gesvdx - Man Page

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

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.

Definition at line 267 of file cgesvdx.f.

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.

Definition at line 260 of file dgesvdx.f.

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.

Definition at line 260 of file sgesvdx.f.

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.

Definition at line 267 of file zgesvdx.f.