LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zqrt13()

subroutine zqrt13 ( integer  scale,
integer  m,
integer  n,
complex*16, dimension( lda, * )  a,
integer  lda,
double precision  norma,
integer, dimension( 4 )  iseed 
)

ZQRT13

Purpose:
 ZQRT13 generates a full-rank matrix that may be scaled to have large
 or small norm.
Parameters
[in]SCALE
          SCALE is INTEGER
          SCALE = 1: normally scaled matrix
          SCALE = 2: matrix scaled up
          SCALE = 3: matrix scaled down
[in]M
          M is INTEGER
          The number of rows of the matrix A.
[in]N
          N is INTEGER
          The number of columns of A.
[out]A
          A is COMPLEX*16 array, dimension (LDA,N)
          The M-by-N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.
[out]NORMA
          NORMA is DOUBLE PRECISION
          The one-norm of A.
[in,out]ISEED
          ISEED is integer array, dimension (4)
          Seed for random number generator
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 90 of file zqrt13.f.

91*
92* -- LAPACK test routine --
93* -- LAPACK is a software package provided by Univ. of Tennessee, --
94* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
95*
96* .. Scalar Arguments ..
97 INTEGER LDA, M, N, SCALE
98 DOUBLE PRECISION NORMA
99* ..
100* .. Array Arguments ..
101 INTEGER ISEED( 4 )
102 COMPLEX*16 A( LDA, * )
103* ..
104*
105* =====================================================================
106*
107* .. Parameters ..
108 DOUBLE PRECISION ONE
109 parameter( one = 1.0d0 )
110* ..
111* .. Local Scalars ..
112 INTEGER INFO, J
113 DOUBLE PRECISION BIGNUM, SMLNUM
114* ..
115* .. External Functions ..
116 DOUBLE PRECISION DLAMCH, DZASUM, ZLANGE
117 EXTERNAL dlamch, dzasum, zlange
118* ..
119* .. External Subroutines ..
120 EXTERNAL zlarnv, zlascl
121* ..
122* .. Intrinsic Functions ..
123 INTRINSIC dble, dcmplx, sign
124* ..
125* .. Local Arrays ..
126 DOUBLE PRECISION DUMMY( 1 )
127* ..
128* .. Executable Statements ..
129*
130 IF( m.LE.0 .OR. n.LE.0 )
131 $ RETURN
132*
133* benign matrix
134*
135 DO 10 j = 1, n
136 CALL zlarnv( 2, iseed, m, a( 1, j ) )
137 IF( j.LE.m ) THEN
138 a( j, j ) = a( j, j ) + dcmplx( sign( dzasum( m, a( 1, j ),
139 $ 1 ), dble( a( j, j ) ) ) )
140 END IF
141 10 CONTINUE
142*
143* scaled versions
144*
145 IF( scale.NE.1 ) THEN
146 norma = zlange( 'Max', m, n, a, lda, dummy )
147 smlnum = dlamch( 'Safe minimum' )
148 bignum = one / smlnum
149 smlnum = smlnum / dlamch( 'Epsilon' )
150 bignum = one / smlnum
151*
152 IF( scale.EQ.2 ) THEN
153*
154* matrix scaled up
155*
156 CALL zlascl( 'General', 0, 0, norma, bignum, m, n, a, lda,
157 $ info )
158 ELSE IF( scale.EQ.3 ) THEN
159*
160* matrix scaled down
161*
162 CALL zlascl( 'General', 0, 0, norma, smlnum, m, n, a, lda,
163 $ info )
164 END IF
165 END IF
166*
167 norma = zlange( 'One-norm', m, n, a, lda, dummy )
168 RETURN
169*
170* End of ZQRT13
171*
dzasum
double precision function dzasum(n, zx, incx)
DZASUM
Definition dzasum.f:72
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
zlange
double precision function zlange(norm, m, n, a, lda, work)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition zlange.f:115
zlarnv
subroutine zlarnv(idist, iseed, n, x)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition zlarnv.f:99
zlascl
subroutine zlascl(type, kl, ku, cfrom, cto, m, n, a, lda, info)
ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition zlascl.f:143
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