with INFO>0, indicating that some +* eigenvectors did not converge, try setting ABSTOL to +* 2*DLAMCH('S'). +* +* See "Computing Small Singular Values of Bidiagonal Matrices +* with Guaranteed High Relative Accuracy," by Demmel and +* Kahan, LAPACK Working Note #3. +* +* M (output) INTEGER +* The total number of eigenvalues found. 0 <= M <= N. +* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. +* +* W (output) DOUBLE PRECISION array, dimension (N) +* If INFO = 0, the selected eigenvalues in ascending order. +* +* Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M)) +* If JOBZ = 'V', then if INFO = 0, the first M columns of Z +* contain the orthonormal eigenvectors of the matrix A +* corresponding to the selected eigenvalues, with the i-th +* column of Z holding the eigenvector associated with W(i). +* If an eigenvector fails to converge, then that column of Z +* contains the latest approximation to the eigenvector, and the +* index of the eigenvector is returned in IFAIL. +* If JOBZ = 'N', then Z is not referenced. +* Note: the user must ensure that at least max(1,M) columns are +* supplied in the array Z; if RANGE = 'V', the exact value of M +* is not known in advance and an upper bound must be used. +* +* LDZ (input) INTEGER +* The leading dimension of the array Z. LDZ >= 1, and if +* JOBZ = 'V', LDZ >= max(1,N). +* +* WORK (workspace) DOUBLE PRECISION array, dimension (8*N) +* +* IWORK (workspace) INTEGER array, dimension (5*N) +* +* IFAIL (output) INTEGER array, dimension (N) +* If JOBZ = 'V', then if INFO = 0, the first M elements of +* IFAIL are zero. If INFO > 0, then IFAIL contains the +* indices of the eigenvectors that failed to converge. +* If JOBZ = 'N', then IFAIL is not referenced. +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: if INFO = i, then i eigenvectors failed to converge. +* Their indices are stored in array IFAIL. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, ONE + PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) +* .. +* .. Local Scalars .. + LOGICAL ALLEIG, INDEIG, TEST, VALEIG, WANTZ + CHARACTER ORDER + INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL, + $ INDISP, INDIWO, INDTAU, INDWRK, ISCALE, ITMP1, + $ J, JJ, NSPLIT + DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, + $ SIGMA, SMLNUM, TMP1, VLL, VUU +* .. +* .. External Functions .. + LOGICAL LSAME + DOUBLE PRECISION DLAMCH, DLANSP + EXTERNAL LSAME, DLAMCH, DLANSP +* .. +* .. External Subroutines .. + EXTERNAL DCOPY, DOPGTR, DOPMTR, DSCAL, DSPTRD, DSTEBZ, + $ DSTEIN, DSTEQR, DSTERF, DSWAP, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN, SQRT +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + ALLEIG = LSAME( RANGE, 'A' ) + VALEIG = LSAME( RANGE, 'V' ) + INDEIG = LSAME( RANGE, 'I' ) +* + INFO = 0 + IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN + INFO = -1 + ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN + INFO = -2 + ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) ) + $ THEN + INFO = -3 + ELSE IF( N.LT.0 ) THEN + INFO = -4 + ELSE + IF( VALEIG ) THEN + IF( N.GT.0 .AND. VU.LE.VL ) + $ INFO = -7 + ELSE IF( INDEIG ) THEN + IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN + INFO = -8 + ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN + INFO = -9 + END IF + END IF + END IF + IF( INFO.EQ.0 ) THEN + IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) + $ INFO = -14 + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DSPEVX', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + M = 0 + IF( N.EQ.0 ) + $ RETURN +* + IF( N.EQ.1 ) THEN + IF( ALLEIG .OR. INDEIG ) THEN + M = 1 + W( 1 ) = AP( 1 ) + ELSE + IF( VL.LT.AP( 1 ) .AND. VU.GE.AP( 1 ) ) THEN + M = 1 + W( 1 ) = AP( 1 ) + END IF + END IF + IF( WANTZ ) + $ Z( 1, 1 ) = ONE + RETURN + END IF +* +* Get machine constants. +* + SAFMIN = DLAMCH( 'Safe minimum' ) + EPS = DLAMCH( 'Precision' ) + SMLNUM = SAFMIN / EPS + BIGNUM = ONE / SMLNUM + RMIN = SQRT( SMLNUM ) + RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ) +* +* Scale matrix to allowable range, if necessary. +* + ISCALE = 0 + ABSTLL = ABSTOL + IF( VALEIG ) THEN + VLL = VL + VUU = VU + ELSE + VLL = ZERO + VUU = ZERO + END IF + ANRM = DLANSP( 'M', UPLO, N, AP, WORK ) + IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN + ISCALE = 1 + SIGMA = RMIN / ANRM + ELSE IF( ANRM.GT.RMAX ) THEN + ISCALE = 1 + SIGMA = RMAX / ANRM + END IF + IF( ISCALE.EQ.1 ) THEN + CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 ) + IF( ABSTOL.GT.0 ) + $ ABSTLL = ABSTOL*SIGMA + IF( VALEIG ) THEN + VLL = VL*SIGMA + VUU = VU*SIGMA + END IF + END IF +* +* Call DSPTRD to reduce symmetric packed matrix to tridiagonal form. +* + INDTAU = 1 + INDE = INDTAU + N + INDD = INDE + N + INDWRK = INDD + N + CALL DSPTRD( UPLO, N, AP, WORK( INDD ), WORK( INDE ), + $ WORK( INDTAU ), IINFO ) +* +* If all eigenvalues are desired and ABSTOL is less than or equal +* to zero, then call DSTERF or DOPGTR and SSTEQR. If this fails +* for some eigenvalue, then try DSTEBZ. +* + TEST = .FALSE. + IF (INDEIG) THEN + IF (IL.EQ.1 .AND. IU.EQ.N) THEN + TEST = .TRUE. + END IF + END IF + IF ((ALLEIG .OR. TEST) .AND. (ABSTOL.LE.ZERO)) THEN + CALL DCOPY( N, WORK( INDD ), 1, W, 1 ) + INDEE = INDWRK + 2*N + IF( .NOT.WANTZ ) THEN + CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 ) + CALL DSTERF( N, W, WORK( INDEE ), INFO ) + ELSE + CALL DOPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ, + $ WORK( INDWRK ), IINFO ) + CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 ) + CALL DSTEQR( JOBZ, N, W, WORK( INDEE ), Z, LDZ, + $ WORK( INDWRK ), INFO ) + IF( INFO.EQ.0 ) THEN + DO 10 I = 1, N + IFAIL( I ) = 0 + 10 CONTINUE + END IF + END IF + IF( INFO.EQ.0 ) THEN + M = N + GO TO 20 + END IF + INFO = 0 + END IF +* +* Otherwise, call DSTEBZ and, if eigenvectors are desired, SSTEIN. +* + IF( WANTZ ) THEN + ORDER = 'B' + ELSE + ORDER = 'E' + END IF + INDIBL = 1 + INDISP = INDIBL + N + INDIWO = INDISP + N + CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, + $ WORK( INDD ), WORK( INDE ), M, NSPLIT, W, + $ IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWRK ), + $ IWORK( INDIWO ), INFO ) +* + IF( WANTZ ) THEN + CALL DSTEIN( N, WORK( INDD ), WORK( INDE ), M, W, + $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ, + $ WORK( INDWRK ), IWORK( INDIWO ), IFAIL, INFO ) +* +* Apply orthogonal matrix used in reduction to tridiagonal +* form to eigenvectors returned by DSTEIN. +* + CALL DOPMTR( 'L', UPLO, 'N', N, M, AP, WORK( INDTAU ), Z, LDZ, + $ WORK( INDWRK ), INFO ) + END IF +* +* If matrix was scaled, then rescale eigenvalues appropriately. +* + 20 CONTINUE + IF( ISCALE.EQ.1 ) THEN + IF( INFO.EQ.0 ) THEN + IMAX = M + ELSE + IMAX = INFO - 1 + END IF + CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) + END IF +* +* If eigenvalues are not in order, then sort them, along with +* eigenvectors. +* + IF( WANTZ ) THEN + DO 40 J = 1, M - 1 + I = 0 + TMP1 = W( J ) + DO 30 JJ = J + 1, M + IF( W( JJ ).LT.TMP1 ) THEN + I = JJ + TMP1 = W( JJ ) + END IF + 30 CONTINUE +* + IF( I.NE.0 ) THEN + ITMP1 = IWORK( INDIBL+I-1 ) + W( I ) = W( J ) + IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 ) + W( J ) = TMP1 + IWORK( INDIBL+J-1 ) = ITMP1 + CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 ) + IF( INFO.NE.0 ) THEN + ITMP1 = IFAIL( I ) + IFAIL( I ) = IFAIL( J ) + IFAIL( J ) = ITMP1 + END IF + END IF + 40 CONTINUE + END IF +* + RETURN +* +* End of DSPEVX +* + END |