LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ scnrm2()

 real(wp) function scnrm2 ( integer n, complex(wp), dimension(*) x, integer incx )

SCNRM2

Purpose:
``` SCNRM2 returns the euclidean norm of a vector via the function
name, so that

SCNRM2 := sqrt( x**H*x )```
Parameters
 [in] N ``` N is INTEGER number of elements in input vector(s)``` [in] X ``` X is COMPLEX array, dimension (N) complex vector with N elements``` [in] INCX ``` INCX is INTEGER, storage spacing between elements of X If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n If INCX = 0, x isn't a vector so there is no need to call this subroutine. If you call it anyway, it will count x(1) in the vector norm N times.```
Date
August 2016
Contributors:
Weslley Pereira, University of Colorado Denver, USA
Further Details:
```  Anderson E. (2017)
Algorithm 978: Safe Scaling in the Level 1 BLAS
ACM Trans Math Softw 44:1--28
https://doi.org/10.1145/3061665

Blue, James L. (1978)
A Portable Fortran Program to Find the Euclidean Norm of a Vector
ACM Trans Math Softw 4:15--23
https://doi.org/10.1145/355769.355771```

Definition at line 89 of file scnrm2.f90.

90 integer, parameter :: wp = kind(1.e0)
91 real(wp) :: SCNRM2
92!
93! -- Reference BLAS level1 routine (version 3.9.1) --
94! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
95! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
96! March 2021
97!
98! .. Constants ..
99 real(wp), parameter :: zero = 0.0_wp
100 real(wp), parameter :: one = 1.0_wp
101 real(wp), parameter :: maxN = huge(0.0_wp)
102! ..
103! .. Blue's scaling constants ..
104 real(wp), parameter :: tsml = real(radix(0._wp), wp)**ceiling( &
105 (minexponent(0._wp) - 1) * 0.5_wp)
106 real(wp), parameter :: tbig = real(radix(0._wp), wp)**floor( &
107 (maxexponent(0._wp) - digits(0._wp) + 1) * 0.5_wp)
108 real(wp), parameter :: ssml = real(radix(0._wp), wp)**( - floor( &
109 (minexponent(0._wp) - digits(0._wp)) * 0.5_wp))
110 real(wp), parameter :: sbig = real(radix(0._wp), wp)**( - ceiling( &
111 (maxexponent(0._wp) + digits(0._wp) - 1) * 0.5_wp))
112! ..
113! .. Scalar Arguments ..
114 integer :: incx, n
115! ..
116! .. Array Arguments ..
117 complex(wp) :: x(*)
118! ..
119! .. Local Scalars ..
120 integer :: i, ix
121 logical :: notbig
122 real(wp) :: abig, amed, asml, ax, scl, sumsq, ymax, ymin
123!
124! Quick return if possible
125!
126 scnrm2 = zero
127 if( n <= 0 ) return
128!
129 scl = one
130 sumsq = zero
131!
132! Compute the sum of squares in 3 accumulators:
133! abig -- sums of squares scaled down to avoid overflow
134! asml -- sums of squares scaled up to avoid underflow
135! amed -- sums of squares that do not require scaling
136! The thresholds and multipliers are
137! tbig -- values bigger than this are scaled down by sbig
138! tsml -- values smaller than this are scaled up by ssml
139!
140 notbig = .true.
141 asml = zero
142 amed = zero
143 abig = zero
144 ix = 1
145 if( incx < 0 ) ix = 1 - (n-1)*incx
146 do i = 1, n
147 ax = abs(real(x(ix)))
148 if (ax > tbig) then
149 abig = abig + (ax*sbig)**2
150 notbig = .false.
151 else if (ax < tsml) then
152 if (notbig) asml = asml + (ax*ssml)**2
153 else
154 amed = amed + ax**2
155 end if
156 ax = abs(aimag(x(ix)))
157 if (ax > tbig) then
158 abig = abig + (ax*sbig)**2
159 notbig = .false.
160 else if (ax < tsml) then
161 if (notbig) asml = asml + (ax*ssml)**2
162 else
163 amed = amed + ax**2
164 end if
165 ix = ix + incx
166 end do
167!
168! Combine abig and amed or amed and asml if more than one
169! accumulator was used.
170!
171 if (abig > zero) then
172!
173! Combine abig and amed if abig > 0.
174!
175 if ( (amed > zero) .or. (amed > maxn) .or. (amed /= amed) ) then
176 abig = abig + (amed*sbig)*sbig
177 end if
178 scl = one / sbig
179 sumsq = abig
180 else if (asml > zero) then
181!
182! Combine amed and asml if asml > 0.
183!
184 if ( (amed > zero) .or. (amed > maxn) .or. (amed /= amed) ) then
185 amed = sqrt(amed)
186 asml = sqrt(asml) / ssml
187 if (asml > amed) then
188 ymin = amed
189 ymax = asml
190 else
191 ymin = asml
192 ymax = amed
193 end if
194 scl = one
195 sumsq = ymax**2*( one + (ymin/ymax)**2 )
196 else
197 scl = one / ssml
198 sumsq = asml
199 end if
200 else
201!
202! Otherwise all values are mid-range
203!
204 scl = one
205 sumsq = amed
206 end if
207 scnrm2 = scl*sqrt( sumsq )
208 return
real(wp) function scnrm2(n, x, incx)
SCNRM2
Definition scnrm2.f90:90
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