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  1. C DLANST SOURCE BP208322 15/10/13 21:15:31 8670
  2. *> \brief \b DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.
  3. *
  4. * =========== DOCUMENTATION ===========
  5. *
  6. * Online html documentation available at
  7. * http://www.netlib.org/lapack/explore-html/
  8. *
  9. *> \htmlonly
  10. *> Download DLANST + dependencies
  11. *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanst.f">
  12. *> [TGZ]</a>
  13. *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanst.f">
  14. *> [ZIP]</a>
  15. *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanst.f">
  16. *> [TXT]</a>
  17. *> \endhtmlonly
  18. *
  19. * Definition:
  20. * ===========
  21. *
  22. * REAL*8 FUNCTION DLANST( NORM, N, D, E )
  23. *
  24. * .. Scalar Arguments ..
  25. * CHARACTER NORM
  26. * INTEGER N
  27. * ..
  28. * .. Array Arguments ..
  29. * REAL*8 D( * ), E( * )
  30. * ..
  31. *
  32. *
  33. *> \par Purpose:
  34. * =============
  35. *>
  36. *> \verbatim
  37. *>
  38. *> DLANST returns the value of the one norm, or the Frobenius norm, or
  39. *> the infinity norm, or the element of largest absolute value of a
  40. *> real symmetric tridiagonal matrix A.
  41. *> \endverbatim
  42. *>
  43. *> \return DLANST
  44. *> \verbatim
  45. *>
  46. *> DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm'
  47. *> (
  48. *> ( norm1(A), NORM = '1', 'O' or 'o'
  49. *> (
  50. *> ( normI(A), NORM = 'I' or 'i'
  51. *> (
  52. *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
  53. *>
  54. *> where norm1 denotes the one norm of a matrix (maximum column sum),
  55. *> normI denotes the infinity norm of a matrix (maximum row sum) and
  56. *> normF denotes the Frobenius norm of a matrix (square root of sum of
  57. *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
  58. *> \endverbatim
  59. *
  60. * Arguments:
  61. * ==========
  62. *
  63. *> \param[in] NORM
  64. *> \verbatim
  65. *> NORM is CHARACTER*1
  66. *> Specifies the value to be returned in DLANST as described
  67. *> above.
  68. *> \endverbatim
  69. *>
  70. *> \param[in] N
  71. *> \verbatim
  72. *> N is INTEGER
  73. *> The order of the matrix A. N >= 0. When N = 0, DLANST is
  74. *> set to zero.
  75. *> \endverbatim
  76. *>
  77. *> \param[in] D
  78. *> \verbatim
  79. *> D is DOUBLE PRECISION array, dimension (N)
  80. *> The diagonal elements of A.
  81. *> \endverbatim
  82. *>
  83. *> \param[in] E
  84. *> \verbatim
  85. *> E is DOUBLE PRECISION array, dimension (N-1)
  86. *> The (n-1) sub-diagonal or super-diagonal elements of A.
  87. *> \endverbatim
  88. *
  89. * Authors:
  90. * ========
  91. *
  92. *> \author Univ. of Tennessee
  93. *> \author Univ. of California Berkeley
  94. *> \author Univ. of Colorado Denver
  95. *> \author NAG Ltd.
  96. *
  97. *> \date September 2012
  98. *
  99. *> \ingroup auxOTHERauxiliary
  100. *
  101. * =====================================================================
  102. FUNCTION DLANST( NORM, N, D, E )
  103. *
  104. * -- LAPACK auxiliary routine (version 3.4.2) --
  105. * -- LAPACK is a software package provided by Univ. of Tennessee, --
  106. * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  107. * September 2012
  108. *
  109. * .. Scalar Arguments ..
  110. REAL*8 DLANST
  111. CHARACTER NORM
  112. INTEGER N
  113. * ..
  114. * .. Array Arguments ..
  115. REAL*8 D( * ), E( * )
  116. * ..
  117. *
  118. * =====================================================================
  119. *
  120. * .. Parameters ..
  121. REAL*8 ONE, ZERO
  122. PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
  123. * ..
  124. * .. Local Scalars ..
  125. INTEGER I
  126. REAL*8 ANORM, SCALE, SUM
  127. * ..
  128. * .. External Functions ..
  129. LOGICAL LSAME, DISNAN
  130. EXTERNAL LSAME, DISNAN
  131. * ..
  132. * .. External Subroutines ..
  133. EXTERNAL DLASSQ
  134. * ..
  135. ** .. Intrinsic Functions ..
  136. * INTRINSIC ABS, SQRT
  137. ** ..
  138. ** .. Executable Statements ..
  139. *
  140. IF( N.LE.0 ) THEN
  141. ANORM = ZERO
  142. ELSE IF( LSAME( NORM, 'M' ) ) THEN
  143. *
  144. * Find max(abs(A(i,j))).
  145. *
  146. ANORM = ABS( D( N ) )
  147. DO 10 I = 1, N - 1
  148. SUM = ABS( D( I ) )
  149. IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM
  150. SUM = ABS( E( I ) )
  151. IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM
  152. 10 CONTINUE
  153. ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.
  154. $ LSAME( NORM, 'I' ) ) THEN
  155. *
  156. * Find norm1(A).
  157. *
  158. IF( N.EQ.1 ) THEN
  159. ANORM = ABS( D( 1 ) )
  160. ELSE
  161. ANORM = ABS( D( 1 ) )+ABS( E( 1 ) )
  162. SUM = ABS( E( N-1 ) )+ABS( D( N ) )
  163. IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM
  164. DO 20 I = 2, N - 1
  165. SUM = ABS( D( I ) )+ABS( E( I ) )+ABS( E( I-1 ) )
  166. IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM
  167. 20 CONTINUE
  168. END IF
  169. ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
  170. *
  171. * Find normF(A).
  172. *
  173. SCALE = ZERO
  174. SUM = ONE
  175. IF( N.GT.1 ) THEN
  176. CALL DLASSQ( N-1, E, 1, SCALE, SUM )
  177. SUM = 2*SUM
  178. END IF
  179. CALL DLASSQ( N, D, 1, SCALE, SUM )
  180. ANORM = SCALE*SQRT( SUM )
  181. END IF
  182. *
  183. DLANST = ANORM
  184. RETURN
  185. *
  186. * End of DLANST
  187. *
  188. END
  189.  
  190.  

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