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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/sspev.f | |
download | lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.gz lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.bz2 lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.zip |
Move LAPACK trunk into position.
Diffstat (limited to 'SRC/sspev.f')
-rw-r--r-- | SRC/sspev.f | 187 |
1 files changed, 187 insertions, 0 deletions
diff --git a/SRC/sspev.f b/SRC/sspev.f new file mode 100644 index 00000000..21ea1dea --- /dev/null +++ b/SRC/sspev.f @@ -0,0 +1,187 @@ + SUBROUTINE SSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO ) +* +* -- LAPACK driver routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER JOBZ, UPLO + INTEGER INFO, LDZ, N +* .. +* .. Array Arguments .. + REAL AP( * ), W( * ), WORK( * ), Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +* SSPEV computes all the eigenvalues and, optionally, eigenvectors of a +* real symmetric matrix A in packed storage. +* +* Arguments +* ========= +* +* JOBZ (input) CHARACTER*1 +* = 'N': Compute eigenvalues only; +* = 'V': Compute eigenvalues and eigenvectors. +* +* 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) REAL 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. +* +* W (output) REAL array, dimension (N) +* If INFO = 0, the eigenvalues in ascending order. +* +* Z (output) REAL array, dimension (LDZ, N) +* If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal +* eigenvectors of the matrix A, with the i-th column of Z +* holding the eigenvector associated with W(i). +* If JOBZ = 'N', then Z is not referenced. +* +* LDZ (input) INTEGER +* The leading dimension of the array Z. LDZ >= 1, and if +* JOBZ = 'V', LDZ >= max(1,N). +* +* WORK (workspace) REAL array, dimension (3*N) +* +* INFO (output) INTEGER +* = 0: successful exit. +* < 0: if INFO = -i, the i-th argument had an illegal value. +* > 0: if INFO = i, the algorithm failed to converge; i +* off-diagonal elements of an intermediate tridiagonal +* form did not converge to zero. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO, ONE + PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) +* .. +* .. Local Scalars .. + LOGICAL WANTZ + INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE + REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, + $ SMLNUM +* .. +* .. External Functions .. + LOGICAL LSAME + REAL SLAMCH, SLANSP + EXTERNAL LSAME, SLAMCH, SLANSP +* .. +* .. External Subroutines .. + EXTERNAL SOPGTR, SSCAL, SSPTRD, SSTEQR, SSTERF, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC SQRT +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) +* + INFO = 0 + IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN + INFO = -1 + ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) ) + $ THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN + INFO = -7 + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'SSPEV ', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( N.EQ.1 ) THEN + W( 1 ) = AP( 1 ) + IF( WANTZ ) + $ Z( 1, 1 ) = ONE + RETURN + END IF +* +* Get machine constants. +* + SAFMIN = SLAMCH( 'Safe minimum' ) + EPS = SLAMCH( 'Precision' ) + SMLNUM = SAFMIN / EPS + BIGNUM = ONE / SMLNUM + RMIN = SQRT( SMLNUM ) + RMAX = SQRT( BIGNUM ) +* +* Scale matrix to allowable range, if necessary. +* + ANRM = SLANSP( 'M', UPLO, N, AP, WORK ) + ISCALE = 0 + 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 SSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 ) + END IF +* +* Call SSPTRD to reduce symmetric packed matrix to tridiagonal form. +* + INDE = 1 + INDTAU = INDE + N + CALL SSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO ) +* +* For eigenvalues only, call SSTERF. For eigenvectors, first call +* SOPGTR to generate the orthogonal matrix, then call SSTEQR. +* + IF( .NOT.WANTZ ) THEN + CALL SSTERF( N, W, WORK( INDE ), INFO ) + ELSE + INDWRK = INDTAU + N + CALL SOPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ, + $ WORK( INDWRK ), IINFO ) + CALL SSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDTAU ), + $ INFO ) + END IF +* +* If matrix was scaled, then rescale eigenvalues appropriately. +* + IF( ISCALE.EQ.1 ) THEN + IF( INFO.EQ.0 ) THEN + IMAX = N + ELSE + IMAX = INFO - 1 + END IF + CALL SSCAL( IMAX, ONE / SIGMA, W, 1 ) + END IF +* + RETURN +* +* End of SSPEV +* + END |