SUBROUTINE SSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, $ IWORK, LIWORK, 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, LIWORK, LWORK, N * .. * .. Array Arguments .. INTEGER IWORK( * ) REAL AP( * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * Purpose * ======= * * SSPEVD computes all the eigenvalues and, optionally, eigenvectors * of a real symmetric matrix A in packed storage. If eigenvectors are * desired, it uses a divide and conquer algorithm. * * The divide and conquer algorithm makes very mild assumptions about * floating point arithmetic. It will work on machines with a guard * digit in add/subtract, or on those binary machines without guard * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or * Cray-2. It could conceivably fail on hexadecimal or decimal machines * without guard digits, but we know of none. * * 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/output) REAL array, dimension (MAX(1,LWORK)) * On exit, if INFO = 0, WORK(1) returns the required LWORK. * * LWORK (input) INTEGER * The dimension of the array WORK. * If N <= 1, LWORK must be at least 1. * If JOBZ = 'N' and N > 1, LWORK must be at least 2*N. * If JOBZ = 'V' and N > 1, LWORK must be at least * 1 + 6*N + N**2. * * If LWORK = -1, then a workspace query is assumed; the routine * only calculates the required sizes of the WORK and IWORK * arrays, returns these values as the first entries of the WORK * and IWORK arrays, and no error message related to LWORK or * LIWORK is issued by XERBLA. * * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) * On exit, if INFO = 0, IWORK(1) returns the required LIWORK. * * LIWORK (input) INTEGER * The dimension of the array IWORK. * If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. * If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. * * If LIWORK = -1, then a workspace query is assumed; the * routine only calculates the required sizes of the WORK and * IWORK arrays, returns these values as the first entries of * the WORK and IWORK arrays, and no error message related to * LWORK or LIWORK is issued by XERBLA. * * 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 = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY, WANTZ INTEGER IINFO, INDE, INDTAU, INDWRK, ISCALE, LIWMIN, $ LLWORK, LWMIN REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, $ SMLNUM * .. * .. External Functions .. LOGICAL LSAME REAL SLAMCH, SLANSP EXTERNAL LSAME, SLAMCH, SLANSP * .. * .. External Subroutines .. EXTERNAL SOPMTR, SSCAL, SSPTRD, SSTEDC, SSTERF, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) * 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.EQ.0 ) THEN IF( N.LE.1 ) THEN LIWMIN = 1 LWMIN = 1 ELSE IF( WANTZ ) THEN LIWMIN = 3 + 5*N LWMIN = 1 + 6*N + N**2 ELSE LIWMIN = 1 LWMIN = 2*N END IF END IF IWORK( 1 ) = LIWMIN WORK( 1 ) = LWMIN * IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -9 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN INFO = -11 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'SSPEVD', -INFO ) RETURN ELSE IF( LQUERY ) THEN 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 * SSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the * tridiagonal matrix, then call SOPMTR to multiply it by the * Householder transformations represented in AP. * IF( .NOT.WANTZ ) THEN CALL SSTERF( N, W, WORK( INDE ), INFO ) ELSE INDWRK = INDTAU + N LLWORK = LWORK - INDWRK + 1 CALL SSTEDC( 'I', N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ), $ LLWORK, IWORK, LIWORK, INFO ) CALL SOPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ, $ WORK( INDWRK ), IINFO ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * IF( ISCALE.EQ.1 ) $ CALL SSCAL( N, ONE / SIGMA, W, 1 ) * WORK( 1 ) = LWMIN IWORK( 1 ) = LIWMIN RETURN * * End of SSPEVD * END