LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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dnrm2.f90
Go to the documentation of this file.
1
2!
3! =========== DOCUMENTATION ===========
4!
5! Online html documentation available at
6! http://www.netlib.org/lapack/explore-html/
7!
8! Definition:
9! ===========
10!
11! DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX)
12!
13! .. Scalar Arguments ..
14! INTEGER INCX,N
15! ..
16! .. Array Arguments ..
17! DOUBLE PRECISION X(*)
18! ..
19!
20!
22! =============
31!
32! Arguments:
33! ==========
34!
55!
56! Authors:
57! ========
58!
60!
62!
64!
66! ==================
69!
71! =====================
87! =====================================================================
88function dnrm2( n, x, incx )
89 integer, parameter :: wp = kind(1.d0)
90 real(wp) :: dnrm2
91!
92! -- Reference BLAS level1 routine (version 3.9.1) --
93! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
94! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
95! March 2021
96!
97! .. Constants ..
98 real(wp), parameter :: zero = 0.0_wp
99 real(wp), parameter :: one = 1.0_wp
100 real(wp), parameter :: maxn = huge(0.0_wp)
101! ..
102! .. Blue's scaling constants ..
103 real(wp), parameter :: tsml = real(radix(0._wp), wp)**ceiling( &
104 (minexponent(0._wp) - 1) * 0.5_wp)
105 real(wp), parameter :: tbig = real(radix(0._wp), wp)**floor( &
106 (maxexponent(0._wp) - digits(0._wp) + 1) * 0.5_wp)
107 real(wp), parameter :: ssml = real(radix(0._wp), wp)**( - floor( &
108 (minexponent(0._wp) - digits(0._wp)) * 0.5_wp))
109 real(wp), parameter :: sbig = real(radix(0._wp), wp)**( - ceiling( &
110 (maxexponent(0._wp) + digits(0._wp) - 1) * 0.5_wp))
111! ..
112! .. Scalar Arguments ..
113 integer :: incx, n
114! ..
115! .. Array Arguments ..
116 real(wp) :: x(*)
117! ..
118! .. Local Scalars ..
119 integer :: i, ix
120 logical :: notbig
121 real(wp) :: abig, amed, asml, ax, scl, sumsq, ymax, ymin
122!
123! Quick return if possible
124!
125 dnrm2 = zero
126 if( n <= 0 ) return
127!
128 scl = one
129 sumsq = zero
130!
131! Compute the sum of squares in 3 accumulators:
132! abig -- sums of squares scaled down to avoid overflow
133! asml -- sums of squares scaled up to avoid underflow
134! amed -- sums of squares that do not require scaling
135! The thresholds and multipliers are
136! tbig -- values bigger than this are scaled down by sbig
137! tsml -- values smaller than this are scaled up by ssml
138!
139 notbig = .true.
140 asml = zero
141 amed = zero
142 abig = zero
143 ix = 1
144 if( incx < 0 ) ix = 1 - (n-1)*incx
145 do i = 1, n
146 ax = abs(x(ix))
147 if (ax > tbig) then
148 abig = abig + (ax*sbig)**2
149 notbig = .false.
150 else if (ax < tsml) then
151 if (notbig) asml = asml + (ax*ssml)**2
152 else
153 amed = amed + ax**2
154 end if
155 ix = ix + incx
156 end do
157!
158! Combine abig and amed or amed and asml if more than one
159! accumulator was used.
160!
161 if (abig > zero) then
162!
163! Combine abig and amed if abig > 0.
164!
165 if ( (amed > zero) .or. (amed > maxn) .or. (amed /= amed) ) then
166 abig = abig + (amed*sbig)*sbig
167 end if
168 scl = one / sbig
169 sumsq = abig
170 else if (asml > zero) then
171!
172! Combine amed and asml if asml > 0.
173!
174 if ( (amed > zero) .or. (amed > maxn) .or. (amed /= amed) ) then
175 amed = sqrt(amed)
176 asml = sqrt(asml) / ssml
177 if (asml > amed) then
178 ymin = amed
179 ymax = asml
180 else
181 ymin = asml
182 ymax = amed
183 end if
184 scl = one
185 sumsq = ymax**2*( one + (ymin/ymax)**2 )
186 else
187 scl = one / ssml
188 sumsq = asml
189 end if
190 else
191!
192! Otherwise all values are mid-range
193!
194 scl = one
195 sumsq = amed
196 end if
197 dnrm2 = scl*sqrt( sumsq )
198 return
199end function
real(wp) function dnrm2(n, x, incx)
DNRM2
Definition dnrm2.f90:89