LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ cqrt12()

 real function cqrt12 ( integer M, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) S, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK )

CQRT12

Purpose:
``` CQRT12 computes the singular values `svlues' of the upper trapezoid
of A(1:M,1:N) and returns the ratio

|| s - svlues||/(||svlues||*eps*max(M,N))```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix A.``` [in] N ``` N is INTEGER The number of columns of the matrix A.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) The M-by-N matrix A. Only the upper trapezoid is referenced.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A.``` [in] S ``` S is REAL array, dimension (min(M,N)) The singular values of the matrix A.``` [out] WORK ` WORK is COMPLEX array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The length of the array WORK. LWORK >= M*N + 2*min(M,N) + max(M,N).``` [out] RWORK ` RWORK is REAL array, dimension (4*min(M,N))`
Date
December 2016

Definition at line 99 of file cqrt12.f.

99 *
100 * -- LAPACK test routine (version 3.7.0) --
101 * -- LAPACK is a software package provided by Univ. of Tennessee, --
102 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
103 * December 2016
104 *
105 * .. Scalar Arguments ..
106  INTEGER lda, lwork, m, n
107 * ..
108 * .. Array Arguments ..
109  REAL rwork( * ), s( * )
110  COMPLEX a( lda, * ), work( lwork )
111 * ..
112 *
113 * =====================================================================
114 *
115 * .. Parameters ..
116  REAL zero, one
117  parameter( zero = 0.0e0, one = 1.0e0 )
118 * ..
119 * .. Local Scalars ..
120  INTEGER i, info, iscl, j, mn
121  REAL anrm, bignum, nrmsvl, smlnum
122 * ..
123 * .. Local Arrays ..
124  REAL dummy( 1 )
125 * ..
126 * .. External Functions ..
127  REAL clange, sasum, slamch, snrm2
128  EXTERNAL clange, sasum, slamch, snrm2
129 * ..
130 * .. External Subroutines ..
131  EXTERNAL cgebd2, clascl, claset, saxpy, sbdsqr, slabad,
132  \$ slascl, xerbla
133 * ..
134 * .. Intrinsic Functions ..
135  INTRINSIC cmplx, max, min, real
136 * ..
137 * .. Executable Statements ..
138 *
139  cqrt12 = zero
140 *
141 * Test that enough workspace is supplied
142 *
143  IF( lwork.LT.m*n+2*min( m, n )+max( m, n ) ) THEN
144  CALL xerbla( 'CQRT12', 7 )
145  RETURN
146  END IF
147 *
148 * Quick return if possible
149 *
150  mn = min( m, n )
151  IF( mn.LE.zero )
152  \$ RETURN
153 *
154  nrmsvl = snrm2( mn, s, 1 )
155 *
156 * Copy upper triangle of A into work
157 *
158  CALL claset( 'Full', m, n, cmplx( zero ), cmplx( zero ), work, m )
159  DO 20 j = 1, n
160  DO 10 i = 1, min( j, m )
161  work( ( j-1 )*m+i ) = a( i, j )
162  10 CONTINUE
163  20 CONTINUE
164 *
165 * Get machine parameters
166 *
167  smlnum = slamch( 'S' ) / slamch( 'P' )
168  bignum = one / smlnum
169  CALL slabad( smlnum, bignum )
170 *
171 * Scale work if max entry outside range [SMLNUM,BIGNUM]
172 *
173  anrm = clange( 'M', m, n, work, m, dummy )
174  iscl = 0
175  IF( anrm.GT.zero .AND. anrm.LT.smlnum ) THEN
176 *
177 * Scale matrix norm up to SMLNUM
178 *
179  CALL clascl( 'G', 0, 0, anrm, smlnum, m, n, work, m, info )
180  iscl = 1
181  ELSE IF( anrm.GT.bignum ) THEN
182 *
183 * Scale matrix norm down to BIGNUM
184 *
185  CALL clascl( 'G', 0, 0, anrm, bignum, m, n, work, m, info )
186  iscl = 1
187  END IF
188 *
189  IF( anrm.NE.zero ) THEN
190 *
191 * Compute SVD of work
192 *
193  CALL cgebd2( m, n, work, m, rwork( 1 ), rwork( mn+1 ),
194  \$ work( m*n+1 ), work( m*n+mn+1 ),
195  \$ work( m*n+2*mn+1 ), info )
196  CALL sbdsqr( 'Upper', mn, 0, 0, 0, rwork( 1 ), rwork( mn+1 ),
197  \$ dummy, mn, dummy, 1, dummy, mn, rwork( 2*mn+1 ),
198  \$ info )
199 *
200  IF( iscl.EQ.1 ) THEN
201  IF( anrm.GT.bignum ) THEN
202  CALL slascl( 'G', 0, 0, bignum, anrm, mn, 1, rwork( 1 ),
203  \$ mn, info )
204  END IF
205  IF( anrm.LT.smlnum ) THEN
206  CALL slascl( 'G', 0, 0, smlnum, anrm, mn, 1, rwork( 1 ),
207  \$ mn, info )
208  END IF
209  END IF
210 *
211  ELSE
212 *
213  DO 30 i = 1, mn
214  rwork( i ) = zero
215  30 CONTINUE
216  END IF
217 *
218 * Compare s and singular values of work
219 *
220  CALL saxpy( mn, -one, s, 1, rwork( 1 ), 1 )
221  cqrt12 = sasum( mn, rwork( 1 ), 1 ) /
222  \$ ( slamch( 'Epsilon' )*REAL( MAX( M, N ) ) )
223  IF( nrmsvl.NE.zero )
224  \$ cqrt12 = cqrt12 / nrmsvl
225 *
226  RETURN
227 *
228 * End of CQRT12
229 *
subroutine sbdsqr(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO)
SBDSQR
Definition: sbdsqr.f:242
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: claset.f:108
real function cqrt12(M, N, A, LDA, S, WORK, LWORK, RWORK)
CQRT12
Definition: cqrt12.f:99
subroutine clascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
CLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: clascl.f:145
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:117
real function snrm2(N, X, INCX)
SNRM2
Definition: snrm2.f:76
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:74
subroutine slascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
SLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: slascl.f:145
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:91
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69