Provided by: liblapack-doc_3.12.0-3build1.1_all bug

NAME

       gesvdx - gesvdx: SVD, bisection

SYNOPSIS

   Functions
       subroutine cgesvdx (jobu, jobvt, range, m, n, a, lda, vl, vu, il, iu, ns, s, u, ldu, vt,
           ldvt, work, lwork, rwork, iwork, info)
            CGESVDX computes the singular value decomposition (SVD) for GE matrices
       subroutine dgesvdx (jobu, jobvt, range, m, n, a, lda, vl, vu, il, iu, ns, s, u, ldu, vt,
           ldvt, work, lwork, iwork, info)
            DGESVDX computes the singular value decomposition (SVD) for GE matrices
       subroutine sgesvdx (jobu, jobvt, range, m, n, a, lda, vl, vu, il, iu, ns, s, u, ldu, vt,
           ldvt, work, lwork, iwork, info)
            SGESVDX computes the singular value decomposition (SVD) for GE matrices
       subroutine zgesvdx (jobu, jobvt, range, m, n, a, lda, vl, vu, il, iu, ns, s, u, ldu, vt,
           ldvt, work, lwork, rwork, iwork, info)
            ZGESVDX computes the singular value decomposition (SVD) for GE matrices

Detailed Description

Function Documentation

   subroutine cgesvdx (character jobu, character jobvt, character range, integer m, integer n,
       complex, dimension( lda, * ) a, integer lda, real vl, real vu, integer il, integer iu,
       integer ns, real, dimension( * ) s, complex, dimension( ldu, * ) u, integer ldu, complex,
       dimension( ldvt, * ) vt, integer ldvt, complex, dimension( * ) work, integer lwork, real,
       dimension( * ) rwork, integer, dimension( * ) iwork, integer info)
        CGESVDX computes the singular value decomposition (SVD) for GE matrices

       Purpose:

             CGESVDX computes the singular value decomposition (SVD) of a complex
             M-by-N matrix A, optionally computing the left and/or right singular
             vectors. The SVD is written

                 A = U * SIGMA * transpose(V)

             where SIGMA is an M-by-N matrix which is zero except for its
             min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
             V is an N-by-N unitary matrix.  The diagonal elements of SIGMA
             are the singular values of A; they are real and non-negative, and
             are returned in descending order.  The first min(m,n) columns of
             U and V are the left and right singular vectors of A.

             CGESVDX uses an eigenvalue problem for obtaining the SVD, which
             allows for the computation of a subset of singular values and
             vectors. See SBDSVDX for details.

             Note that the routine returns V**T, not V.

       Parameters
           JOBU

                     JOBU is CHARACTER*1
                     Specifies options for computing all or part of the matrix U:
                     = 'V':  the first min(m,n) columns of U (the left singular
                             vectors) or as specified by RANGE are returned in
                             the array U;
                     = 'N':  no columns of U (no left singular vectors) are
                             computed.

           JOBVT

                     JOBVT is CHARACTER*1
                      Specifies options for computing all or part of the matrix
                      V**T:
                      = 'V':  the first min(m,n) rows of V**T (the right singular
                              vectors) or as specified by RANGE are returned in
                              the array VT;
                      = 'N':  no rows of V**T (no right singular vectors) are
                              computed.

           RANGE

                     RANGE is CHARACTER*1
                     = 'A': all singular values will be found.
                     = 'V': all singular values in the half-open interval (VL,VU]
                            will be found.
                     = 'I': the IL-th through IU-th singular values will be found.

           M

                     M is INTEGER
                     The number of rows of the input matrix A.  M >= 0.

           N

                     N is INTEGER
                     The number of columns of the input matrix A.  N >= 0.

           A

                     A is COMPLEX array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit, the contents of A are destroyed.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           VL

                     VL is REAL
                     If RANGE='V', the lower bound of the interval to
                     be searched for singular values. VU > VL.
                     Not referenced if RANGE = 'A' or 'I'.

           VU

                     VU is REAL
                     If RANGE='V', the upper bound of the interval to
                     be searched for singular values. VU > VL.
                     Not referenced if RANGE = 'A' or 'I'.

           IL

                     IL is INTEGER
                     If RANGE='I', the index of the
                     smallest singular value to be returned.
                     1 <= IL <= IU <= min(M,N), if min(M,N) > 0.
                     Not referenced if RANGE = 'A' or 'V'.

           IU

                     IU is INTEGER
                     If RANGE='I', the index of the
                     largest singular value to be returned.
                     1 <= IL <= IU <= min(M,N), if min(M,N) > 0.
                     Not referenced if RANGE = 'A' or 'V'.

           NS

                     NS is INTEGER
                     The total number of singular values found,
                     0 <= NS <= min(M,N).
                     If RANGE = 'A', NS = min(M,N); if RANGE = 'I', NS = IU-IL+1.

           S

                     S is REAL array, dimension (min(M,N))
                     The singular values of A, sorted so that S(i) >= S(i+1).

           U

                     U is COMPLEX array, dimension (LDU,UCOL)
                     If JOBU = 'V', U contains columns of U (the left singular
                     vectors, stored columnwise) as specified by RANGE; if
                     JOBU = 'N', U is not referenced.
                     Note: The user must ensure that UCOL >= NS; if RANGE = 'V',
                     the exact value of NS is not known in advance and an upper
                     bound must be used.

           LDU

                     LDU is INTEGER
                     The leading dimension of the array U.  LDU >= 1; if
                     JOBU = 'V', LDU >= M.

           VT

                     VT is COMPLEX array, dimension (LDVT,N)
                     If JOBVT = 'V', VT contains the rows of V**T (the right singular
                     vectors, stored rowwise) as specified by RANGE; if JOBVT = 'N',
                     VT is not referenced.
                     Note: The user must ensure that LDVT >= NS; if RANGE = 'V',
                     the exact value of NS is not known in advance and an upper
                     bound must be used.

           LDVT

                     LDVT is INTEGER
                     The leading dimension of the array VT.  LDVT >= 1; if
                     JOBVT = 'V', LDVT >= NS (see above).

           WORK

                     WORK is COMPLEX array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK;

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     LWORK >= MAX(1,MIN(M,N)*(MIN(M,N)+4)) for the paths (see
                     comments inside the code):
                        - PATH 1  (M much larger than N)
                        - PATH 1t (N much larger than M)
                     LWORK >= MAX(1,MIN(M,N)*2+MAX(M,N)) for the other paths.
                     For good performance, LWORK should generally be larger.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           RWORK

                     RWORK is REAL array, dimension (MAX(1,LRWORK))
                     LRWORK >= MIN(M,N)*(MIN(M,N)*2+15*MIN(M,N)).

           IWORK

                     IWORK is INTEGER array, dimension (12*MIN(M,N))
                     If INFO = 0, the first NS elements of IWORK are zero. If INFO > 0,
                     then IWORK contains the indices of the eigenvectors that failed
                     to converge in SBDSVDX/SSTEVX.

           INFO

                INFO is INTEGER
                      = 0:  successful exit
                      < 0:  if INFO = -i, the i-th argument had an illegal value
                      > 0:  if INFO = i, then i eigenvectors failed to converge
                            in SBDSVDX/SSTEVX.
                            if INFO = N*2 + 1, an internal error occurred in
                            SBDSVDX

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   subroutine dgesvdx (character jobu, character jobvt, character range, integer m, integer n,
       double precision, dimension( lda, * ) a, integer lda, double precision vl, double
       precision vu, integer il, integer iu, integer ns, double precision, dimension( * ) s,
       double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldvt, *
       ) vt, integer ldvt, double precision, dimension( * ) work, integer lwork, integer,
       dimension( * ) iwork, integer info)
        DGESVDX computes the singular value decomposition (SVD) for GE matrices

       Purpose:

             DGESVDX computes the singular value decomposition (SVD) of a real
             M-by-N matrix A, optionally computing the left and/or right singular
             vectors. The SVD is written

                 A = U * SIGMA * transpose(V)

             where SIGMA is an M-by-N matrix which is zero except for its
             min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
             V is an N-by-N orthogonal matrix.  The diagonal elements of SIGMA
             are the singular values of A; they are real and non-negative, and
             are returned in descending order.  The first min(m,n) columns of
             U and V are the left and right singular vectors of A.

             DGESVDX uses an eigenvalue problem for obtaining the SVD, which
             allows for the computation of a subset of singular values and
             vectors. See DBDSVDX for details.

             Note that the routine returns V**T, not V.

       Parameters
           JOBU

                     JOBU is CHARACTER*1
                     Specifies options for computing all or part of the matrix U:
                     = 'V':  the first min(m,n) columns of U (the left singular
                             vectors) or as specified by RANGE are returned in
                             the array U;
                     = 'N':  no columns of U (no left singular vectors) are
                             computed.

           JOBVT

                     JOBVT is CHARACTER*1
                      Specifies options for computing all or part of the matrix
                      V**T:
                      = 'V':  the first min(m,n) rows of V**T (the right singular
                              vectors) or as specified by RANGE are returned in
                              the array VT;
                      = 'N':  no rows of V**T (no right singular vectors) are
                              computed.

           RANGE

                     RANGE is CHARACTER*1
                     = 'A': all singular values will be found.
                     = 'V': all singular values in the half-open interval (VL,VU]
                            will be found.
                     = 'I': the IL-th through IU-th singular values will be found.

           M

                     M is INTEGER
                     The number of rows of the input matrix A.  M >= 0.

           N

                     N is INTEGER
                     The number of columns of the input matrix A.  N >= 0.

           A

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit, the contents of A are destroyed.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           VL

                     VL is DOUBLE PRECISION
                     If RANGE='V', the lower bound of the interval to
                     be searched for singular values. VU > VL.
                     Not referenced if RANGE = 'A' or 'I'.

           VU

                     VU is DOUBLE PRECISION
                     If RANGE='V', the upper bound of the interval to
                     be searched for singular values. VU > VL.
                     Not referenced if RANGE = 'A' or 'I'.

           IL

                     IL is INTEGER
                     If RANGE='I', the index of the
                     smallest singular value to be returned.
                     1 <= IL <= IU <= min(M,N), if min(M,N) > 0.
                     Not referenced if RANGE = 'A' or 'V'.

           IU

                     IU is INTEGER
                     If RANGE='I', the index of the
                     largest singular value to be returned.
                     1 <= IL <= IU <= min(M,N), if min(M,N) > 0.
                     Not referenced if RANGE = 'A' or 'V'.

           NS

                     NS is INTEGER
                     The total number of singular values found,
                     0 <= NS <= min(M,N).
                     If RANGE = 'A', NS = min(M,N); if RANGE = 'I', NS = IU-IL+1.

           S

                     S is DOUBLE PRECISION array, dimension (min(M,N))
                     The singular values of A, sorted so that S(i) >= S(i+1).

           U

                     U is DOUBLE PRECISION array, dimension (LDU,UCOL)
                     If JOBU = 'V', U contains columns of U (the left singular
                     vectors, stored columnwise) as specified by RANGE; if
                     JOBU = 'N', U is not referenced.
                     Note: The user must ensure that UCOL >= NS; if RANGE = 'V',
                     the exact value of NS is not known in advance and an upper
                     bound must be used.

           LDU

                     LDU is INTEGER
                     The leading dimension of the array U.  LDU >= 1; if
                     JOBU = 'V', LDU >= M.

           VT

                     VT is DOUBLE PRECISION array, dimension (LDVT,N)
                     If JOBVT = 'V', VT contains the rows of V**T (the right singular
                     vectors, stored rowwise) as specified by RANGE; if JOBVT = 'N',
                     VT is not referenced.
                     Note: The user must ensure that LDVT >= NS; if RANGE = 'V',
                     the exact value of NS is not known in advance and an upper
                     bound must be used.

           LDVT

                     LDVT is INTEGER
                     The leading dimension of the array VT.  LDVT >= 1; if
                     JOBVT = 'V', LDVT >= NS (see above).

           WORK

                     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK;

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     LWORK >= MAX(1,MIN(M,N)*(MIN(M,N)+4)) for the paths (see
                     comments inside the code):
                        - PATH 1  (M much larger than N)
                        - PATH 1t (N much larger than M)
                     LWORK >= MAX(1,MIN(M,N)*2+MAX(M,N)) for the other paths.
                     For good performance, LWORK should generally be larger.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           IWORK

                     IWORK is INTEGER array, dimension (12*MIN(M,N))
                     If INFO = 0, the first NS elements of IWORK are zero. If INFO > 0,
                     then IWORK contains the indices of the eigenvectors that failed
                     to converge in DBDSVDX/DSTEVX.

           INFO

                INFO is INTEGER
                      = 0:  successful exit
                      < 0:  if INFO = -i, the i-th argument had an illegal value
                      > 0:  if INFO = i, then i eigenvectors failed to converge
                            in DBDSVDX/DSTEVX.
                            if INFO = N*2 + 1, an internal error occurred in
                            DBDSVDX

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   subroutine sgesvdx (character jobu, character jobvt, character range, integer m, integer n,
       real, dimension( lda, * ) a, integer lda, real vl, real vu, integer il, integer iu,
       integer ns, real, dimension( * ) s, real, dimension( ldu, * ) u, integer ldu, real,
       dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) work, integer lwork, integer,
       dimension( * ) iwork, integer info)
        SGESVDX computes the singular value decomposition (SVD) for GE matrices

       Purpose:

             SGESVDX computes the singular value decomposition (SVD) of a real
             M-by-N matrix A, optionally computing the left and/or right singular
             vectors. The SVD is written

                 A = U * SIGMA * transpose(V)

             where SIGMA is an M-by-N matrix which is zero except for its
             min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
             V is an N-by-N orthogonal matrix.  The diagonal elements of SIGMA
             are the singular values of A; they are real and non-negative, and
             are returned in descending order.  The first min(m,n) columns of
             U and V are the left and right singular vectors of A.

             SGESVDX uses an eigenvalue problem for obtaining the SVD, which
             allows for the computation of a subset of singular values and
             vectors. See SBDSVDX for details.

             Note that the routine returns V**T, not V.

       Parameters
           JOBU

                     JOBU is CHARACTER*1
                     Specifies options for computing all or part of the matrix U:
                     = 'V':  the first min(m,n) columns of U (the left singular
                             vectors) or as specified by RANGE are returned in
                             the array U;
                     = 'N':  no columns of U (no left singular vectors) are
                             computed.

           JOBVT

                     JOBVT is CHARACTER*1
                      Specifies options for computing all or part of the matrix
                      V**T:
                      = 'V':  the first min(m,n) rows of V**T (the right singular
                              vectors) or as specified by RANGE are returned in
                              the array VT;
                      = 'N':  no rows of V**T (no right singular vectors) are
                              computed.

           RANGE

                     RANGE is CHARACTER*1
                     = 'A': all singular values will be found.
                     = 'V': all singular values in the half-open interval (VL,VU]
                            will be found.
                     = 'I': the IL-th through IU-th singular values will be found.

           M

                     M is INTEGER
                     The number of rows of the input matrix A.  M >= 0.

           N

                     N is INTEGER
                     The number of columns of the input matrix A.  N >= 0.

           A

                     A is REAL array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit, the contents of A are destroyed.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           VL

                     VL is REAL
                     If RANGE='V', the lower bound of the interval to
                     be searched for singular values. VU > VL.
                     Not referenced if RANGE = 'A' or 'I'.

           VU

                     VU is REAL
                     If RANGE='V', the upper bound of the interval to
                     be searched for singular values. VU > VL.
                     Not referenced if RANGE = 'A' or 'I'.

           IL

                     IL is INTEGER
                     If RANGE='I', the index of the
                     smallest singular value to be returned.
                     1 <= IL <= IU <= min(M,N), if min(M,N) > 0.
                     Not referenced if RANGE = 'A' or 'V'.

           IU

                     IU is INTEGER
                     If RANGE='I', the index of the
                     largest singular value to be returned.
                     1 <= IL <= IU <= min(M,N), if min(M,N) > 0.
                     Not referenced if RANGE = 'A' or 'V'.

           NS

                     NS is INTEGER
                     The total number of singular values found,
                     0 <= NS <= min(M,N).
                     If RANGE = 'A', NS = min(M,N); if RANGE = 'I', NS = IU-IL+1.

           S

                     S is REAL array, dimension (min(M,N))
                     The singular values of A, sorted so that S(i) >= S(i+1).

           U

                     U is REAL array, dimension (LDU,UCOL)
                     If JOBU = 'V', U contains columns of U (the left singular
                     vectors, stored columnwise) as specified by RANGE; if
                     JOBU = 'N', U is not referenced.
                     Note: The user must ensure that UCOL >= NS; if RANGE = 'V',
                     the exact value of NS is not known in advance and an upper
                     bound must be used.

           LDU

                     LDU is INTEGER
                     The leading dimension of the array U.  LDU >= 1; if
                     JOBU = 'V', LDU >= M.

           VT

                     VT is REAL array, dimension (LDVT,N)
                     If JOBVT = 'V', VT contains the rows of V**T (the right singular
                     vectors, stored rowwise) as specified by RANGE; if JOBVT = 'N',
                     VT is not referenced.
                     Note: The user must ensure that LDVT >= NS; if RANGE = 'V',
                     the exact value of NS is not known in advance and an upper
                     bound must be used.

           LDVT

                     LDVT is INTEGER
                     The leading dimension of the array VT.  LDVT >= 1; if
                     JOBVT = 'V', LDVT >= NS (see above).

           WORK

                     WORK is REAL array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK;

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     LWORK >= MAX(1,MIN(M,N)*(MIN(M,N)+4)) for the paths (see
                     comments inside the code):
                        - PATH 1  (M much larger than N)
                        - PATH 1t (N much larger than M)
                     LWORK >= MAX(1,MIN(M,N)*2+MAX(M,N)) for the other paths.
                     For good performance, LWORK should generally be larger.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           IWORK

                     IWORK is INTEGER array, dimension (12*MIN(M,N))
                     If INFO = 0, the first NS elements of IWORK are zero. If INFO > 0,
                     then IWORK contains the indices of the eigenvectors that failed
                     to converge in SBDSVDX/SSTEVX.

           INFO

                INFO is INTEGER
                      = 0:  successful exit
                      < 0:  if INFO = -i, the i-th argument had an illegal value
                      > 0:  if INFO = i, then i eigenvectors failed to converge
                            in SBDSVDX/SSTEVX.
                            if INFO = N*2 + 1, an internal error occurred in
                            SBDSVDX

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   subroutine zgesvdx (character jobu, character jobvt, character range, integer m, integer n,
       complex*16, dimension( lda, * ) a, integer lda, double precision vl, double precision vu,
       integer il, integer iu, integer ns, double precision, dimension( * ) s, complex*16,
       dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldvt, * ) vt, integer ldvt,
       complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork,
       integer, dimension( * ) iwork, integer info)
        ZGESVDX computes the singular value decomposition (SVD) for GE matrices

       Purpose:

             ZGESVDX computes the singular value decomposition (SVD) of a complex
             M-by-N matrix A, optionally computing the left and/or right singular
             vectors. The SVD is written

                 A = U * SIGMA * transpose(V)

             where SIGMA is an M-by-N matrix which is zero except for its
             min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
             V is an N-by-N unitary matrix.  The diagonal elements of SIGMA
             are the singular values of A; they are real and non-negative, and
             are returned in descending order.  The first min(m,n) columns of
             U and V are the left and right singular vectors of A.

             ZGESVDX uses an eigenvalue problem for obtaining the SVD, which
             allows for the computation of a subset of singular values and
             vectors. See DBDSVDX for details.

             Note that the routine returns V**T, not V.

       Parameters
           JOBU

                     JOBU is CHARACTER*1
                     Specifies options for computing all or part of the matrix U:
                     = 'V':  the first min(m,n) columns of U (the left singular
                             vectors) or as specified by RANGE are returned in
                             the array U;
                     = 'N':  no columns of U (no left singular vectors) are
                             computed.

           JOBVT

                     JOBVT is CHARACTER*1
                      Specifies options for computing all or part of the matrix
                      V**T:
                      = 'V':  the first min(m,n) rows of V**T (the right singular
                              vectors) or as specified by RANGE are returned in
                              the array VT;
                      = 'N':  no rows of V**T (no right singular vectors) are
                              computed.

           RANGE

                     RANGE is CHARACTER*1
                     = 'A': all singular values will be found.
                     = 'V': all singular values in the half-open interval (VL,VU]
                            will be found.
                     = 'I': the IL-th through IU-th singular values will be found.

           M

                     M is INTEGER
                     The number of rows of the input matrix A.  M >= 0.

           N

                     N is INTEGER
                     The number of columns of the input matrix A.  N >= 0.

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit, the contents of A are destroyed.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           VL

                     VL is DOUBLE PRECISION
                     If RANGE='V', the lower bound of the interval to
                     be searched for singular values. VU > VL.
                     Not referenced if RANGE = 'A' or 'I'.

           VU

                     VU is DOUBLE PRECISION
                     If RANGE='V', the upper bound of the interval to
                     be searched for singular values. VU > VL.
                     Not referenced if RANGE = 'A' or 'I'.

           IL

                     IL is INTEGER
                     If RANGE='I', the index of the
                     smallest singular value to be returned.
                     1 <= IL <= IU <= min(M,N), if min(M,N) > 0.
                     Not referenced if RANGE = 'A' or 'V'.

           IU

                     IU is INTEGER
                     If RANGE='I', the index of the
                     largest singular value to be returned.
                     1 <= IL <= IU <= min(M,N), if min(M,N) > 0.
                     Not referenced if RANGE = 'A' or 'V'.

           NS

                     NS is INTEGER
                     The total number of singular values found,
                     0 <= NS <= min(M,N).
                     If RANGE = 'A', NS = min(M,N); if RANGE = 'I', NS = IU-IL+1.

           S

                     S is DOUBLE PRECISION array, dimension (min(M,N))
                     The singular values of A, sorted so that S(i) >= S(i+1).

           U

                     U is COMPLEX*16 array, dimension (LDU,UCOL)
                     If JOBU = 'V', U contains columns of U (the left singular
                     vectors, stored columnwise) as specified by RANGE; if
                     JOBU = 'N', U is not referenced.
                     Note: The user must ensure that UCOL >= NS; if RANGE = 'V',
                     the exact value of NS is not known in advance and an upper
                     bound must be used.

           LDU

                     LDU is INTEGER
                     The leading dimension of the array U.  LDU >= 1; if
                     JOBU = 'V', LDU >= M.

           VT

                     VT is COMPLEX*16 array, dimension (LDVT,N)
                     If JOBVT = 'V', VT contains the rows of V**T (the right singular
                     vectors, stored rowwise) as specified by RANGE; if JOBVT = 'N',
                     VT is not referenced.
                     Note: The user must ensure that LDVT >= NS; if RANGE = 'V',
                     the exact value of NS is not known in advance and an upper
                     bound must be used.

           LDVT

                     LDVT is INTEGER
                     The leading dimension of the array VT.  LDVT >= 1; if
                     JOBVT = 'V', LDVT >= NS (see above).

           WORK

                     WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK;

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     LWORK >= MAX(1,MIN(M,N)*(MIN(M,N)+4)) for the paths (see
                     comments inside the code):
                        - PATH 1  (M much larger than N)
                        - PATH 1t (N much larger than M)
                     LWORK >= MAX(1,MIN(M,N)*2+MAX(M,N)) for the other paths.
                     For good performance, LWORK should generally be larger.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
                     LRWORK >= MIN(M,N)*(MIN(M,N)*2+15*MIN(M,N)).

           IWORK

                     IWORK is INTEGER array, dimension (12*MIN(M,N))
                     If INFO = 0, the first NS elements of IWORK are zero. If INFO > 0,
                     then IWORK contains the indices of the eigenvectors that failed
                     to converge in DBDSVDX/DSTEVX.

           INFO

                INFO is INTEGER
                      = 0:  successful exit
                      < 0:  if INFO = -i, the i-th argument had an illegal value
                      > 0:  if INFO = i, then i eigenvectors failed to converge
                            in DBDSVDX/DSTEVX.
                            if INFO = N*2 + 1, an internal error occurred in
                            DBDSVDX

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

Author

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