LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ sqrt12()

real function sqrt12 ( integer  M,
integer  N,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( * )  S,
real, dimension( lwork )  WORK,
integer  LWORK 
)

SQRT12

Purpose:
 SQRT12 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 REAL 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 REAL array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK. LWORK >= max(M*N + 4*min(M,N) +
          max(M,N), M*N+2*MIN( M, N )+4*N).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 91 of file sqrt12.f.

91 *
92 * -- LAPACK test routine (version 3.7.0) --
93 * -- LAPACK is a software package provided by Univ. of Tennessee, --
94 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
95 * December 2016
96 *
97 * .. Scalar Arguments ..
98  INTEGER lda, lwork, m, n
99 * ..
100 * .. Array Arguments ..
101  REAL a( lda, * ), s( * ), work( lwork )
102 * ..
103 *
104 * =====================================================================
105 *
106 * .. Parameters ..
107  REAL zero, one
108  parameter( zero = 0.0e0, one = 1.0e0 )
109 * ..
110 * .. Local Scalars ..
111  INTEGER i, info, iscl, j, mn
112  REAL anrm, bignum, nrmsvl, smlnum
113 * ..
114 * .. External Functions ..
115  REAL sasum, slamch, slange, snrm2
116  EXTERNAL sasum, slamch, slange, snrm2
117 * ..
118 * .. External Subroutines ..
119  EXTERNAL saxpy, sbdsqr, sgebd2, slabad, slascl, slaset,
120  $ xerbla
121 * ..
122 * .. Intrinsic Functions ..
123  INTRINSIC max, min, real
124 * ..
125 * .. Local Arrays ..
126  REAL dummy( 1 )
127 * ..
128 * .. Executable Statements ..
129 *
130  sqrt12 = zero
131 *
132 * Test that enough workspace is supplied
133 *
134  IF( lwork.LT.max( m*n+4*min( m, n )+max( m, n ),
135  $ m*n+2*min( m, n )+4*n) ) THEN
136  CALL xerbla( 'SQRT12', 7 )
137  RETURN
138  END IF
139 *
140 * Quick return if possible
141 *
142  mn = min( m, n )
143  IF( mn.LE.zero )
144  $ RETURN
145 *
146  nrmsvl = snrm2( mn, s, 1 )
147 *
148 * Copy upper triangle of A into work
149 *
150  CALL slaset( 'Full', m, n, zero, zero, work, m )
151  DO 20 j = 1, n
152  DO 10 i = 1, min( j, m )
153  work( ( j-1 )*m+i ) = a( i, j )
154  10 CONTINUE
155  20 CONTINUE
156 *
157 * Get machine parameters
158 *
159  smlnum = slamch( 'S' ) / slamch( 'P' )
160  bignum = one / smlnum
161  CALL slabad( smlnum, bignum )
162 *
163 * Scale work if max entry outside range [SMLNUM,BIGNUM]
164 *
165  anrm = slange( 'M', m, n, work, m, dummy )
166  iscl = 0
167  IF( anrm.GT.zero .AND. anrm.LT.smlnum ) THEN
168 *
169 * Scale matrix norm up to SMLNUM
170 *
171  CALL slascl( 'G', 0, 0, anrm, smlnum, m, n, work, m, info )
172  iscl = 1
173  ELSE IF( anrm.GT.bignum ) THEN
174 *
175 * Scale matrix norm down to BIGNUM
176 *
177  CALL slascl( 'G', 0, 0, anrm, bignum, m, n, work, m, info )
178  iscl = 1
179  END IF
180 *
181  IF( anrm.NE.zero ) THEN
182 *
183 * Compute SVD of work
184 *
185  CALL sgebd2( m, n, work, m, work( m*n+1 ), work( m*n+mn+1 ),
186  $ work( m*n+2*mn+1 ), work( m*n+3*mn+1 ),
187  $ work( m*n+4*mn+1 ), info )
188  CALL sbdsqr( 'Upper', mn, 0, 0, 0, work( m*n+1 ),
189  $ work( m*n+mn+1 ), dummy, mn, dummy, 1, dummy, mn,
190  $ work( m*n+2*mn+1 ), info )
191 *
192  IF( iscl.EQ.1 ) THEN
193  IF( anrm.GT.bignum ) THEN
194  CALL slascl( 'G', 0, 0, bignum, anrm, mn, 1,
195  $ work( m*n+1 ), mn, info )
196  END IF
197  IF( anrm.LT.smlnum ) THEN
198  CALL slascl( 'G', 0, 0, smlnum, anrm, mn, 1,
199  $ work( m*n+1 ), mn, info )
200  END IF
201  END IF
202 *
203  ELSE
204 *
205  DO 30 i = 1, mn
206  work( m*n+i ) = zero
207  30 CONTINUE
208  END IF
209 *
210 * Compare s and singular values of work
211 *
212  CALL saxpy( mn, -one, s, 1, work( m*n+1 ), 1 )
213  sqrt12 = sasum( mn, work( m*n+1 ), 1 ) /
214  $ ( slamch( 'Epsilon' )*REAL( MAX( M, N ) ) )
215  IF( nrmsvl.NE.zero )
216  $ sqrt12 = sqrt12 / nrmsvl
217 *
218  RETURN
219 *
220 * End of SQRT12
221 *
subroutine sbdsqr(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO)
SBDSQR
Definition: sbdsqr.f:242
real function sqrt12(M, N, A, LDA, S, WORK, LWORK)
SQRT12
Definition: sqrt12.f:91
subroutine sgebd2(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO)
SGEBD2 reduces a general matrix to bidiagonal form using an unblocked algorithm.
Definition: sgebd2.f:191
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:116
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 slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: slaset.f:112
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
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:76
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