#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zlalsa_(integer *icompq, integer *smlsiz, integer *n, integer *nrhs, doublecomplex *b, integer *ldb, doublecomplex *bx, integer *ldbx, doublereal *u, integer *ldu, doublereal *vt, integer * k, doublereal *difl, doublereal *difr, doublereal *z__, doublereal * poles, integer *givptr, integer *givcol, integer *ldgcol, integer * perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal * rwork, integer *iwork, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZLALSA is an itermediate 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 orthorgonal matrices.). If ICOMPQ = 0, ZLALSA applies the inverse of the left singular vector matrix of an upper bidiagonal matrix to the right hand side; and if ICOMPQ = 1, ZLALSA applies the right singular vector matrix to the right hand side. The singular vector matrices were generated in compact form by ZLALSA. Arguments ========= ICOMPQ (input) INTEGER Specifies whether the left or the right singular vector matrix is involved. = 0: Left singular vector matrix = 1: Right singular vector matrix SMLSIZ (input) INTEGER The maximum size of the subproblems at the bottom of the computation tree. N (input) INTEGER The row and column dimensions of the upper bidiagonal matrix. NRHS (input) INTEGER The number of columns of B and BX. NRHS must be at least 1. B (input/output) COMPLEX*16 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. LDB (input) INTEGER The leading dimension of B in the calling subprogram. LDB must be at least max(1,MAX( M, N ) ). BX (output) COMPLEX*16 array, dimension ( LDBX, NRHS ) On exit, the result of applying the left or right singular vector matrix to B. LDBX (input) INTEGER The leading dimension of BX. U (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ). On entry, U contains the left singular vector matrices of all subproblems at the bottom level. LDU (input) INTEGER, LDU = > N. The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z. VT (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ). On entry, VT' contains the right singular vector matrices of all subproblems at the bottom level. K (input) INTEGER array, dimension ( N ). DIFL (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ). where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. DIFR (input) DOUBLE PRECISION 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. Z (input) DOUBLE PRECISION 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. POLES (input) DOUBLE PRECISION 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. GIVPTR (input) INTEGER array, dimension ( N ). On entry, GIVPTR( I ) records the number of Givens rotations performed on the I-th problem on the computation tree. GIVCOL (input) 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. LDGCOL (input) INTEGER, LDGCOL = > N. The leading dimension of arrays GIVCOL and PERM. PERM (input) INTEGER array, dimension ( LDGCOL, NLVL ). On entry, PERM(*, I) records permutations done on the I-th level of the computation tree. GIVNUM (input) DOUBLE PRECISION 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. C (input) DOUBLE PRECISION 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. S (input) DOUBLE PRECISION 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. RWORK (workspace) DOUBLE PRECISION array, dimension at least max ( N, (SMLSZ+1)*NRHS*3 ). IWORK (workspace) INTEGER array. The dimension must be at least 3 * N INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. Further Details =============== Based on contributions by Ming Gu and Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA Osni Marques, LBNL/NERSC, USA ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static doublereal c_b9 = 1.; static doublereal c_b10 = 0.; static integer c__2 = 2; /* System generated locals */ integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1, difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset, z_dim1, z_offset, b_dim1, b_offset, bx_dim1, bx_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublecomplex z__1; /* Builtin functions */ double d_imag(doublecomplex *); integer pow_ii(integer *, integer *); /* Local variables */ static integer i__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl, ndb1, nlp1, lvl2, nrp1, jcol, nlvl, sqre, jrow, jimag; extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); static integer jreal, inode, ndiml, ndimr; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlals0_(integer *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *), dlasdt_(integer *, integer *, integer * , integer *, integer *, integer *, integer *), xerbla_(char *, integer *); b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; bx_dim1 = *ldbx; bx_offset = 1 + bx_dim1; bx -= bx_offset; givnum_dim1 = *ldu; givnum_offset = 1 + givnum_dim1; givnum -= givnum_offset; poles_dim1 = *ldu; poles_offset = 1 + poles_dim1; poles -= poles_offset; z_dim1 = *ldu; z_offset = 1 + z_dim1; z__ -= z_offset; difr_dim1 = *ldu; difr_offset = 1 + difr_dim1; difr -= difr_offset; difl_dim1 = *ldu; difl_offset = 1 + difl_dim1; difl -= difl_offset; vt_dim1 = *ldu; vt_offset = 1 + vt_dim1; vt -= vt_offset; u_dim1 = *ldu; u_offset = 1 + u_dim1; u -= u_offset; --k; --givptr; perm_dim1 = *ldgcol; perm_offset = 1 + perm_dim1; perm -= perm_offset; givcol_dim1 = *ldgcol; givcol_offset = 1 + givcol_dim1; givcol -= givcol_offset; --c__; --s; --rwork; --iwork; /* Function Body */ *info = 0; if (*icompq < 0 || *icompq > 1) { *info = -1; } else if (*smlsiz < 3) { *info = -2; } else if (*n < *smlsiz) { *info = -3; } else if (*nrhs < 1) { *info = -4; } else if (*ldb < *n) { *info = -6; } else if (*ldbx < *n) { *info = -8; } else if (*ldu < *n) { *info = -10; } else if (*ldgcol < *n) { *info = -19; } if (*info != 0) { i__1 = -(*info); xerbla_("ZLALSA", &i__1); return 0; } /* Book-keeping and setting up the computation tree. */ inode = 1; ndiml = inode + *n; ndimr = ndiml + *n; dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], smlsiz); /* The following code applies back the left singular vector factors. For applying back the right singular vector factors, go to 170. */ if (*icompq == 1) { goto L170; } /* The nodes on the bottom level of the tree were solved by DLASDQ. The corresponding left and right singular vector matrices are in explicit form. First apply back the left singular vector matrices. */ ndb1 = (nd + 1) / 2; i__1 = nd; for (i__ = ndb1; i__ <= i__1; ++i__) { /* IC : center row of each node NL : number of rows of left subproblem NR : number of rows of right subproblem NLF: starting row of the left subproblem NRF: starting row of the right subproblem */ i1 = i__ - 1; ic = iwork[inode + i1]; nl = iwork[ndiml + i1]; nr = iwork[ndimr + i1]; nlf = ic - nl; nrf = ic + 1; /* Since B and BX are complex, the following call to DGEMM is performed in two steps (real and imaginary parts). CALL DGEMM( 'T', 'N', NL, NRHS, NL, ONE, U( NLF, 1 ), LDU, $ B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX ) */ j = nl * *nrhs << 1; i__2 = *nrhs; for (jcol = 1; jcol <= i__2; ++jcol) { i__3 = nlf + nl - 1; for (jrow = nlf; jrow <= i__3; ++jrow) { ++j; i__4 = jrow + jcol * b_dim1; rwork[j] = b[i__4].r; /* L10: */ } /* L20: */ } dgemm_("T", "N", &nl, nrhs, &nl, &c_b9, &u[nlf + u_dim1], ldu, &rwork[ (nl * *nrhs << 1) + 1], &nl, &c_b10, &rwork[1], &nl); j = nl * *nrhs << 1; i__2 = *nrhs; for (jcol = 1; jcol <= i__2; ++jcol) { i__3 = nlf + nl - 1; for (jrow = nlf; jrow <= i__3; ++jrow) { ++j; rwork[j] = d_imag(&b[jrow + jcol * b_dim1]); /* L30: */ } /* L40: */ } dgemm_("T", "N", &nl, nrhs, &nl, &c_b9, &u[nlf + u_dim1], ldu, &rwork[ (nl * *nrhs << 1) + 1], &nl, &c_b10, &rwork[nl * *nrhs + 1], & nl); jreal = 0; jimag = nl * *nrhs; i__2 = *nrhs; for (jcol = 1; jcol <= i__2; ++jcol) { i__3 = nlf + nl - 1; for (jrow = nlf; jrow <= i__3; ++jrow) { ++jreal; ++jimag; i__4 = jrow + jcol * bx_dim1; i__5 = jreal; i__6 = jimag; z__1.r = rwork[i__5], z__1.i = rwork[i__6]; bx[i__4].r = z__1.r, bx[i__4].i = z__1.i; /* L50: */ } /* L60: */ } /* Since B and BX are complex, the following call to DGEMM is performed in two steps (real and imaginary parts). CALL DGEMM( 'T', 'N', NR, NRHS, NR, ONE, U( NRF, 1 ), LDU, $ B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX ) */ j = nr * *nrhs << 1; i__2 = *nrhs; for (jcol = 1; jcol <= i__2; ++jcol) { i__3 = nrf + nr - 1; for (jrow = nrf; jrow <= i__3; ++jrow) { ++j; i__4 = jrow + jcol * b_dim1; rwork[j] = b[i__4].r; /* L70: */ } /* L80: */ } dgemm_("T", "N", &nr, nrhs, &nr, &c_b9, &u[nrf + u_dim1], ldu, &rwork[ (nr * *nrhs << 1) + 1], &nr, &c_b10, &rwork[1], &nr); j = nr * *nrhs << 1; i__2 = *nrhs; for (jcol = 1; jcol <= i__2; ++jcol) { i__3 = nrf + nr - 1; for (jrow = nrf; jrow <= i__3; ++jrow) { ++j; rwork[j] = d_imag(&b[jrow + jcol * b_dim1]); /* L90: */ } /* L100: */ } dgemm_("T", "N", &nr, nrhs, &nr, &c_b9, &u[nrf + u_dim1], ldu, &rwork[ (nr * *nrhs << 1) + 1], &nr, &c_b10, &rwork[nr * *nrhs + 1], & nr); jreal = 0; jimag = nr * *nrhs; i__2 = *nrhs; for (jcol = 1; jcol <= i__2; ++jcol) { i__3 = nrf + nr - 1; for (jrow = nrf; jrow <= i__3; ++jrow) { ++jreal; ++jimag; i__4 = jrow + jcol * bx_dim1; i__5 = jreal; i__6 = jimag; z__1.r = rwork[i__5], z__1.i = rwork[i__6]; bx[i__4].r = z__1.r, bx[i__4].i = z__1.i; /* L110: */ } /* L120: */ } /* L130: */ } /* Next copy the rows of B that correspond to unchanged rows in the bidiagonal matrix to BX. */ i__1 = nd; for (i__ = 1; i__ <= i__1; ++i__) { ic = iwork[inode + i__ - 1]; zcopy_(nrhs, &b[ic + b_dim1], ldb, &bx[ic + bx_dim1], ldbx); /* L140: */ } /* Finally go through the left singular vector matrices of all the other subproblems bottom-up on the tree. */ j = pow_ii(&c__2, &nlvl); sqre = 0; for (lvl = nlvl; lvl >= 1; --lvl) { lvl2 = (lvl << 1) - 1; /* find the first node LF and last node LL on the current level LVL */ if (lvl == 1) { lf = 1; ll = 1; } else { i__1 = lvl - 1; lf = pow_ii(&c__2, &i__1); ll = (lf << 1) - 1; } i__1 = ll; for (i__ = lf; i__ <= i__1; ++i__) { im1 = i__ - 1; ic = iwork[inode + im1]; nl = iwork[ndiml + im1]; nr = iwork[ndimr + im1]; nlf = ic - nl; nrf = ic + 1; --j; zlals0_(icompq, &nl, &nr, &sqre, nrhs, &bx[nlf + bx_dim1], ldbx, & b[nlf + b_dim1], ldb, &perm[nlf + lvl * perm_dim1], & givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, & givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[ j], &s[j], &rwork[1], info); /* L150: */ } /* L160: */ } goto L330; /* ICOMPQ = 1: applying back the right singular vector factors. */ L170: /* First now go through the right singular vector matrices of all the tree nodes top-down. */ j = 0; i__1 = nlvl; for (lvl = 1; lvl <= i__1; ++lvl) { lvl2 = (lvl << 1) - 1; /* Find the first node LF and last node LL on the current level LVL. */ if (lvl == 1) { lf = 1; ll = 1; } else { i__2 = lvl - 1; lf = pow_ii(&c__2, &i__2); ll = (lf << 1) - 1; } i__2 = lf; for (i__ = ll; i__ >= i__2; --i__) { im1 = i__ - 1; ic = iwork[inode + im1]; nl = iwork[ndiml + im1]; nr = iwork[ndimr + im1]; nlf = ic - nl; nrf = ic + 1; if (i__ == ll) { sqre = 0; } else { sqre = 1; } ++j; zlals0_(icompq, &nl, &nr, &sqre, nrhs, &b[nlf + b_dim1], ldb, &bx[ nlf + bx_dim1], ldbx, &perm[nlf + lvl * perm_dim1], & givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, & givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[ j], &s[j], &rwork[1], info); /* L180: */ } /* L190: */ } /* The nodes on the bottom level of the tree were solved by DLASDQ. The corresponding right singular vector matrices are in explicit form. Apply them back. */ ndb1 = (nd + 1) / 2; i__1 = nd; for (i__ = ndb1; i__ <= i__1; ++i__) { i1 = i__ - 1; ic = iwork[inode + i1]; nl = iwork[ndiml + i1]; nr = iwork[ndimr + i1]; nlp1 = nl + 1; if (i__ == nd) { nrp1 = nr; } else { nrp1 = nr + 1; } nlf = ic - nl; nrf = ic + 1; /* Since B and BX are complex, the following call to DGEMM is performed in two steps (real and imaginary parts). CALL DGEMM( 'T', 'N', NLP1, NRHS, NLP1, ONE, VT( NLF, 1 ), LDU, $ B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX ) */ j = nlp1 * *nrhs << 1; i__2 = *nrhs; for (jcol = 1; jcol <= i__2; ++jcol) { i__3 = nlf + nlp1 - 1; for (jrow = nlf; jrow <= i__3; ++jrow) { ++j; i__4 = jrow + jcol * b_dim1; rwork[j] = b[i__4].r; /* L200: */ } /* L210: */ } dgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b9, &vt[nlf + vt_dim1], ldu, & rwork[(nlp1 * *nrhs << 1) + 1], &nlp1, &c_b10, &rwork[1], & nlp1); j = nlp1 * *nrhs << 1; i__2 = *nrhs; for (jcol = 1; jcol <= i__2; ++jcol) { i__3 = nlf + nlp1 - 1; for (jrow = nlf; jrow <= i__3; ++jrow) { ++j; rwork[j] = d_imag(&b[jrow + jcol * b_dim1]); /* L220: */ } /* L230: */ } dgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b9, &vt[nlf + vt_dim1], ldu, & rwork[(nlp1 * *nrhs << 1) + 1], &nlp1, &c_b10, &rwork[nlp1 * * nrhs + 1], &nlp1); jreal = 0; jimag = nlp1 * *nrhs; i__2 = *nrhs; for (jcol = 1; jcol <= i__2; ++jcol) { i__3 = nlf + nlp1 - 1; for (jrow = nlf; jrow <= i__3; ++jrow) { ++jreal; ++jimag; i__4 = jrow + jcol * bx_dim1; i__5 = jreal; i__6 = jimag; z__1.r = rwork[i__5], z__1.i = rwork[i__6]; bx[i__4].r = z__1.r, bx[i__4].i = z__1.i; /* L240: */ } /* L250: */ } /* Since B and BX are complex, the following call to DGEMM is performed in two steps (real and imaginary parts). CALL DGEMM( 'T', 'N', NRP1, NRHS, NRP1, ONE, VT( NRF, 1 ), LDU, $ B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX ) */ j = nrp1 * *nrhs << 1; i__2 = *nrhs; for (jcol = 1; jcol <= i__2; ++jcol) { i__3 = nrf + nrp1 - 1; for (jrow = nrf; jrow <= i__3; ++jrow) { ++j; i__4 = jrow + jcol * b_dim1; rwork[j] = b[i__4].r; /* L260: */ } /* L270: */ } dgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b9, &vt[nrf + vt_dim1], ldu, & rwork[(nrp1 * *nrhs << 1) + 1], &nrp1, &c_b10, &rwork[1], & nrp1); j = nrp1 * *nrhs << 1; i__2 = *nrhs; for (jcol = 1; jcol <= i__2; ++jcol) { i__3 = nrf + nrp1 - 1; for (jrow = nrf; jrow <= i__3; ++jrow) { ++j; rwork[j] = d_imag(&b[jrow + jcol * b_dim1]); /* L280: */ } /* L290: */ } dgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b9, &vt[nrf + vt_dim1], ldu, & rwork[(nrp1 * *nrhs << 1) + 1], &nrp1, &c_b10, &rwork[nrp1 * * nrhs + 1], &nrp1); jreal = 0; jimag = nrp1 * *nrhs; i__2 = *nrhs; for (jcol = 1; jcol <= i__2; ++jcol) { i__3 = nrf + nrp1 - 1; for (jrow = nrf; jrow <= i__3; ++jrow) { ++jreal; ++jimag; i__4 = jrow + jcol * bx_dim1; i__5 = jreal; i__6 = jimag; z__1.r = rwork[i__5], z__1.i = rwork[i__6]; bx[i__4].r = z__1.r, bx[i__4].i = z__1.i; /* L300: */ } /* L310: */ } /* L320: */ } L330: return 0; /* End of ZLALSA */ } /* zlalsa_ */