--- rpl/lapack/lapack/dgesvj.f 2015/11/26 11:44:15 1.14
+++ rpl/lapack/lapack/dgesvj.f 2020/05/21 21:45:57 1.20
@@ -2,25 +2,25 @@
*
* =========== DOCUMENTATION ===========
*
-* Online html documentation available at
-* http://www.netlib.org/lapack/explore-html/
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
-*> Download DGESVJ + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DGESVJ + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V,
* LDV, WORK, LWORK, INFO )
-*
+*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDV, LWORK, M, MV, N
* CHARACTER*1 JOBA, JOBU, JOBV
@@ -29,7 +29,7 @@
* DOUBLE PRECISION A( LDA, * ), SVA( N ), V( LDV, * ),
* $ WORK( LWORK )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -54,7 +54,7 @@
*
*> \param[in] JOBA
*> \verbatim
-*> JOBA is CHARACTER* 1
+*> JOBA is CHARACTER*1
*> Specifies the structure of A.
*> = 'L': The input matrix A is lower triangular;
*> = 'U': The input matrix A is upper triangular;
@@ -90,20 +90,20 @@
*> JOBV is CHARACTER*1
*> Specifies whether to compute the right singular vectors, that
*> is, the matrix V:
-*> = 'V' : the matrix V is computed and returned in the array V
-*> = 'A' : the Jacobi rotations are applied to the MV-by-N
+*> = 'V': the matrix V is computed and returned in the array V
+*> = 'A': the Jacobi rotations are applied to the MV-by-N
*> array V. In other words, the right singular vector
*> matrix V is not computed explicitly, instead it is
*> applied to an MV-by-N matrix initially stored in the
*> 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
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
-*> The number of rows of the input matrix A. 1/DLAMCH('E') > M >= 0.
+*> The number of rows of the input matrix A. 1/DLAMCH('E') > M >= 0.
*> \endverbatim
*>
*> \param[in] N
@@ -118,8 +118,8 @@
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> On entry, the M-by-N matrix A.
*> On exit :
-*> If JOBU .EQ. 'U' .OR. JOBU .EQ. 'C' :
-*> If INFO .EQ. 0 :
+*> If JOBU = 'U' .OR. JOBU = 'C' :
+*> If INFO = 0 :
*> RANKA orthonormal columns of U are returned in the
*> leading RANKA columns of the array A. Here RANKA <= N
*> is the number of computed singular values of A that are
@@ -129,9 +129,9 @@
*> in the array WORK as RANKA=NINT(WORK(2)). Also see the
*> descriptions of SVA and WORK. The computed columns of U
*> 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.
-*> If INFO .GT. 0 :
+*> If INFO > 0 :
*> the procedure DGESVJ did not converge in the given number
*> of iterations (sweeps). In that case, the computed
*> columns of U may not be orthogonal up to TOL. The output
@@ -140,8 +140,8 @@
*> input matrix A in the sense that the residual
*> ||A-SCALE*U*SIGMA*V^T||_2 / ||A||_2 is small.
*>
-*> If JOBU .EQ. 'N' :
-*> If INFO .EQ. 0 :
+*> If JOBU = 'N' :
+*> If INFO = 0 :
*> Note that the left singular vectors are 'for free' in the
*> one-sided Jacobi SVD algorithm. However, if only the
*> singular values are needed, the level of numerical
@@ -150,7 +150,7 @@
*> numerically orthogonal up to approximately M*EPS. Thus,
*> on exit, A contains the columns of U scaled with the
*> corresponding singular values.
-*> If INFO .GT. 0 :
+*> If INFO > 0 :
*> the procedure DGESVJ did not converge in the given number
*> of iterations (sweeps).
*> \endverbatim
@@ -165,9 +165,9 @@
*> \verbatim
*> SVA is DOUBLE PRECISION array, dimension (N)
*> On exit :
-*> If INFO .EQ. 0 :
+*> If INFO = 0 :
*> 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.
*> During the computation SVA contains the Euclidean column
*> norms of the iterated matrices in the array A.
@@ -175,7 +175,7 @@
*> The singular values of A are SCALE*SVA(1:N), and this
*> factored representation is due to the fact that some of the
*> 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
*> iterations (sweeps) and SCALE*SVA(1:N) may not be accurate.
*> \endverbatim
@@ -183,7 +183,7 @@
*> \param[in] MV
*> \verbatim
*> 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.
*> \endverbatim
*>
@@ -201,16 +201,16 @@
*> \param[in] LDV
*> \verbatim
*> LDV is INTEGER
-*> The leading dimension of the array V, LDV .GE. 1.
-*> If JOBV .EQ. 'V', then LDV .GE. max(1,N).
-*> If JOBV .EQ. 'A', then LDV .GE. max(1,MV) .
+*> The leading dimension of the array V, LDV >= 1.
+*> If JOBV = 'V', then LDV >= max(1,N).
+*> If JOBV = 'A', then LDV >= max(1,MV) .
*> \endverbatim
*>
*> \param[in,out] WORK
*> \verbatim
-*> WORK is DOUBLE PRECISION array, dimension max(4,M+N).
+*> WORK is DOUBLE PRECISION array, dimension (LWORK)
*> On entry :
-*> If JOBU .EQ. 'C' :
+*> If JOBU = 'C' :
*> WORK(1) = CTOL, where CTOL defines the threshold for convergence.
*> The process stops if all columns of A are mutually
*> orthogonal up to CTOL*EPS, EPS=DLAMCH('E').
@@ -230,7 +230,7 @@
*> WORK(5) = max_{i.NE.j} |COS(A(:,i),A(:,j))| in the last sweep.
*> This is useful information in cases when DGESVJ did
*> 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
*> Jacobi rotation angles in the last sweep. It can be
*> useful for a post festum analysis.
@@ -245,9 +245,9 @@
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
-*> = 0 : successful exit.
-*> < 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: successful exit.
+*> < 0: if INFO = -i, then the i-th argument had an illegal value
+*> > 0: DGESVJ did not converge in the maximal allowed number (30)
*> of sweeps. The output may still be useful. See the
*> description of WORK.
*> \endverbatim
@@ -255,12 +255,12 @@
* Authors:
* ========
*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
-*> \date November 2015
+*> \date June 2017
*
*> \ingroup doubleGEcomputational
*
@@ -337,10 +337,10 @@
SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V,
$ LDV, WORK, LWORK, INFO )
*
-* -- LAPACK computational routine (version 3.6.0) --
+* -- LAPACK computational routine (version 3.7.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2015
+* June 2017
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDV, LWORK, M, MV, N
@@ -1261,7 +1261,7 @@
MXSINJ = MAX( MXSINJ, DABS( SN ) )
SVA( q ) = AAQQ*DSQRT( MAX( ZERO,
$ ONE+T*APOAQ*AAPQ ) )
- AAPP = AAPP*DSQRT( MAX( ZERO,
+ AAPP = AAPP*DSQRT( MAX( ZERO,
$ ONE-T*AQOAP*AAPQ ) )
*
APOAQ = WORK( p ) / WORK( q )