Annotation of rpl/lapack/lapack/dspev.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
! 2: *
! 3: * -- LAPACK driver routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER JOBZ, UPLO
! 10: INTEGER INFO, LDZ, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DSPEV computes all the eigenvalues and, optionally, eigenvectors of a
! 20: * real symmetric matrix A in packed storage.
! 21: *
! 22: * Arguments
! 23: * =========
! 24: *
! 25: * JOBZ (input) CHARACTER*1
! 26: * = 'N': Compute eigenvalues only;
! 27: * = 'V': Compute eigenvalues and eigenvectors.
! 28: *
! 29: * UPLO (input) CHARACTER*1
! 30: * = 'U': Upper triangle of A is stored;
! 31: * = 'L': Lower triangle of A is stored.
! 32: *
! 33: * N (input) INTEGER
! 34: * The order of the matrix A. N >= 0.
! 35: *
! 36: * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 37: * On entry, the upper or lower triangle of the symmetric matrix
! 38: * A, packed columnwise in a linear array. The j-th column of A
! 39: * is stored in the array AP as follows:
! 40: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 41: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
! 42: *
! 43: * On exit, AP is overwritten by values generated during the
! 44: * reduction to tridiagonal form. If UPLO = 'U', the diagonal
! 45: * and first superdiagonal of the tridiagonal matrix T overwrite
! 46: * the corresponding elements of A, and if UPLO = 'L', the
! 47: * diagonal and first subdiagonal of T overwrite the
! 48: * corresponding elements of A.
! 49: *
! 50: * W (output) DOUBLE PRECISION array, dimension (N)
! 51: * If INFO = 0, the eigenvalues in ascending order.
! 52: *
! 53: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
! 54: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
! 55: * eigenvectors of the matrix A, with the i-th column of Z
! 56: * holding the eigenvector associated with W(i).
! 57: * If JOBZ = 'N', then Z is not referenced.
! 58: *
! 59: * LDZ (input) INTEGER
! 60: * The leading dimension of the array Z. LDZ >= 1, and if
! 61: * JOBZ = 'V', LDZ >= max(1,N).
! 62: *
! 63: * WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
! 64: *
! 65: * INFO (output) INTEGER
! 66: * = 0: successful exit.
! 67: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 68: * > 0: if INFO = i, the algorithm failed to converge; i
! 69: * off-diagonal elements of an intermediate tridiagonal
! 70: * form did not converge to zero.
! 71: *
! 72: * =====================================================================
! 73: *
! 74: * .. Parameters ..
! 75: DOUBLE PRECISION ZERO, ONE
! 76: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 77: * ..
! 78: * .. Local Scalars ..
! 79: LOGICAL WANTZ
! 80: INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE
! 81: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 82: $ SMLNUM
! 83: * ..
! 84: * .. External Functions ..
! 85: LOGICAL LSAME
! 86: DOUBLE PRECISION DLAMCH, DLANSP
! 87: EXTERNAL LSAME, DLAMCH, DLANSP
! 88: * ..
! 89: * .. External Subroutines ..
! 90: EXTERNAL DOPGTR, DSCAL, DSPTRD, DSTEQR, DSTERF, XERBLA
! 91: * ..
! 92: * .. Intrinsic Functions ..
! 93: INTRINSIC SQRT
! 94: * ..
! 95: * .. Executable Statements ..
! 96: *
! 97: * Test the input parameters.
! 98: *
! 99: WANTZ = LSAME( JOBZ, 'V' )
! 100: *
! 101: INFO = 0
! 102: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 103: INFO = -1
! 104: ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) )
! 105: $ THEN
! 106: INFO = -2
! 107: ELSE IF( N.LT.0 ) THEN
! 108: INFO = -3
! 109: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 110: INFO = -7
! 111: END IF
! 112: *
! 113: IF( INFO.NE.0 ) THEN
! 114: CALL XERBLA( 'DSPEV ', -INFO )
! 115: RETURN
! 116: END IF
! 117: *
! 118: * Quick return if possible
! 119: *
! 120: IF( N.EQ.0 )
! 121: $ RETURN
! 122: *
! 123: IF( N.EQ.1 ) THEN
! 124: W( 1 ) = AP( 1 )
! 125: IF( WANTZ )
! 126: $ Z( 1, 1 ) = ONE
! 127: RETURN
! 128: END IF
! 129: *
! 130: * Get machine constants.
! 131: *
! 132: SAFMIN = DLAMCH( 'Safe minimum' )
! 133: EPS = DLAMCH( 'Precision' )
! 134: SMLNUM = SAFMIN / EPS
! 135: BIGNUM = ONE / SMLNUM
! 136: RMIN = SQRT( SMLNUM )
! 137: RMAX = SQRT( BIGNUM )
! 138: *
! 139: * Scale matrix to allowable range, if necessary.
! 140: *
! 141: ANRM = DLANSP( 'M', UPLO, N, AP, WORK )
! 142: ISCALE = 0
! 143: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 144: ISCALE = 1
! 145: SIGMA = RMIN / ANRM
! 146: ELSE IF( ANRM.GT.RMAX ) THEN
! 147: ISCALE = 1
! 148: SIGMA = RMAX / ANRM
! 149: END IF
! 150: IF( ISCALE.EQ.1 ) THEN
! 151: CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
! 152: END IF
! 153: *
! 154: * Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
! 155: *
! 156: INDE = 1
! 157: INDTAU = INDE + N
! 158: CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO )
! 159: *
! 160: * For eigenvalues only, call DSTERF. For eigenvectors, first call
! 161: * DOPGTR to generate the orthogonal matrix, then call DSTEQR.
! 162: *
! 163: IF( .NOT.WANTZ ) THEN
! 164: CALL DSTERF( N, W, WORK( INDE ), INFO )
! 165: ELSE
! 166: INDWRK = INDTAU + N
! 167: CALL DOPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ,
! 168: $ WORK( INDWRK ), IINFO )
! 169: CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDTAU ),
! 170: $ INFO )
! 171: END IF
! 172: *
! 173: * If matrix was scaled, then rescale eigenvalues appropriately.
! 174: *
! 175: IF( ISCALE.EQ.1 ) THEN
! 176: IF( INFO.EQ.0 ) THEN
! 177: IMAX = N
! 178: ELSE
! 179: IMAX = INFO - 1
! 180: END IF
! 181: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 182: END IF
! 183: *
! 184: RETURN
! 185: *
! 186: * End of DSPEV
! 187: *
! 188: END
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