Annotation of rpl/lapack/lapack/dspevd.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
! 2: $ 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, LDZ, LIWORK, LWORK, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: INTEGER IWORK( * )
! 15: DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * DSPEVD computes all the eigenvalues and, optionally, eigenvectors
! 22: * of a real symmetric matrix A in packed storage. If eigenvectors are
! 23: * desired, it uses 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: * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 47: * On entry, the upper or lower triangle of the symmetric matrix
! 48: * A, packed columnwise in a linear array. The j-th column of A
! 49: * is stored in the array AP as follows:
! 50: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 51: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
! 52: *
! 53: * On exit, AP is overwritten by values generated during the
! 54: * reduction to tridiagonal form. If UPLO = 'U', the diagonal
! 55: * and first superdiagonal of the tridiagonal matrix T overwrite
! 56: * the corresponding elements of A, and if UPLO = 'L', the
! 57: * diagonal and first subdiagonal of T overwrite the
! 58: * corresponding elements of A.
! 59: *
! 60: * W (output) DOUBLE PRECISION array, dimension (N)
! 61: * If INFO = 0, the eigenvalues in ascending order.
! 62: *
! 63: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
! 64: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
! 65: * eigenvectors of the matrix A, with the i-th column of Z
! 66: * holding the eigenvector associated with W(i).
! 67: * If JOBZ = 'N', then Z is not referenced.
! 68: *
! 69: * LDZ (input) INTEGER
! 70: * The leading dimension of the array Z. LDZ >= 1, and if
! 71: * JOBZ = 'V', LDZ >= max(1,N).
! 72: *
! 73: * WORK (workspace/output) DOUBLE PRECISION array,
! 74: * dimension (LWORK)
! 75: * On exit, if INFO = 0, WORK(1) returns the required LWORK.
! 76: *
! 77: * LWORK (input) INTEGER
! 78: * The dimension of the array WORK.
! 79: * If N <= 1, LWORK must be at least 1.
! 80: * If JOBZ = 'N' and N > 1, LWORK must be at least 2*N.
! 81: * If JOBZ = 'V' and N > 1, LWORK must be at least
! 82: * 1 + 6*N + N**2.
! 83: *
! 84: * If LWORK = -1, then a workspace query is assumed; the routine
! 85: * only calculates the required sizes of the WORK and IWORK
! 86: * arrays, returns these values as the first entries of the WORK
! 87: * and IWORK arrays, and no error message related to LWORK or
! 88: * LIWORK is issued by XERBLA.
! 89: *
! 90: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
! 91: * On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
! 92: *
! 93: * LIWORK (input) INTEGER
! 94: * The dimension of the array IWORK.
! 95: * If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
! 96: * If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
! 97: *
! 98: * If LIWORK = -1, then a workspace query is assumed; the
! 99: * routine only calculates the required sizes of the WORK and
! 100: * IWORK arrays, returns these values as the first entries of
! 101: * the WORK and IWORK arrays, and no error message related to
! 102: * LWORK or LIWORK is issued by XERBLA.
! 103: *
! 104: * INFO (output) INTEGER
! 105: * = 0: successful exit
! 106: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 107: * > 0: if INFO = i, the algorithm failed to converge; i
! 108: * off-diagonal elements of an intermediate tridiagonal
! 109: * form did not converge to zero.
! 110: *
! 111: * =====================================================================
! 112: *
! 113: * .. Parameters ..
! 114: DOUBLE PRECISION ZERO, ONE
! 115: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 116: * ..
! 117: * .. Local Scalars ..
! 118: LOGICAL LQUERY, WANTZ
! 119: INTEGER IINFO, INDE, INDTAU, INDWRK, ISCALE, LIWMIN,
! 120: $ LLWORK, LWMIN
! 121: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 122: $ SMLNUM
! 123: * ..
! 124: * .. External Functions ..
! 125: LOGICAL LSAME
! 126: DOUBLE PRECISION DLAMCH, DLANSP
! 127: EXTERNAL LSAME, DLAMCH, DLANSP
! 128: * ..
! 129: * .. External Subroutines ..
! 130: EXTERNAL DOPMTR, DSCAL, DSPTRD, DSTEDC, DSTERF, XERBLA
! 131: * ..
! 132: * .. Intrinsic Functions ..
! 133: INTRINSIC SQRT
! 134: * ..
! 135: * .. Executable Statements ..
! 136: *
! 137: * Test the input parameters.
! 138: *
! 139: WANTZ = LSAME( JOBZ, 'V' )
! 140: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 141: *
! 142: INFO = 0
! 143: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 144: INFO = -1
! 145: ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) )
! 146: $ THEN
! 147: INFO = -2
! 148: ELSE IF( N.LT.0 ) THEN
! 149: INFO = -3
! 150: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 151: INFO = -7
! 152: END IF
! 153: *
! 154: IF( INFO.EQ.0 ) THEN
! 155: IF( N.LE.1 ) THEN
! 156: LIWMIN = 1
! 157: LWMIN = 1
! 158: ELSE
! 159: IF( WANTZ ) THEN
! 160: LIWMIN = 3 + 5*N
! 161: LWMIN = 1 + 6*N + N**2
! 162: ELSE
! 163: LIWMIN = 1
! 164: LWMIN = 2*N
! 165: END IF
! 166: END IF
! 167: IWORK( 1 ) = LIWMIN
! 168: WORK( 1 ) = LWMIN
! 169: *
! 170: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 171: INFO = -9
! 172: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 173: INFO = -11
! 174: END IF
! 175: END IF
! 176: *
! 177: IF( INFO.NE.0 ) THEN
! 178: CALL XERBLA( 'DSPEVD', -INFO )
! 179: RETURN
! 180: ELSE IF( LQUERY ) THEN
! 181: RETURN
! 182: END IF
! 183: *
! 184: * Quick return if possible
! 185: *
! 186: IF( N.EQ.0 )
! 187: $ RETURN
! 188: *
! 189: IF( N.EQ.1 ) THEN
! 190: W( 1 ) = AP( 1 )
! 191: IF( WANTZ )
! 192: $ Z( 1, 1 ) = ONE
! 193: RETURN
! 194: END IF
! 195: *
! 196: * Get machine constants.
! 197: *
! 198: SAFMIN = DLAMCH( 'Safe minimum' )
! 199: EPS = DLAMCH( 'Precision' )
! 200: SMLNUM = SAFMIN / EPS
! 201: BIGNUM = ONE / SMLNUM
! 202: RMIN = SQRT( SMLNUM )
! 203: RMAX = SQRT( BIGNUM )
! 204: *
! 205: * Scale matrix to allowable range, if necessary.
! 206: *
! 207: ANRM = DLANSP( 'M', UPLO, N, AP, WORK )
! 208: ISCALE = 0
! 209: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 210: ISCALE = 1
! 211: SIGMA = RMIN / ANRM
! 212: ELSE IF( ANRM.GT.RMAX ) THEN
! 213: ISCALE = 1
! 214: SIGMA = RMAX / ANRM
! 215: END IF
! 216: IF( ISCALE.EQ.1 ) THEN
! 217: CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
! 218: END IF
! 219: *
! 220: * Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
! 221: *
! 222: INDE = 1
! 223: INDTAU = INDE + N
! 224: CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO )
! 225: *
! 226: * For eigenvalues only, call DSTERF. For eigenvectors, first call
! 227: * DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
! 228: * tridiagonal matrix, then call DOPMTR to multiply it by the
! 229: * Householder transformations represented in AP.
! 230: *
! 231: IF( .NOT.WANTZ ) THEN
! 232: CALL DSTERF( N, W, WORK( INDE ), INFO )
! 233: ELSE
! 234: INDWRK = INDTAU + N
! 235: LLWORK = LWORK - INDWRK + 1
! 236: CALL DSTEDC( 'I', N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
! 237: $ LLWORK, IWORK, LIWORK, INFO )
! 238: CALL DOPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ,
! 239: $ WORK( INDWRK ), IINFO )
! 240: END IF
! 241: *
! 242: * If matrix was scaled, then rescale eigenvalues appropriately.
! 243: *
! 244: IF( ISCALE.EQ.1 )
! 245: $ CALL DSCAL( N, ONE / SIGMA, W, 1 )
! 246: *
! 247: WORK( 1 ) = LWMIN
! 248: IWORK( 1 ) = LIWMIN
! 249: RETURN
! 250: *
! 251: * End of DSPEVD
! 252: *
! 253: END
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