Annotation of rpl/lapack/lapack/zpteqr.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPTEQR( 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( * )
! 14: COMPLEX*16 Z( LDZ, * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZPTEQR computes all eigenvalues and, optionally, eigenvectors of a
! 21: * symmetric positive definite tridiagonal matrix by first factoring the
! 22: * matrix using DPTTRF and then calling ZBDSQR to compute the singular
! 23: * values of the bidiagonal factor.
! 24: *
! 25: * This routine computes the eigenvalues of the positive definite
! 26: * tridiagonal matrix to high relative accuracy. This means that if the
! 27: * eigenvalues range over many orders of magnitude in size, then the
! 28: * small eigenvalues and corresponding eigenvectors will be computed
! 29: * more accurately than, for example, with the standard QR method.
! 30: *
! 31: * The eigenvectors of a full or band positive definite Hermitian matrix
! 32: * can also be found if ZHETRD, ZHPTRD, or ZHBTRD has been used to
! 33: * reduce this matrix to tridiagonal form. (The reduction to
! 34: * tridiagonal form, however, may preclude the possibility of obtaining
! 35: * high relative accuracy in the small eigenvalues of the original
! 36: * matrix, if these eigenvalues range over many orders of magnitude.)
! 37: *
! 38: * Arguments
! 39: * =========
! 40: *
! 41: * COMPZ (input) CHARACTER*1
! 42: * = 'N': Compute eigenvalues only.
! 43: * = 'V': Compute eigenvectors of original Hermitian
! 44: * matrix also. Array Z contains the unitary matrix
! 45: * used to reduce the original matrix to tridiagonal
! 46: * form.
! 47: * = 'I': Compute eigenvectors of tridiagonal matrix also.
! 48: *
! 49: * N (input) INTEGER
! 50: * The order of the matrix. N >= 0.
! 51: *
! 52: * D (input/output) DOUBLE PRECISION array, dimension (N)
! 53: * On entry, the n diagonal elements of the tridiagonal 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) COMPLEX*16 array, dimension (LDZ, N)
! 63: * On entry, if COMPZ = 'V', the unitary matrix used in the
! 64: * reduction to tridiagonal form.
! 65: * On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
! 66: * original Hermitian 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: COMPLEX*16 CZERO, CONE
! 94: PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
! 95: $ CONE = ( 1.0D+0, 0.0D+0 ) )
! 96: * ..
! 97: * .. External Functions ..
! 98: LOGICAL LSAME
! 99: EXTERNAL LSAME
! 100: * ..
! 101: * .. External Subroutines ..
! 102: EXTERNAL DPTTRF, XERBLA, ZBDSQR, ZLASET
! 103: * ..
! 104: * .. Local Arrays ..
! 105: COMPLEX*16 C( 1, 1 ), VT( 1, 1 )
! 106: * ..
! 107: * .. Local Scalars ..
! 108: INTEGER I, ICOMPZ, NRU
! 109: * ..
! 110: * .. Intrinsic Functions ..
! 111: INTRINSIC MAX, SQRT
! 112: * ..
! 113: * .. Executable Statements ..
! 114: *
! 115: * Test the input parameters.
! 116: *
! 117: INFO = 0
! 118: *
! 119: IF( LSAME( COMPZ, 'N' ) ) THEN
! 120: ICOMPZ = 0
! 121: ELSE IF( LSAME( COMPZ, 'V' ) ) THEN
! 122: ICOMPZ = 1
! 123: ELSE IF( LSAME( COMPZ, 'I' ) ) THEN
! 124: ICOMPZ = 2
! 125: ELSE
! 126: ICOMPZ = -1
! 127: END IF
! 128: IF( ICOMPZ.LT.0 ) THEN
! 129: INFO = -1
! 130: ELSE IF( N.LT.0 ) THEN
! 131: INFO = -2
! 132: ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1,
! 133: $ N ) ) ) THEN
! 134: INFO = -6
! 135: END IF
! 136: IF( INFO.NE.0 ) THEN
! 137: CALL XERBLA( 'ZPTEQR', -INFO )
! 138: RETURN
! 139: END IF
! 140: *
! 141: * Quick return if possible
! 142: *
! 143: IF( N.EQ.0 )
! 144: $ RETURN
! 145: *
! 146: IF( N.EQ.1 ) THEN
! 147: IF( ICOMPZ.GT.0 )
! 148: $ Z( 1, 1 ) = CONE
! 149: RETURN
! 150: END IF
! 151: IF( ICOMPZ.EQ.2 )
! 152: $ CALL ZLASET( 'Full', N, N, CZERO, CONE, Z, LDZ )
! 153: *
! 154: * Call DPTTRF to factor the matrix.
! 155: *
! 156: CALL DPTTRF( N, D, E, INFO )
! 157: IF( INFO.NE.0 )
! 158: $ RETURN
! 159: DO 10 I = 1, N
! 160: D( I ) = SQRT( D( I ) )
! 161: 10 CONTINUE
! 162: DO 20 I = 1, N - 1
! 163: E( I ) = E( I )*D( I )
! 164: 20 CONTINUE
! 165: *
! 166: * Call ZBDSQR to compute the singular values/vectors of the
! 167: * bidiagonal factor.
! 168: *
! 169: IF( ICOMPZ.GT.0 ) THEN
! 170: NRU = N
! 171: ELSE
! 172: NRU = 0
! 173: END IF
! 174: CALL ZBDSQR( 'Lower', N, 0, NRU, 0, D, E, VT, 1, Z, LDZ, C, 1,
! 175: $ WORK, INFO )
! 176: *
! 177: * Square the singular values.
! 178: *
! 179: IF( INFO.EQ.0 ) THEN
! 180: DO 30 I = 1, N
! 181: D( I ) = D( I )*D( I )
! 182: 30 CONTINUE
! 183: ELSE
! 184: INFO = N + INFO
! 185: END IF
! 186: *
! 187: RETURN
! 188: *
! 189: * End of ZPTEQR
! 190: *
! 191: END
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