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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine clals0 | ( | integer | ICOMPQ, |
integer | NL, | ||
integer | NR, | ||
integer | SQRE, | ||
integer | NRHS, | ||
complex, dimension( ldb, * ) | B, | ||
integer | LDB, | ||
complex, dimension( ldbx, * ) | BX, | ||
integer | LDBX, | ||
integer, dimension( * ) | PERM, | ||
integer | GIVPTR, | ||
integer, dimension( ldgcol, * ) | GIVCOL, | ||
integer | LDGCOL, | ||
real, dimension( ldgnum, * ) | GIVNUM, | ||
integer | LDGNUM, | ||
real, dimension( ldgnum, * ) | POLES, | ||
real, dimension( * ) | DIFL, | ||
real, dimension( ldgnum, * ) | DIFR, | ||
real, dimension( * ) | Z, | ||
integer | K, | ||
real | C, | ||
real | S, | ||
real, dimension( * ) | RWORK, | ||
integer | INFO | ||
) |
CLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.
Download CLALS0 + dependencies [TGZ] [ZIP] [TXT]
CLALS0 applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach. For the left singular vector matrix, three types of orthogonal matrices are involved: (1L) Givens rotations: the number of such rotations is GIVPTR; the pairs of columns/rows they were applied to are stored in GIVCOL; and the C- and S-values of these rotations are stored in GIVNUM. (2L) Permutation. The (NL+1)-st row of B is to be moved to the first row, and for J=2:N, PERM(J)-th row of B is to be moved to the J-th row. (3L) The left singular vector matrix of the remaining matrix. For the right singular vector matrix, four types of orthogonal matrices are involved: (1R) The right singular vector matrix of the remaining matrix. (2R) If SQRE = 1, one extra Givens rotation to generate the right null space. (3R) The inverse transformation of (2L). (4R) The inverse transformation of (1L).
[in] | ICOMPQ | ICOMPQ is INTEGER Specifies whether singular vectors are to be computed in factored form: = 0: Left singular vector matrix. = 1: Right singular vector matrix. |
[in] | NL | NL is INTEGER The row dimension of the upper block. NL >= 1. |
[in] | NR | NR is INTEGER The row dimension of the lower block. NR >= 1. |
[in] | SQRE | SQRE is INTEGER = 0: the lower block is an NR-by-NR square matrix. = 1: the lower block is an NR-by-(NR+1) rectangular matrix. The bidiagonal matrix has row dimension N = NL + NR + 1, and column dimension M = N + SQRE. |
[in] | NRHS | NRHS is INTEGER The number of columns of B and BX. NRHS must be at least 1. |
[in,out] | B | B is COMPLEX 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. LDB must be at least max(1,MAX( M, N ) ). |
[out] | BX | BX is COMPLEX array, dimension ( LDBX, NRHS ) |
[in] | LDBX | LDBX is INTEGER The leading dimension of BX. |
[in] | PERM | PERM is INTEGER array, dimension ( N ) The permutations (from deflation and sorting) applied to the two blocks. |
[in] | GIVPTR | GIVPTR is INTEGER The number of Givens rotations which took place in this subproblem. |
[in] | GIVCOL | GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation. |
[in] | LDGCOL | LDGCOL is INTEGER The leading dimension of GIVCOL, must be at least N. |
[in] | GIVNUM | GIVNUM is REAL array, dimension ( LDGNUM, 2 ) Each number indicates the C or S value used in the corresponding Givens rotation. |
[in] | LDGNUM | LDGNUM is INTEGER The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K. |
[in] | POLES | POLES is REAL array, dimension ( LDGNUM, 2 ) On entry, POLES(1:K, 1) contains the new singular values obtained from solving the secular equation, and POLES(1:K, 2) is an array containing the poles in the secular equation. |
[in] | DIFL | DIFL is REAL array, dimension ( K ). On entry, DIFL(I) is the distance between I-th updated (undeflated) singular value and the I-th (undeflated) old singular value. |
[in] | DIFR | DIFR is REAL array, dimension ( LDGNUM, 2 ). On entry, DIFR(I, 1) contains the distances between I-th updated (undeflated) singular value and the I+1-th (undeflated) old singular value. And DIFR(I, 2) is the normalizing factor for the I-th right singular vector. |
[in] | Z | Z is REAL array, dimension ( K ) Contain the components of the deflation-adjusted updating row vector. |
[in] | K | K is INTEGER Contains the dimension of the non-deflated matrix, This is the order of the related secular equation. 1 <= K <=N. |
[in] | C | C is REAL C contains garbage if SQRE =0 and the C-value of a Givens rotation related to the right null space if SQRE = 1. |
[in] | S | S is REAL S contains garbage if SQRE =0 and the S-value of a Givens rotation related to the right null space if SQRE = 1. |
[out] | RWORK | RWORK is REAL array, dimension ( K*(1+NRHS) + 2*NRHS ) |
[out] | INFO | INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. |
Definition at line 272 of file clals0.f.