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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine slalsa | ( | integer | icompq, |
| integer | smlsiz, | ||
| integer | n, | ||
| integer | nrhs, | ||
| real, dimension( ldb, * ) | b, | ||
| integer | ldb, | ||
| real, dimension( ldbx, * ) | bx, | ||
| integer | ldbx, | ||
| real, dimension( ldu, * ) | u, | ||
| integer | ldu, | ||
| real, dimension( ldu, * ) | vt, | ||
| integer, dimension( * ) | k, | ||
| real, dimension( ldu, * ) | difl, | ||
| real, dimension( ldu, * ) | difr, | ||
| real, dimension( ldu, * ) | z, | ||
| real, dimension( ldu, * ) | poles, | ||
| integer, dimension( * ) | givptr, | ||
| integer, dimension( ldgcol, * ) | givcol, | ||
| integer | ldgcol, | ||
| integer, dimension( ldgcol, * ) | perm, | ||
| real, dimension( ldu, * ) | givnum, | ||
| real, dimension( * ) | c, | ||
| real, dimension( * ) | s, | ||
| real, dimension( * ) | work, | ||
| integer, dimension( * ) | iwork, | ||
| integer | info ) |
SLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.
Download SLALSA + dependencies [TGZ] [ZIP] [TXT]
!> !> SLALSA is an intermediate step in solving the least squares problem !> by computing the SVD of the coefficient matrix in compact form (The !> singular vectors are computed as products of simple orthogonal !> matrices.). !> !> If ICOMPQ = 0, SLALSA applies the inverse of the left singular vector !> matrix of an upper bidiagonal matrix to the right hand side; and if !> ICOMPQ = 1, SLALSA applies the right singular vector matrix to the !> right hand side. The singular vector matrices were generated in !> compact form by SLALSA. !>
| [in] | ICOMPQ | !> ICOMPQ is INTEGER !> Specifies whether the left or the right singular vector !> matrix is involved. !> = 0: Left singular vector matrix !> = 1: Right singular vector matrix !> |
| [in] | SMLSIZ | !> SMLSIZ is INTEGER !> The maximum size of the subproblems at the bottom of the !> computation tree. !> |
| [in] | N | !> N is INTEGER !> The row and column dimensions of the upper bidiagonal matrix. !> |
| [in] | NRHS | !> NRHS is INTEGER !> The number of columns of B and BX. NRHS must be at least 1. !> |
| [in,out] | B | !> B is REAL array, dimension ( LDB, NRHS ) !> On input, B contains the right hand sides of the least !> squares problem in rows 1 through M. !> On output, B contains the solution X in rows 1 through N. !> |
| [in] | LDB | !> LDB is INTEGER !> The leading dimension of B in the calling subprogram. !> LDB must be at least max(1,MAX( M, N ) ). !> |
| [out] | BX | !> BX is REAL array, dimension ( LDBX, NRHS ) !> On exit, the result of applying the left or right singular !> vector matrix to B. !> |
| [in] | LDBX | !> LDBX is INTEGER !> The leading dimension of BX. !> |
| [in] | U | !> U is REAL array, dimension ( LDU, SMLSIZ ). !> On entry, U contains the left singular vector matrices of all !> subproblems at the bottom level. !> |
| [in] | LDU | !> LDU is INTEGER, LDU = > N. !> The leading dimension of arrays U, VT, DIFL, DIFR, !> POLES, GIVNUM, and Z. !> |
| [in] | VT | !> VT is REAL array, dimension ( LDU, SMLSIZ+1 ). !> On entry, VT**T contains the right singular vector matrices of !> all subproblems at the bottom level. !> |
| [in] | K | !> K is INTEGER array, dimension ( N ). !> |
| [in] | DIFL | !> DIFL is REAL array, dimension ( LDU, NLVL ). !> where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. !> |
| [in] | DIFR | !> DIFR is REAL array, dimension ( LDU, 2 * NLVL ). !> On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record !> distances between singular values on the I-th level and !> singular values on the (I -1)-th level, and DIFR(*, 2 * I) !> record the normalizing factors of the right singular vectors !> matrices of subproblems on I-th level. !> |
| [in] | Z | !> Z is REAL array, dimension ( LDU, NLVL ). !> On entry, Z(1, I) contains the components of the deflation- !> adjusted updating row vector for subproblems on the I-th !> level. !> |
| [in] | POLES | !> POLES is REAL array, dimension ( LDU, 2 * NLVL ). !> On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old !> singular values involved in the secular equations on the I-th !> level. !> |
| [in] | GIVPTR | !> GIVPTR is INTEGER array, dimension ( N ). !> On entry, GIVPTR( I ) records the number of Givens !> rotations performed on the I-th problem on the computation !> tree. !> |
| [in] | GIVCOL | !> GIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ). !> On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the !> locations of Givens rotations performed on the I-th level on !> the computation tree. !> |
| [in] | LDGCOL | !> LDGCOL is INTEGER, LDGCOL = > N. !> The leading dimension of arrays GIVCOL and PERM. !> |
| [in] | PERM | !> PERM is INTEGER array, dimension ( LDGCOL, NLVL ). !> On entry, PERM(*, I) records permutations done on the I-th !> level of the computation tree. !> |
| [in] | GIVNUM | !> GIVNUM is REAL array, dimension ( LDU, 2 * NLVL ). !> On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S- !> values of Givens rotations performed on the I-th level on the !> computation tree. !> |
| [in] | C | !> C is REAL array, dimension ( N ). !> On entry, if the I-th subproblem is not square, !> C( I ) contains the C-value of a Givens rotation related to !> the right null space of the I-th subproblem. !> |
| [in] | S | !> S is REAL array, dimension ( N ). !> On entry, if the I-th subproblem is not square, !> S( I ) contains the S-value of a Givens rotation related to !> the right null space of the I-th subproblem. !> |
| [out] | WORK | !> WORK is REAL array, dimension (N) !> |
| [out] | IWORK | !> IWORK is INTEGER array, dimension (3*N) !> |
| [out] | INFO | !> INFO is INTEGER !> = 0: successful exit. !> < 0: if INFO = -i, the i-th argument had an illegal value. !> |
1.15.0