#include "blaswrap.h" /* dlasd1.f -- translated by f2c (version 20061008). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" /* Table of constant values */ static integer c__0 = 0; static doublereal c_b7 = 1.; static integer c__1 = 1; static integer c_n1 = -1; /* Subroutine */ int dlasd1_(integer *nl, integer *nr, integer *sqre, doublereal *d__, doublereal *alpha, doublereal *beta, doublereal *u, integer *ldu, doublereal *vt, integer *ldvt, integer *idxq, integer * iwork, doublereal *work, integer *info) { /* System generated locals */ integer u_dim1, u_offset, vt_dim1, vt_offset, i__1; doublereal d__1, d__2; /* Local variables */ static integer i__, k, m, n, n1, n2, iq, iz, iu2, ldq, idx, ldu2, ivt2, idxc, idxp, ldvt2; extern /* Subroutine */ int dlasd2_(integer *, integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, integer *, integer *, integer *, integer *, integer *), dlasd3_( integer *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, integer *, doublereal *, integer *), dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dlamrg_(integer *, integer *, doublereal *, integer *, integer *, integer *); static integer isigma; extern /* Subroutine */ int xerbla_(char *, integer *); static doublereal orgnrm; static integer coltyp; /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DLASD1 computes the SVD of an upper bidiagonal N-by-M matrix B, where N = NL + NR + 1 and M = N + SQRE. DLASD1 is called from DLASD0. A related subroutine DLASD7 handles the case in which the singular values (and the singular vectors in factored form) are desired. DLASD1 computes the SVD as follows: ( D1(in) 0 0 0 ) B = U(in) * ( Z1' a Z2' b ) * VT(in) ( 0 0 D2(in) 0 ) = U(out) * ( D(out) 0) * VT(out) where Z' = (Z1' a Z2' b) = u' VT', and u is a vector of dimension M with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros elsewhere; and the entry b is empty if SQRE = 0. The left singular vectors of the original matrix are stored in U, and the transpose of the right singular vectors are stored in VT, and the singular values are in D. The algorithm consists of three stages: The first stage consists of deflating the size of the problem when there are multiple singular values or when there are zeros in the Z vector. For each such occurence the dimension of the secular equation problem is reduced by one. This stage is performed by the routine DLASD2. The second stage consists of calculating the updated singular values. This is done by finding the square roots of the roots of the secular equation via the routine DLASD4 (as called by DLASD3). This routine also calculates the singular vectors of the current problem. The final stage consists of computing the updated singular vectors directly using the updated singular values. The singular vectors for the current problem are multiplied with the singular vectors from the overall problem. Arguments ========= NL (input) INTEGER The row dimension of the upper block. NL >= 1. NR (input) INTEGER The row dimension of the lower block. NR >= 1. SQRE (input) 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. D (input/output) DOUBLE PRECISION array, dimension (N = NL+NR+1). On entry D(1:NL,1:NL) contains the singular values of the upper block; and D(NL+2:N) contains the singular values of the lower block. On exit D(1:N) contains the singular values of the modified matrix. ALPHA (input/output) DOUBLE PRECISION Contains the diagonal element associated with the added row. BETA (input/output) DOUBLE PRECISION Contains the off-diagonal element associated with the added row. U (input/output) DOUBLE PRECISION array, dimension(LDU,N) On entry U(1:NL, 1:NL) contains the left singular vectors of the upper block; U(NL+2:N, NL+2:N) contains the left singular vectors of the lower block. On exit U contains the left singular vectors of the bidiagonal matrix. LDU (input) INTEGER The leading dimension of the array U. LDU >= max( 1, N ). VT (input/output) DOUBLE PRECISION array, dimension(LDVT,M) where M = N + SQRE. On entry VT(1:NL+1, 1:NL+1)' contains the right singular vectors of the upper block; VT(NL+2:M, NL+2:M)' contains the right singular vectors of the lower block. On exit VT' contains the right singular vectors of the bidiagonal matrix. LDVT (input) INTEGER The leading dimension of the array VT. LDVT >= max( 1, M ). IDXQ (output) INTEGER array, dimension(N) This contains the permutation which will reintegrate the subproblem just solved back into sorted order, i.e. D( IDXQ( I = 1, N ) ) will be in ascending order. IWORK (workspace) INTEGER array, dimension( 4 * N ) WORK (workspace) DOUBLE PRECISION array, dimension( 3*M**2 + 2*M ) INFO (output) 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 Further Details =============== Based on contributions by Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA ===================================================================== Test the input parameters. Parameter adjustments */ --d__; u_dim1 = *ldu; u_offset = 1 + u_dim1; u -= u_offset; vt_dim1 = *ldvt; vt_offset = 1 + vt_dim1; vt -= vt_offset; --idxq; --iwork; --work; /* Function Body */ *info = 0; if (*nl < 1) { *info = -1; } else if (*nr < 1) { *info = -2; } else if (*sqre < 0 || *sqre > 1) { *info = -3; } if (*info != 0) { i__1 = -(*info); xerbla_("DLASD1", &i__1); return 0; } n = *nl + *nr + 1; m = n + *sqre; /* The following values are for bookkeeping purposes only. They are integer pointers which indicate the portion of the workspace used by a particular array in DLASD2 and DLASD3. */ ldu2 = n; ldvt2 = m; iz = 1; isigma = iz + m; iu2 = isigma + n; ivt2 = iu2 + ldu2 * n; iq = ivt2 + ldvt2 * m; idx = 1; idxc = idx + n; coltyp = idxc + n; idxp = coltyp + n; /* Scale. Computing MAX */ d__1 = abs(*alpha), d__2 = abs(*beta); orgnrm = max(d__1,d__2); d__[*nl + 1] = 0.; i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { if ((d__1 = d__[i__], abs(d__1)) > orgnrm) { orgnrm = (d__1 = d__[i__], abs(d__1)); } /* L10: */ } dlascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info); *alpha /= orgnrm; *beta /= orgnrm; /* Deflate singular values. */ dlasd2_(nl, nr, sqre, &k, &d__[1], &work[iz], alpha, beta, &u[u_offset], ldu, &vt[vt_offset], ldvt, &work[isigma], &work[iu2], &ldu2, & work[ivt2], &ldvt2, &iwork[idxp], &iwork[idx], &iwork[idxc], & idxq[1], &iwork[coltyp], info); /* Solve Secular Equation and update singular vectors. */ ldq = k; dlasd3_(nl, nr, sqre, &k, &d__[1], &work[iq], &ldq, &work[isigma], &u[ u_offset], ldu, &work[iu2], &ldu2, &vt[vt_offset], ldvt, &work[ ivt2], &ldvt2, &iwork[idxc], &iwork[coltyp], &work[iz], info); if (*info != 0) { return 0; } /* Unscale. */ dlascl_("G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info); /* Prepare the IDXQ sorting permutation. */ n1 = k; n2 = n - k; dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]); return 0; /* End of DLASD1 */ } /* dlasd1_ */