LAPACK 3.11.0 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```

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 ..
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 CALL dlabad( smlnum, bignum )
150 smlnum = smlnum / dlamch( 'Epsilon' )
151 bignum = one / smlnum
152*
153 IF( scale.EQ.2 ) THEN
154*
155* matrix scaled up
156*
157 CALL zlascl( 'General', 0, 0, norma, bignum, m, n, a, lda,
158 \$ info )
159 ELSE IF( scale.EQ.3 ) THEN
160*
161* matrix scaled down
162*
163 CALL zlascl( 'General', 0, 0, norma, smlnum, m, n, a, lda,
164 \$ info )
165 END IF
166 END IF
167*
168 norma = zlange( 'One-norm', m, n, a, lda, dummy )
169 RETURN
170*
171* End of ZQRT13
172*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
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
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
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:99
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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