LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
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double
Singular Value
Collaboration diagram for double:

Functions/Subroutines

subroutine dgesdd (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, IWORK, INFO)
 DGESDD
subroutine dgesvd (JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO)
  DGESVD computes the singular value decomposition (SVD) for GE matrices

Detailed Description

This is the group of double singular value driver functions for GE matrices

Function/Subroutine Documentation

subroutine dgesdd ( character  JOBZ,
integer  M,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
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 
)

DGESDD

Download DGESDD + dependencies [TGZ] [ZIP] [TXT]
Purpose: 
 DGESDD computes the singular value decomposition (SVD) of a real
 M-by-N matrix A, optionally computing the left and right singular
 vectors.  If singular vectors are desired, it uses a
 divide-and-conquer algorithm.

 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.

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

 The divide and conquer algorithm makes very mild assumptions about
 floating point arithmetic. It will work on machines with a guard
 digit in add/subtract, or on those binary machines without guard
 digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
 Cray-2. It could conceivably fail on hexadecimal or decimal machines
 without guard digits, but we know of none.
Parameters
[in]JOBZ
          JOBZ is CHARACTER*1
          Specifies options for computing all or part of the matrix U:
          = 'A':  all M columns of U and all N rows of V**T are
                  returned in the arrays U and VT;
          = 'S':  the first min(M,N) columns of U and the first
                  min(M,N) rows of V**T are returned in the arrays U
                  and VT;
          = 'O':  If M >= N, the first N columns of U are overwritten
                  on the array A and all rows of V**T are returned in
                  the array VT;
                  otherwise, all columns of U are returned in the
                  array U and the first M rows of V**T are overwritten
                  in the array A;
          = 'N':  no columns of U or rows of V**T are computed.
[in]M
          M is INTEGER
          The number of rows of the input matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the input matrix A.  N >= 0.
[in,out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit,
          if JOBZ = 'O',  A is overwritten with the first N columns
                          of U (the left singular vectors, stored
                          columnwise) if M >= N;
                          A is overwritten with the first M rows
                          of V**T (the right singular vectors, stored
                          rowwise) otherwise.
          if JOBZ .ne. 'O', the contents of A are destroyed.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[out]S
          S is DOUBLE PRECISION array, dimension (min(M,N))
          The singular values of A, sorted so that S(i) >= S(i+1).
[out]U
          U is DOUBLE PRECISION array, dimension (LDU,UCOL)
          UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
          UCOL = min(M,N) if JOBZ = 'S'.
          If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
          orthogonal matrix U;
          if JOBZ = 'S', U contains the first min(M,N) columns of U
          (the left singular vectors, stored columnwise);
          if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
[in]LDU
          LDU is INTEGER
          The leading dimension of the array U.  LDU >= 1; if
          JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
[out]VT
          VT is DOUBLE PRECISION array, dimension (LDVT,N)
          If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
          N-by-N orthogonal matrix V**T;
          if JOBZ = 'S', VT contains the first min(M,N) rows of
          V**T (the right singular vectors, stored rowwise);
          if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
[in]LDVT
          LDVT is INTEGER
          The leading dimension of the array VT.  LDVT >= 1; if
          JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
          if JOBZ = 'S', LDVT >= min(M,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK;
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK. LWORK >= 1.
          If JOBZ = 'N',
            LWORK >= 3*min(M,N) + max(max(M,N),7*min(M,N)).
          If JOBZ = 'O',
            LWORK >= 3*min(M,N) + 
                     max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)).
          If JOBZ = 'S' or 'A'
            LWORK >= 3*min(M,N) +
                     max(max(M,N),4*min(M,N)*min(M,N)+4*min(M,N)).
          For good performance, LWORK should generally be larger.
          If LWORK = -1 but other input arguments are legal, WORK(1)
          returns the optimal LWORK.
[out]IWORK
          IWORK is INTEGER array, dimension (8*min(M,N))
[out]INFO
          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  DBDSDC did not converge, updating process failed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
Contributors:
Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 217 of file dgesdd.f.

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subroutine dgesvd ( character  JOBU,
character  JOBVT,
integer  M,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
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  INFO 
)

DGESVD computes the singular value decomposition (SVD) for GE matrices

Download DGESVD + dependencies [TGZ] [ZIP] [TXT]
Purpose: 
 DGESVD 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.

 Note that the routine returns V**T, not V.
Parameters
[in]JOBU
          JOBU is CHARACTER*1
          Specifies options for computing all or part of the matrix U:
          = 'A':  all M columns of U are returned in array U:
          = 'S':  the first min(m,n) columns of U (the left singular
                  vectors) are returned in the array U;
          = 'O':  the first min(m,n) columns of U (the left singular
                  vectors) are overwritten on the array A;
          = 'N':  no columns of U (no left singular vectors) are
                  computed.
[in]JOBVT
          JOBVT is CHARACTER*1
          Specifies options for computing all or part of the matrix
          V**T:
          = 'A':  all N rows of V**T are returned in the array VT;
          = 'S':  the first min(m,n) rows of V**T (the right singular
                  vectors) are returned in the array VT;
          = 'O':  the first min(m,n) rows of V**T (the right singular
                  vectors) are overwritten on the array A;
          = 'N':  no rows of V**T (no right singular vectors) are
                  computed.

          JOBVT and JOBU cannot both be 'O'.
[in]M
          M is INTEGER
          The number of rows of the input matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the input matrix A.  N >= 0.
[in,out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit,
          if JOBU = 'O',  A is overwritten with the first min(m,n)
                          columns of U (the left singular vectors,
                          stored columnwise);
          if JOBVT = 'O', A is overwritten with the first min(m,n)
                          rows of V**T (the right singular vectors,
                          stored rowwise);
          if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A
                          are destroyed.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[out]S
          S is DOUBLE PRECISION array, dimension (min(M,N))
          The singular values of A, sorted so that S(i) >= S(i+1).
[out]U
          U is DOUBLE PRECISION array, dimension (LDU,UCOL)
          (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'.
          If JOBU = 'A', U contains the M-by-M orthogonal matrix U;
          if JOBU = 'S', U contains the first min(m,n) columns of U
          (the left singular vectors, stored columnwise);
          if JOBU = 'N' or 'O', U is not referenced.
[in]LDU
          LDU is INTEGER
          The leading dimension of the array U.  LDU >= 1; if
          JOBU = 'S' or 'A', LDU >= M.
[out]VT
          VT is DOUBLE PRECISION array, dimension (LDVT,N)
          If JOBVT = 'A', VT contains the N-by-N orthogonal matrix
          V**T;
          if JOBVT = 'S', VT contains the first min(m,n) rows of
          V**T (the right singular vectors, stored rowwise);
          if JOBVT = 'N' or 'O', VT is not referenced.
[in]LDVT
          LDVT is INTEGER
          The leading dimension of the array VT.  LDVT >= 1; if
          JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK;
          if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged
          superdiagonal elements of an upper bidiagonal matrix B
          whose diagonal is in S (not necessarily sorted). B
          satisfies A = U * B * VT, so it has the same singular values
          as A, and singular vectors related by U and VT.
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
          LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code):
             - PATH 1  (M much larger than N, JOBU='N') 
             - PATH 1t (N much larger than M, JOBVT='N')
          LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(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.
[out]INFO
          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  if DBDSQR did not converge, INFO specifies how many
                superdiagonals of an intermediate bidiagonal form B
                did not converge to zero. See the description of WORK
                above for details.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
April 2012

Definition at line 211 of file dgesvd.f.

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