Annotation of rpl/lapack/lapack/dpteqr.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
! 2: *
! 3: * -- LAPACK 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 COMPZ
! 10: INTEGER INFO, LDZ, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DPTEQR computes all eigenvalues and, optionally, eigenvectors of a
! 20: * symmetric positive definite tridiagonal matrix by first factoring the
! 21: * matrix using DPTTRF, and then calling DBDSQR to compute the singular
! 22: * values of the bidiagonal factor.
! 23: *
! 24: * This routine computes the eigenvalues of the positive definite
! 25: * tridiagonal matrix to high relative accuracy. This means that if the
! 26: * eigenvalues range over many orders of magnitude in size, then the
! 27: * small eigenvalues and corresponding eigenvectors will be computed
! 28: * more accurately than, for example, with the standard QR method.
! 29: *
! 30: * The eigenvectors of a full or band symmetric positive definite matrix
! 31: * can also be found if DSYTRD, DSPTRD, or DSBTRD has been used to
! 32: * reduce this matrix to tridiagonal form. (The reduction to tridiagonal
! 33: * form, however, may preclude the possibility of obtaining high
! 34: * relative accuracy in the small eigenvalues of the original matrix, if
! 35: * these eigenvalues range over many orders of magnitude.)
! 36: *
! 37: * Arguments
! 38: * =========
! 39: *
! 40: * COMPZ (input) CHARACTER*1
! 41: * = 'N': Compute eigenvalues only.
! 42: * = 'V': Compute eigenvectors of original symmetric
! 43: * matrix also. Array Z contains the orthogonal
! 44: * matrix used to reduce the original matrix to
! 45: * tridiagonal form.
! 46: * = 'I': Compute eigenvectors of tridiagonal matrix also.
! 47: *
! 48: * N (input) INTEGER
! 49: * The order of the matrix. N >= 0.
! 50: *
! 51: * D (input/output) DOUBLE PRECISION array, dimension (N)
! 52: * On entry, the n diagonal elements of the tridiagonal
! 53: * matrix.
! 54: * On normal exit, D contains the eigenvalues, in descending
! 55: * order.
! 56: *
! 57: * E (input/output) DOUBLE PRECISION array, dimension (N-1)
! 58: * On entry, the (n-1) subdiagonal elements of the tridiagonal
! 59: * matrix.
! 60: * On exit, E has been destroyed.
! 61: *
! 62: * Z (input/output) DOUBLE PRECISION array, dimension (LDZ, N)
! 63: * On entry, if COMPZ = 'V', the orthogonal matrix used in the
! 64: * reduction to tridiagonal form.
! 65: * On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
! 66: * original symmetric matrix;
! 67: * if COMPZ = 'I', the orthonormal eigenvectors of the
! 68: * tridiagonal matrix.
! 69: * If INFO > 0 on exit, Z contains the eigenvectors associated
! 70: * with only the stored eigenvalues.
! 71: * If COMPZ = 'N', then Z is not referenced.
! 72: *
! 73: * LDZ (input) INTEGER
! 74: * The leading dimension of the array Z. LDZ >= 1, and if
! 75: * COMPZ = 'V' or 'I', LDZ >= max(1,N).
! 76: *
! 77: * WORK (workspace) DOUBLE PRECISION array, dimension (4*N)
! 78: *
! 79: * INFO (output) INTEGER
! 80: * = 0: successful exit.
! 81: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 82: * > 0: if INFO = i, and i is:
! 83: * <= N the Cholesky factorization of the matrix could
! 84: * not be performed because the i-th principal minor
! 85: * was not positive definite.
! 86: * > N the SVD algorithm failed to converge;
! 87: * if INFO = N+i, i off-diagonal elements of the
! 88: * bidiagonal factor did not converge to zero.
! 89: *
! 90: * =====================================================================
! 91: *
! 92: * .. Parameters ..
! 93: DOUBLE PRECISION ZERO, ONE
! 94: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 95: * ..
! 96: * .. External Functions ..
! 97: LOGICAL LSAME
! 98: EXTERNAL LSAME
! 99: * ..
! 100: * .. External Subroutines ..
! 101: EXTERNAL DBDSQR, DLASET, DPTTRF, XERBLA
! 102: * ..
! 103: * .. Local Arrays ..
! 104: DOUBLE PRECISION C( 1, 1 ), VT( 1, 1 )
! 105: * ..
! 106: * .. Local Scalars ..
! 107: INTEGER I, ICOMPZ, NRU
! 108: * ..
! 109: * .. Intrinsic Functions ..
! 110: INTRINSIC MAX, SQRT
! 111: * ..
! 112: * .. Executable Statements ..
! 113: *
! 114: * Test the input parameters.
! 115: *
! 116: INFO = 0
! 117: *
! 118: IF( LSAME( COMPZ, 'N' ) ) THEN
! 119: ICOMPZ = 0
! 120: ELSE IF( LSAME( COMPZ, 'V' ) ) THEN
! 121: ICOMPZ = 1
! 122: ELSE IF( LSAME( COMPZ, 'I' ) ) THEN
! 123: ICOMPZ = 2
! 124: ELSE
! 125: ICOMPZ = -1
! 126: END IF
! 127: IF( ICOMPZ.LT.0 ) THEN
! 128: INFO = -1
! 129: ELSE IF( N.LT.0 ) THEN
! 130: INFO = -2
! 131: ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1,
! 132: $ N ) ) ) THEN
! 133: INFO = -6
! 134: END IF
! 135: IF( INFO.NE.0 ) THEN
! 136: CALL XERBLA( 'DPTEQR', -INFO )
! 137: RETURN
! 138: END IF
! 139: *
! 140: * Quick return if possible
! 141: *
! 142: IF( N.EQ.0 )
! 143: $ RETURN
! 144: *
! 145: IF( N.EQ.1 ) THEN
! 146: IF( ICOMPZ.GT.0 )
! 147: $ Z( 1, 1 ) = ONE
! 148: RETURN
! 149: END IF
! 150: IF( ICOMPZ.EQ.2 )
! 151: $ CALL DLASET( 'Full', N, N, ZERO, ONE, Z, LDZ )
! 152: *
! 153: * Call DPTTRF to factor the matrix.
! 154: *
! 155: CALL DPTTRF( N, D, E, INFO )
! 156: IF( INFO.NE.0 )
! 157: $ RETURN
! 158: DO 10 I = 1, N
! 159: D( I ) = SQRT( D( I ) )
! 160: 10 CONTINUE
! 161: DO 20 I = 1, N - 1
! 162: E( I ) = E( I )*D( I )
! 163: 20 CONTINUE
! 164: *
! 165: * Call DBDSQR to compute the singular values/vectors of the
! 166: * bidiagonal factor.
! 167: *
! 168: IF( ICOMPZ.GT.0 ) THEN
! 169: NRU = N
! 170: ELSE
! 171: NRU = 0
! 172: END IF
! 173: CALL DBDSQR( 'Lower', N, 0, NRU, 0, D, E, VT, 1, Z, LDZ, C, 1,
! 174: $ WORK, INFO )
! 175: *
! 176: * Square the singular values.
! 177: *
! 178: IF( INFO.EQ.0 ) THEN
! 179: DO 30 I = 1, N
! 180: D( I ) = D( I )*D( I )
! 181: 30 CONTINUE
! 182: ELSE
! 183: INFO = N + INFO
! 184: END IF
! 185: *
! 186: RETURN
! 187: *
! 188: * End of DPTEQR
! 189: *
! 190: END
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