/* -- translated by f2c (version 20100827). 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__9 = 9; static integer c__0 = 0; static doublereal c_b15 = 1.; static integer c__1 = 1; static doublereal c_b29 = 0.; /* Subroutine */ int splicingdbdsdc_(char *uplo, char *compq, integer *n, doublereal * d__, doublereal *e, doublereal *u, integer *ldu, doublereal *vt, integer *ldvt, doublereal *q, integer *iq, doublereal *work, integer * iwork, integer *info) { /* System generated locals */ integer u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2; doublereal d__1; /* Builtin functions */ double d_sign(doublereal *, doublereal *), log(doublereal); /* Local variables */ static integer i__, j, k; static doublereal p, r__; static integer z__, ic, ii, kk; static doublereal cs; static integer is, iu; static doublereal sn; static integer nm1; static doublereal eps; static integer ivt, difl, difr, ierr, perm, mlvl, sqre; extern logical splicinglsame_(char *, char *); extern /* Subroutine */ int splicingdlasr_(char *, char *, char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *), splicingdcopy_(integer *, doublereal *, integer * , doublereal *, integer *), splicingdswap_(integer *, doublereal *, integer *, doublereal *, integer *); static integer poles, iuplo, nsize, start; extern /* Subroutine */ int splicingdlasd0_(integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, integer *, doublereal *, integer *); extern doublereal splicingdlamch_(char *); extern /* Subroutine */ int splicingdlasda_(integer *, integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *), splicingdlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), splicingdlasdq_(char *, integer *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *), splicingdlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *), splicingdlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *); extern integer splicingilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int splicingxerbla_(char *, integer *, ftnlen); static integer givcol; extern doublereal splicingdlanst_(char *, integer *, doublereal *, doublereal *); static integer icompq; static doublereal orgnrm; static integer givnum, givptr, qstart, smlsiz, wstart, smlszp; /* -- LAPACK routine (version 3.3.1) -- -- LAPACK is a software package provided by Univ. of Tennessee, -- -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -- April 2011 -- Purpose ======= DBDSDC computes the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT, using a divide and conquer method, where S is a diagonal matrix with non-negative diagonal elements (the singular values of B), and U and VT are orthogonal matrices of left and right singular vectors, respectively. DBDSDC can be used to compute all singular values, and optionally, singular vectors or singular vectors in compact form. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See DLASD3 for details. The code currently calls DLASDQ if singular values only are desired. However, it can be slightly modified to compute singular values using the divide and conquer method. Arguments ========= UPLO (input) CHARACTER*1 = 'U': B is upper bidiagonal. = 'L': B is lower bidiagonal. COMPQ (input) CHARACTER*1 Specifies whether singular vectors are to be computed as follows: = 'N': Compute singular values only; = 'P': Compute singular values and compute singular vectors in compact form; = 'I': Compute singular values and singular vectors. N (input) INTEGER The order of the matrix B. N >= 0. D (input/output) DOUBLE PRECISION array, dimension (N) On entry, the n diagonal elements of the bidiagonal matrix B. On exit, if INFO=0, the singular values of B. E (input/output) DOUBLE PRECISION array, dimension (N-1) On entry, the elements of E contain the offdiagonal elements of the bidiagonal matrix whose SVD is desired. On exit, E has been destroyed. U (output) DOUBLE PRECISION array, dimension (LDU,N) If COMPQ = 'I', then: On exit, if INFO = 0, U contains the left singular vectors of the bidiagonal matrix. For other values of COMPQ, U is not referenced. LDU (input) INTEGER The leading dimension of the array U. LDU >= 1. If singular vectors are desired, then LDU >= max( 1, N ). VT (output) DOUBLE PRECISION array, dimension (LDVT,N) If COMPQ = 'I', then: On exit, if INFO = 0, VT**T contains the right singular vectors of the bidiagonal matrix. For other values of COMPQ, VT is not referenced. LDVT (input) INTEGER The leading dimension of the array VT. LDVT >= 1. If singular vectors are desired, then LDVT >= max( 1, N ). Q (output) DOUBLE PRECISION array, dimension (LDQ) If COMPQ = 'P', then: On exit, if INFO = 0, Q and IQ contain the left and right singular vectors in a compact form, requiring O(N log N) space instead of 2*N**2. In particular, Q contains all the DOUBLE PRECISION data in LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1)))) words of memory, where SMLSIZ is returned by ILAENV and is equal to the maximum size of the subproblems at the bottom of the computation tree (usually about 25). For other values of COMPQ, Q is not referenced. IQ (output) INTEGER array, dimension (LDIQ) If COMPQ = 'P', then: On exit, if INFO = 0, Q and IQ contain the left and right singular vectors in a compact form, requiring O(N log N) space instead of 2*N**2. In particular, IQ contains all INTEGER data in LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1)))) words of memory, where SMLSIZ is returned by ILAENV and is equal to the maximum size of the subproblems at the bottom of the computation tree (usually about 25). For other values of COMPQ, IQ is not referenced. WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) If COMPQ = 'N' then LWORK >= (4 * N). If COMPQ = 'P' then LWORK >= (6 * N). If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N). IWORK (workspace) INTEGER array, dimension (8*N) INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The algorithm failed to compute a singular value. The update process of divide and conquer failed. Further Details =============== Based on contributions by Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA ===================================================================== Changed dimension statement in comment describing E from (N) to (N-1). Sven, 17 Feb 05. ===================================================================== Test the input parameters. Parameter adjustments */ --d__; --e; u_dim1 = *ldu; u_offset = 1 + u_dim1; u -= u_offset; vt_dim1 = *ldvt; vt_offset = 1 + vt_dim1; vt -= vt_offset; --q; --iq; --work; --iwork; /* Function Body */ *info = 0; iuplo = 0; if (splicinglsame_(uplo, "U")) { iuplo = 1; } if (splicinglsame_(uplo, "L")) { iuplo = 2; } if (splicinglsame_(compq, "N")) { icompq = 0; } else if (splicinglsame_(compq, "P")) { icompq = 1; } else if (splicinglsame_(compq, "I")) { icompq = 2; } else { icompq = -1; } if (iuplo == 0) { *info = -1; } else if (icompq < 0) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ldu < 1 || icompq == 2 && *ldu < *n) { *info = -7; } else if (*ldvt < 1 || icompq == 2 && *ldvt < *n) { *info = -9; } if (*info != 0) { i__1 = -(*info); splicingxerbla_("DBDSDC", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } smlsiz = splicingilaenv_(&c__9, "DBDSDC", " ", &c__0, &c__0, &c__0, &c__0, ( ftnlen)6, (ftnlen)1); if (*n == 1) { if (icompq == 1) { q[1] = d_sign(&c_b15, &d__[1]); q[smlsiz * *n + 1] = 1.; } else if (icompq == 2) { u[u_dim1 + 1] = d_sign(&c_b15, &d__[1]); vt[vt_dim1 + 1] = 1.; } d__[1] = abs(d__[1]); return 0; } nm1 = *n - 1; /* If matrix lower bidiagonal, rotate to be upper bidiagonal by applying Givens rotations on the left */ wstart = 1; qstart = 3; if (icompq == 1) { splicingdcopy_(n, &d__[1], &c__1, &q[1], &c__1); i__1 = *n - 1; splicingdcopy_(&i__1, &e[1], &c__1, &q[*n + 1], &c__1); } if (iuplo == 2) { qstart = 5; wstart = (*n << 1) - 1; i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { splicingdlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); d__[i__] = r__; e[i__] = sn * d__[i__ + 1]; d__[i__ + 1] = cs * d__[i__ + 1]; if (icompq == 1) { q[i__ + (*n << 1)] = cs; q[i__ + *n * 3] = sn; } else if (icompq == 2) { work[i__] = cs; work[nm1 + i__] = -sn; } /* L10: */ } } /* If ICOMPQ = 0, use DLASDQ to compute the singular values. */ if (icompq == 0) { splicingdlasdq_("U", &c__0, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[ vt_offset], ldvt, &u[u_offset], ldu, &u[u_offset], ldu, &work[ wstart], info); goto L40; } /* If N is smaller than the minimum divide size SMLSIZ, then solve the problem with another solver. */ if (*n <= smlsiz) { if (icompq == 2) { splicingdlaset_("A", n, n, &c_b29, &c_b15, &u[u_offset], ldu); splicingdlaset_("A", n, n, &c_b29, &c_b15, &vt[vt_offset], ldvt); splicingdlasdq_("U", &c__0, n, n, n, &c__0, &d__[1], &e[1], &vt[vt_offset] , ldvt, &u[u_offset], ldu, &u[u_offset], ldu, &work[ wstart], info); } else if (icompq == 1) { iu = 1; ivt = iu + *n; splicingdlaset_("A", n, n, &c_b29, &c_b15, &q[iu + (qstart - 1) * *n], n); splicingdlaset_("A", n, n, &c_b29, &c_b15, &q[ivt + (qstart - 1) * *n], n); splicingdlasdq_("U", &c__0, n, n, n, &c__0, &d__[1], &e[1], &q[ivt + ( qstart - 1) * *n], n, &q[iu + (qstart - 1) * *n], n, &q[ iu + (qstart - 1) * *n], n, &work[wstart], info); } goto L40; } if (icompq == 2) { splicingdlaset_("A", n, n, &c_b29, &c_b15, &u[u_offset], ldu); splicingdlaset_("A", n, n, &c_b29, &c_b15, &vt[vt_offset], ldvt); } /* Scale. */ orgnrm = splicingdlanst_("M", n, &d__[1], &e[1]); if (orgnrm == 0.) { return 0; } splicingdlascl_("G", &c__0, &c__0, &orgnrm, &c_b15, n, &c__1, &d__[1], n, &ierr); splicingdlascl_("G", &c__0, &c__0, &orgnrm, &c_b15, &nm1, &c__1, &e[1], &nm1, & ierr); eps = splicingdlamch_("Epsilon") * .9; mlvl = (integer) (log((doublereal) (*n) / (doublereal) (smlsiz + 1)) / log(2.)) + 1; smlszp = smlsiz + 1; if (icompq == 1) { iu = 1; ivt = smlsiz + 1; difl = ivt + smlszp; difr = difl + mlvl; z__ = difr + (mlvl << 1); ic = z__ + mlvl; is = ic + 1; poles = is + 1; givnum = poles + (mlvl << 1); k = 1; givptr = 2; perm = 3; givcol = perm + mlvl; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if ((d__1 = d__[i__], abs(d__1)) < eps) { d__[i__] = d_sign(&eps, &d__[i__]); } /* L20: */ } start = 1; sqre = 0; i__1 = nm1; for (i__ = 1; i__ <= i__1; ++i__) { if ((d__1 = e[i__], abs(d__1)) < eps || i__ == nm1) { /* Subproblem found. First determine its size and then apply divide and conquer on it. */ if (i__ < nm1) { /* A subproblem with E(I) small for I < NM1. */ nsize = i__ - start + 1; } else if ((d__1 = e[i__], abs(d__1)) >= eps) { /* A subproblem with E(NM1) not too small but I = NM1. */ nsize = *n - start + 1; } else { /* A subproblem with E(NM1) small. This implies an 1-by-1 subproblem at D(N). Solve this 1-by-1 problem first. */ nsize = i__ - start + 1; if (icompq == 2) { u[*n + *n * u_dim1] = d_sign(&c_b15, &d__[*n]); vt[*n + *n * vt_dim1] = 1.; } else if (icompq == 1) { q[*n + (qstart - 1) * *n] = d_sign(&c_b15, &d__[*n]); q[*n + (smlsiz + qstart - 1) * *n] = 1.; } d__[*n] = (d__1 = d__[*n], abs(d__1)); } if (icompq == 2) { splicingdlasd0_(&nsize, &sqre, &d__[start], &e[start], &u[start + start * u_dim1], ldu, &vt[start + start * vt_dim1], ldvt, &smlsiz, &iwork[1], &work[wstart], info); } else { splicingdlasda_(&icompq, &smlsiz, &nsize, &sqre, &d__[start], &e[ start], &q[start + (iu + qstart - 2) * *n], n, &q[ start + (ivt + qstart - 2) * *n], &iq[start + k * *n], &q[start + (difl + qstart - 2) * *n], &q[start + ( difr + qstart - 2) * *n], &q[start + (z__ + qstart - 2) * *n], &q[start + (poles + qstart - 2) * *n], &iq[ start + givptr * *n], &iq[start + givcol * *n], n, & iq[start + perm * *n], &q[start + (givnum + qstart - 2) * *n], &q[start + (ic + qstart - 2) * *n], &q[ start + (is + qstart - 2) * *n], &work[wstart], & iwork[1], info); } if (*info != 0) { return 0; } start = i__ + 1; } /* L30: */ } /* Unscale */ splicingdlascl_("G", &c__0, &c__0, &c_b15, &orgnrm, n, &c__1, &d__[1], n, &ierr); L40: /* Use Selection Sort to minimize swaps of singular vectors */ i__1 = *n; for (ii = 2; ii <= i__1; ++ii) { i__ = ii - 1; kk = i__; p = d__[i__]; i__2 = *n; for (j = ii; j <= i__2; ++j) { if (d__[j] > p) { kk = j; p = d__[j]; } /* L50: */ } if (kk != i__) { d__[kk] = d__[i__]; d__[i__] = p; if (icompq == 1) { iq[i__] = kk; } else if (icompq == 2) { splicingdswap_(n, &u[i__ * u_dim1 + 1], &c__1, &u[kk * u_dim1 + 1], & c__1); splicingdswap_(n, &vt[i__ + vt_dim1], ldvt, &vt[kk + vt_dim1], ldvt); } } else if (icompq == 1) { iq[i__] = i__; } /* L60: */ } /* If ICOMPQ = 1, use IQ(N,1) as the indicator for UPLO */ if (icompq == 1) { if (iuplo == 1) { iq[*n] = 1; } else { iq[*n] = 0; } } /* If B is lower bidiagonal, update U by those Givens rotations which rotated B to be upper bidiagonal */ if (iuplo == 2 && icompq == 2) { splicingdlasr_("L", "V", "B", n, n, &work[1], &work[*n], &u[u_offset], ldu); } return 0; /* End of DBDSDC */ } /* splicingdbdsdc_ */