Developer Reference for Intel® oneAPI Math Kernel Library for C
?lasda
Computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e . Used by ?bdsdc .
Syntax
call 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)
call 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)void slasda(lapack_int *icompq, lapack_int *smlsiz, lapack_int *n, lapack_int *sqre,
float *d, float *e, float *u, lapack_int *ldu, float *vt, lapack_int *k,
float *difl, float *difr, float *z, float *poles, lapack_int *givptr,
lapack_int *givcol, lapack_int *ldgcol, lapack_int *perm, float *givnum,
float *c, float *s, float *work, lapack_int *iwork, lapack_int *info);
void dlasda(lapack_int *icompq, lapack_int *smlsiz, lapack_int *n, lapack_int *sqre,
double *d, double *e, double *u, lapack_int *ldu, double *vt, lapack_int *k,
double *difl, double *difr, double *z, double *poles, lapack_int *givptr,
lapack_int *givcol, lapack_int *ldgcol, lapack_int *perm, double *givnum,
double *c, double *s, double *work, lapack_int *iwork, lapack_int *info);Include Files
mkl.h
Description
Using a divide and conquer approach, ?lasda computes the singular value decomposition ( SVD ) of a real upper bidiagonal n -by- m matrix B with diagonal d and off-diagonal e , where m = n + sqre .
The algorithm computes the singular values in the SVDB = U*S*VT . The orthogonal matrices U and VT are optionally computed in compact form. A related subroutine ?lasd0 (Computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by ?bdsdc.) computes the singular values and the singular vectors in explicit form.
Input Parameters
- icompq
-
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
-
INTEGER . The maximum size of the subproblems at the bottom of the computation tree.
n
The row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array d .
sqre
Specifies the column dimension of the bidiagonal matrix.
If sqre = 0 : the bidiagonal matrix has column dimension m = n If sqre = 1 : the bidiagonal matrix has column dimension m = n + 1 .
- d
-
REAL for slasda DOUBLE PRECISION for dlasda . Array, DIMENSION ( n ). On entry, d contains the main diagonal of the bidiagonal matrix.
- e
-
REAL for slasda DOUBLE PRECISION for dlasda . Array, DIMENSION ( m - 1 ). Contains the subdiagonal entries of the bidiagonal matrix. On exit, e is destroyed.
ldu
The leading dimension of arrays u , vt , difl , difr , poles , givnum , and z . ldu≥n .
ldgcol
The leading dimension of arrays givcol and perm . ldgcol≥n .
- work
-
REAL for slasda DOUBLE PRECISION for dlasda . Workspace array, DIMENSION (6n+(smlsiz+1)^{2}) .
- iwork
-
INTEGER . Workspace array, Dimension must be at least (7 n ).
Output Parameters
- d
-
On exit d , if info = 0 , contains the singular values of the bidiagonal matrix.
- u
-
REAL for slasda DOUBLE PRECISION for dlasda . Array, DIMENSION ( ldu , smlsiz ) if icompq =1 . Not referenced if icompq = 0 . If icompq = 1 , on exit, u contains the left singular vector matrices of all subproblems at the bottom level.
- vt
-
REAL for slasda DOUBLE PRECISION for dlasda . Array, DIMENSION ( ldu , smlsiz +1 ) if icompq = 1 , and not referenced if icompq = 0 . If icompq = 1 , on exit, vt ‘ contains the right singular vector matrices of all subproblems at the bottom level.
- k
-
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
-
REAL for slasda DOUBLE PRECISION for dlasda . Array, DIMENSION ( ldu , nlvl ), where nlvl = floor(log_{2}(n/smlsiz)) .
- difr
-
REAL for slasda DOUBLE PRECISION for dlasda . 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 , 2i ) contains the normalizing factors for the right singular vector matrix. See ?lasd8 for details.
- z
-
REAL for slasda DOUBLE PRECISION for dlasda . 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
-
REAL for slasda DOUBLE PRECISION for dlasda . 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
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
-
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.
perm
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
-
REAL for slasda DOUBLE PRECISION for dlasda . 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
-
REAL for slasda DOUBLE PRECISION for dlasda . 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
-
REAL for slasda DOUBLE PRECISION for dlasda . Array, DIMENSION ( n ) 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.
info
INTEGER .
= 0: successful exit.
< 0: if info = - i , the i -th argument had an illegal value
> 0: If info = 1 , an singular value did not converge