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Diff for /rpl/lapack/lapack/dgesvj.f between versions 1.19 and 1.20

version 1.19, 2018/05/29 07:17:52 version 1.20, 2020/05/21 21:45:57
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 *>          JOBV is CHARACTER*1  *>          JOBV is CHARACTER*1
 *>          Specifies whether to compute the right singular vectors, that  *>          Specifies whether to compute the right singular vectors, that
 *>          is, the matrix V:  *>          is, the matrix V:
 *>          = 'V' : the matrix V is computed and returned in the array V  *>          = 'V':  the matrix V is computed and returned in the array V
 *>          = 'A' : the Jacobi rotations are applied to the MV-by-N  *>          = 'A':  the Jacobi rotations are applied to the MV-by-N
 *>                  array V. In other words, the right singular vector  *>                  array V. In other words, the right singular vector
 *>                  matrix V is not computed explicitly, instead it is  *>                  matrix V is not computed explicitly, instead it is
 *>                  applied to an MV-by-N matrix initially stored in the  *>                  applied to an MV-by-N matrix initially stored in the
 *>                  first MV rows of V.  *>                  first MV rows of V.
 *>          = 'N' : the matrix V is not computed and the array V is not  *>          = 'N':  the matrix V is not computed and the array V is not
 *>                  referenced  *>                  referenced
 *> \endverbatim  *> \endverbatim
 *>  *>
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 *>          A is DOUBLE PRECISION array, dimension (LDA,N)  *>          A is DOUBLE PRECISION array, dimension (LDA,N)
 *>          On entry, the M-by-N matrix A.  *>          On entry, the M-by-N matrix A.
 *>          On exit :  *>          On exit :
 *>          If JOBU .EQ. 'U' .OR. JOBU .EQ. 'C' :  *>          If JOBU = 'U' .OR. JOBU = 'C' :
 *>                 If INFO .EQ. 0 :  *>                 If INFO = 0 :
 *>                 RANKA orthonormal columns of U are returned in the  *>                 RANKA orthonormal columns of U are returned in the
 *>                 leading RANKA columns of the array A. Here RANKA <= N  *>                 leading RANKA columns of the array A. Here RANKA <= N
 *>                 is the number of computed singular values of A that are  *>                 is the number of computed singular values of A that are
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 *>                 in the array WORK as RANKA=NINT(WORK(2)). Also see the  *>                 in the array WORK as RANKA=NINT(WORK(2)). Also see the
 *>                 descriptions of SVA and WORK. The computed columns of U  *>                 descriptions of SVA and WORK. The computed columns of U
 *>                 are mutually numerically orthogonal up to approximately  *>                 are mutually numerically orthogonal up to approximately
 *>                 TOL=DSQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU.EQ.'C'),  *>                 TOL=DSQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU = 'C'),
 *>                 see the description of JOBU.  *>                 see the description of JOBU.
 *>                 If INFO .GT. 0 :  *>                 If INFO > 0 :
 *>                 the procedure DGESVJ did not converge in the given number  *>                 the procedure DGESVJ did not converge in the given number
 *>                 of iterations (sweeps). In that case, the computed  *>                 of iterations (sweeps). In that case, the computed
 *>                 columns of U may not be orthogonal up to TOL. The output  *>                 columns of U may not be orthogonal up to TOL. The output
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 *>                 input matrix A in the sense that the residual  *>                 input matrix A in the sense that the residual
 *>                 ||A-SCALE*U*SIGMA*V^T||_2 / ||A||_2 is small.  *>                 ||A-SCALE*U*SIGMA*V^T||_2 / ||A||_2 is small.
 *>  *>
 *>          If JOBU .EQ. 'N' :  *>          If JOBU = 'N' :
 *>                 If INFO .EQ. 0 :  *>                 If INFO = 0 :
 *>                 Note that the left singular vectors are 'for free' in the  *>                 Note that the left singular vectors are 'for free' in the
 *>                 one-sided Jacobi SVD algorithm. However, if only the  *>                 one-sided Jacobi SVD algorithm. However, if only the
 *>                 singular values are needed, the level of numerical  *>                 singular values are needed, the level of numerical
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 *>                 numerically orthogonal up to approximately M*EPS. Thus,  *>                 numerically orthogonal up to approximately M*EPS. Thus,
 *>                 on exit, A contains the columns of U scaled with the  *>                 on exit, A contains the columns of U scaled with the
 *>                 corresponding singular values.  *>                 corresponding singular values.
 *>                 If INFO .GT. 0 :  *>                 If INFO > 0 :
 *>                 the procedure DGESVJ did not converge in the given number  *>                 the procedure DGESVJ did not converge in the given number
 *>                 of iterations (sweeps).  *>                 of iterations (sweeps).
 *> \endverbatim  *> \endverbatim
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 *> \verbatim  *> \verbatim
 *>          SVA is DOUBLE PRECISION array, dimension (N)  *>          SVA is DOUBLE PRECISION array, dimension (N)
 *>          On exit :  *>          On exit :
 *>          If INFO .EQ. 0 :  *>          If INFO = 0 :
 *>          depending on the value SCALE = WORK(1), we have:  *>          depending on the value SCALE = WORK(1), we have:
 *>                 If SCALE .EQ. ONE :  *>                 If SCALE = ONE :
 *>                 SVA(1:N) contains the computed singular values of A.  *>                 SVA(1:N) contains the computed singular values of A.
 *>                 During the computation SVA contains the Euclidean column  *>                 During the computation SVA contains the Euclidean column
 *>                 norms of the iterated matrices in the array A.  *>                 norms of the iterated matrices in the array A.
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 *>                 The singular values of A are SCALE*SVA(1:N), and this  *>                 The singular values of A are SCALE*SVA(1:N), and this
 *>                 factored representation is due to the fact that some of the  *>                 factored representation is due to the fact that some of the
 *>                 singular values of A might underflow or overflow.  *>                 singular values of A might underflow or overflow.
 *>          If INFO .GT. 0 :  *>          If INFO > 0 :
 *>          the procedure DGESVJ did not converge in the given number of  *>          the procedure DGESVJ did not converge in the given number of
 *>          iterations (sweeps) and SCALE*SVA(1:N) may not be accurate.  *>          iterations (sweeps) and SCALE*SVA(1:N) may not be accurate.
 *> \endverbatim  *> \endverbatim
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 *> \param[in] MV  *> \param[in] MV
 *> \verbatim  *> \verbatim
 *>          MV is INTEGER  *>          MV is INTEGER
 *>          If JOBV .EQ. 'A', then the product of Jacobi rotations in DGESVJ  *>          If JOBV = 'A', then the product of Jacobi rotations in DGESVJ
 *>          is applied to the first MV rows of V. See the description of JOBV.  *>          is applied to the first MV rows of V. See the description of JOBV.
 *> \endverbatim  *> \endverbatim
 *>  *>
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 *> \param[in] LDV  *> \param[in] LDV
 *> \verbatim  *> \verbatim
 *>          LDV is INTEGER  *>          LDV is INTEGER
 *>          The leading dimension of the array V, LDV .GE. 1.  *>          The leading dimension of the array V, LDV >= 1.
 *>          If JOBV .EQ. 'V', then LDV .GE. max(1,N).  *>          If JOBV = 'V', then LDV >= max(1,N).
 *>          If JOBV .EQ. 'A', then LDV .GE. max(1,MV) .  *>          If JOBV = 'A', then LDV >= max(1,MV) .
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in,out] WORK  *> \param[in,out] WORK
 *> \verbatim  *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (LWORK)  *>          WORK is DOUBLE PRECISION array, dimension (LWORK)
 *>          On entry :  *>          On entry :
 *>          If JOBU .EQ. 'C' :  *>          If JOBU = 'C' :
 *>          WORK(1) = CTOL, where CTOL defines the threshold for convergence.  *>          WORK(1) = CTOL, where CTOL defines the threshold for convergence.
 *>                    The process stops if all columns of A are mutually  *>                    The process stops if all columns of A are mutually
 *>                    orthogonal up to CTOL*EPS, EPS=DLAMCH('E').  *>                    orthogonal up to CTOL*EPS, EPS=DLAMCH('E').
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 *>          WORK(5) = max_{i.NE.j} |COS(A(:,i),A(:,j))| in the last sweep.  *>          WORK(5) = max_{i.NE.j} |COS(A(:,i),A(:,j))| in the last sweep.
 *>                    This is useful information in cases when DGESVJ did  *>                    This is useful information in cases when DGESVJ did
 *>                    not converge, as it can be used to estimate whether  *>                    not converge, as it can be used to estimate whether
 *>                    the output is stil useful and for post festum analysis.  *>                    the output is still useful and for post festum analysis.
 *>          WORK(6) = the largest absolute value over all sines of the  *>          WORK(6) = the largest absolute value over all sines of the
 *>                    Jacobi rotation angles in the last sweep. It can be  *>                    Jacobi rotation angles in the last sweep. It can be
 *>                    useful for a post festum analysis.  *>                    useful for a post festum analysis.
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 *> \param[out] INFO  *> \param[out] INFO
 *> \verbatim  *> \verbatim
 *>          INFO is INTEGER  *>          INFO is INTEGER
 *>          = 0 : successful exit.  *>          = 0:  successful exit.
 *>          < 0 : if INFO = -i, then the i-th argument had an illegal value  *>          < 0:  if INFO = -i, then the i-th argument had an illegal value
 *>          > 0 : DGESVJ did not converge in the maximal allowed number (30)  *>          > 0:  DGESVJ did not converge in the maximal allowed number (30)
 *>                of sweeps. The output may still be useful. See the  *>                of sweeps. The output may still be useful. See the
 *>                description of WORK.  *>                description of WORK.
 *> \endverbatim  *> \endverbatim
Removed from v.1.19  
changed lines
  Added in v.1.20

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