--- 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 )