lasda - Man Page

subroutine dlasda (icompq, smlsiz, n, sqre, d, e, u, ldu, vt, k, difl, difr, z, poles, givptr, givcol, ldgcol, perm, givnum, c, s, work, iwork, info)
DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.
subroutine slasda (icompq, smlsiz, n, sqre, d, e, u, ldu, vt, k, difl, difr, z, poles, givptr, givcol, ldgcol, perm, givnum, c, s, work, iwork, info)
SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.  

Purpose:

 Using a divide and conquer approach, DLASDA computes the singular
 value decomposition (SVD) of a real upper bidiagonal N-by-M matrix
 B with diagonal D and offdiagonal E, where M = N + SQRE. The
 algorithm computes the singular values in the SVD B = U * S * VT.
 The orthogonal matrices U and VT are optionally computed in
 compact form.

 A related subroutine, DLASD0, computes the singular values and
 the singular vectors in explicit form.

Parameters

ICOMPQ

          ICOMPQ is INTEGER
         Specifies whether singular vectors are to be computed
         in compact form, as follows
         = 0: Compute singular values only.
         = 1: Compute singular vectors of upper bidiagonal
              matrix in compact form.

SMLSIZ

          SMLSIZ is INTEGER
         The maximum size of the subproblems at the bottom of the
         computation tree.

N

          N is INTEGER
         The row dimension of the upper bidiagonal matrix. This is
         also the dimension of the main diagonal array D.

SQRE

          SQRE is INTEGER
         Specifies the column dimension of the bidiagonal matrix.
         = 0: The bidiagonal matrix has column dimension M = N;
         = 1: The bidiagonal matrix has column dimension M = N + 1.

D

          D is DOUBLE PRECISION array, dimension ( N )
         On entry D contains the main diagonal of the bidiagonal
         matrix. On exit D, if INFO = 0, contains its singular values.

E

          E is DOUBLE PRECISION array, dimension ( M-1 )
         Contains the subdiagonal entries of the bidiagonal matrix.
         On exit, E has been destroyed.

U

          U is DOUBLE PRECISION array,
         dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced
         if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left
         singular vector matrices of all subproblems at the bottom
         level.

LDU

          LDU is INTEGER, LDU = > N.
         The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
         GIVNUM, and Z.

VT

          VT is DOUBLE PRECISION array,
         dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced
         if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right
         singular vector matrices of all subproblems at the bottom
         level.

K

          K is INTEGER array,
         dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.
         If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th
         secular equation on the computation tree.

DIFL

          DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ),
         where NLVL = floor(log_2 (N/SMLSIZ))).

DIFR

          DIFR is DOUBLE PRECISION array,
                  dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and
                  dimension ( N ) if ICOMPQ = 0.
         If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1)
         record distances between singular values on the I-th
         level and singular values on the (I -1)-th level, and
         DIFR(1:N, 2 * I ) contains the normalizing factors for
         the right singular vector matrix. See DLASD8 for details.

Z

          Z is DOUBLE PRECISION array,
                  dimension ( LDU, NLVL ) if ICOMPQ = 1 and
                  dimension ( N ) if ICOMPQ = 0.
         The first K elements of Z(1, I) contain the components of
         the deflation-adjusted updating row vector for subproblems
         on the I-th level.

POLES

          POLES is DOUBLE PRECISION array,
         dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced
         if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and
         POLES(1, 2*I) contain  the new and old singular values
         involved in the secular equations on the I-th level.

GIVPTR

          GIVPTR is INTEGER array,
         dimension ( N ) if ICOMPQ = 1, and not referenced if
         ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records
         the number of Givens rotations performed on the I-th
         problem on the computation tree.

GIVCOL

          GIVCOL is INTEGER array,
         dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not
         referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
         GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations
         of Givens rotations performed on the I-th level on the
         computation tree.

LDGCOL

          LDGCOL is INTEGER, LDGCOL = > N.
         The leading dimension of arrays GIVCOL and PERM.

PERM

          PERM is INTEGER array,
         dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced
         if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records
         permutations done on the I-th level of the computation tree.

GIVNUM

          GIVNUM is DOUBLE PRECISION array,
         dimension ( LDU,  2 * NLVL ) if ICOMPQ = 1, and not
         referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
         GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S-
         values of Givens rotations performed on the I-th level on
         the computation tree.

C

          C is DOUBLE PRECISION array,
         dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0.
         If ICOMPQ = 1 and the I-th subproblem is not square, on exit,
         C( I ) contains the C-value of a Givens rotation related to
         the right null space of the I-th subproblem.

S

          S is DOUBLE PRECISION array, dimension ( N ) if
         ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1
         and the I-th subproblem is not square, on exit, S( I )
         contains the S-value of a Givens rotation related to
         the right null space of the I-th subproblem.

WORK

          WORK is DOUBLE PRECISION array, dimension
         (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).

IWORK

          IWORK is INTEGER array, dimension (7*N)

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  if INFO = 1, a singular value did not converge

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 270 of file dlasda.f.

SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.  

Purpose:

 Using a divide and conquer approach, SLASDA computes the singular
 value decomposition (SVD) of a real upper bidiagonal N-by-M matrix
 B with diagonal D and offdiagonal E, where M = N + SQRE. The
 algorithm computes the singular values in the SVD B = U * S * VT.
 The orthogonal matrices U and VT are optionally computed in
 compact form.

 A related subroutine, SLASD0, computes the singular values and
 the singular vectors in explicit form.

Parameters

ICOMPQ

          ICOMPQ is INTEGER
         Specifies whether singular vectors are to be computed
         in compact form, as follows
         = 0: Compute singular values only.
         = 1: Compute singular vectors of upper bidiagonal
              matrix in compact form.

SMLSIZ

          SMLSIZ is INTEGER
         The maximum size of the subproblems at the bottom of the
         computation tree.

N

          N is INTEGER
         The row dimension of the upper bidiagonal matrix. This is
         also the dimension of the main diagonal array D.

SQRE

          SQRE is INTEGER
         Specifies the column dimension of the bidiagonal matrix.
         = 0: The bidiagonal matrix has column dimension M = N;
         = 1: The bidiagonal matrix has column dimension M = N + 1.

D

          D is REAL array, dimension ( N )
         On entry D contains the main diagonal of the bidiagonal
         matrix. On exit D, if INFO = 0, contains its singular values.

E

          E is REAL array, dimension ( M-1 )
         Contains the subdiagonal entries of the bidiagonal matrix.
         On exit, E has been destroyed.

U

          U is REAL array,
         dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced
         if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left
         singular vector matrices of all subproblems at the bottom
         level.

LDU

          LDU is INTEGER, LDU = > N.
         The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
         GIVNUM, and Z.

VT

          VT is REAL array,
         dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced
         if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right
         singular vector matrices of all subproblems at the bottom
         level.

K

          K is INTEGER array, dimension ( N )
         if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.
         If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th
         secular equation on the computation tree.

DIFL

          DIFL is REAL array, dimension ( LDU, NLVL ),
         where NLVL = floor(log_2 (N/SMLSIZ))).

DIFR

          DIFR is REAL array,
                  dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and
                  dimension ( N ) if ICOMPQ = 0.
         If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1)
         record distances between singular values on the I-th
         level and singular values on the (I -1)-th level, and
         DIFR(1:N, 2 * I ) contains the normalizing factors for
         the right singular vector matrix. See SLASD8 for details.

Z

          Z is REAL array,
                  dimension ( LDU, NLVL ) if ICOMPQ = 1 and
                  dimension ( N ) if ICOMPQ = 0.
         The first K elements of Z(1, I) contain the components of
         the deflation-adjusted updating row vector for subproblems
         on the I-th level.

POLES

          POLES is REAL array,
         dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced
         if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and
         POLES(1, 2*I) contain  the new and old singular values
         involved in the secular equations on the I-th level.

GIVPTR

          GIVPTR is INTEGER array,
         dimension ( N ) if ICOMPQ = 1, and not referenced if
         ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records
         the number of Givens rotations performed on the I-th
         problem on the computation tree.

GIVCOL

          GIVCOL is INTEGER array,
         dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not
         referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
         GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations
         of Givens rotations performed on the I-th level on the
         computation tree.

LDGCOL

          LDGCOL is INTEGER, LDGCOL = > N.
         The leading dimension of arrays GIVCOL and PERM.

PERM

          PERM is INTEGER array, dimension ( LDGCOL, NLVL )
         if ICOMPQ = 1, and not referenced
         if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records
         permutations done on the I-th level of the computation tree.

GIVNUM

          GIVNUM is REAL array,
         dimension ( LDU,  2 * NLVL ) if ICOMPQ = 1, and not
         referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
         GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S-
         values of Givens rotations performed on the I-th level on
         the computation tree.

C

          C is REAL array,
         dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0.
         If ICOMPQ = 1 and the I-th subproblem is not square, on exit,
         C( I ) contains the C-value of a Givens rotation related to
         the right null space of the I-th subproblem.

S

          S is REAL array, dimension ( N ) if
         ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1
         and the I-th subproblem is not square, on exit, S( I )
         contains the S-value of a Givens rotation related to
         the right null space of the I-th subproblem.

WORK

          WORK is REAL array, dimension
         (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).

IWORK

          IWORK is INTEGER array, dimension (7*N).

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  if INFO = 1, a singular value did not converge

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 270 of file slasda.f.