/* -- translated by f2c (version 20191129). 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__1 = 1; static logical c_false = FALSE_; static integer c__2 = 2; static doublereal c_b26 = 1.; static doublereal c_b30 = 0.; static logical c_true = TRUE_; /* > \brief \b DTRSYL =========== DOCUMENTATION =========== Online html documentation available at http://www.netlib.org/lapack/explore-html/ > \htmlonly > Download DTRSYL + dependencies > > [TGZ] > > [ZIP] > > [TXT] > \endhtmlonly Definition: =========== SUBROUTINE DTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC, SCALE, INFO ) CHARACTER TRANA, TRANB INTEGER INFO, ISGN, LDA, LDB, LDC, M, N DOUBLE PRECISION SCALE DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ) > \par Purpose: ============= > > \verbatim > > DTRSYL solves the real Sylvester matrix equation: > > op(A)*X + X*op(B) = scale*C or > op(A)*X - X*op(B) = scale*C, > > where op(A) = A or A**T, and A and B are both upper quasi- > triangular. A is M-by-M and B is N-by-N; the right hand side C and > the solution X are M-by-N; and scale is an output scale factor, set > <= 1 to avoid overflow in X. > > A and B must be in Schur canonical form (as returned by DHSEQR), that > is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; > each 2-by-2 diagonal block has its diagonal elements equal and its > off-diagonal elements of opposite sign. > \endverbatim Arguments: ========== > \param[in] TRANA > \verbatim > TRANA is CHARACTER*1 > Specifies the option op(A): > = 'N': op(A) = A (No transpose) > = 'T': op(A) = A**T (Transpose) > = 'C': op(A) = A**H (Conjugate transpose = Transpose) > \endverbatim > > \param[in] TRANB > \verbatim > TRANB is CHARACTER*1 > Specifies the option op(B): > = 'N': op(B) = B (No transpose) > = 'T': op(B) = B**T (Transpose) > = 'C': op(B) = B**H (Conjugate transpose = Transpose) > \endverbatim > > \param[in] ISGN > \verbatim > ISGN is INTEGER > Specifies the sign in the equation: > = +1: solve op(A)*X + X*op(B) = scale*C > = -1: solve op(A)*X - X*op(B) = scale*C > \endverbatim > > \param[in] M > \verbatim > M is INTEGER > The order of the matrix A, and the number of rows in the > matrices X and C. M >= 0. > \endverbatim > > \param[in] N > \verbatim > N is INTEGER > The order of the matrix B, and the number of columns in the > matrices X and C. N >= 0. > \endverbatim > > \param[in] A > \verbatim > A is DOUBLE PRECISION array, dimension (LDA,M) > The upper quasi-triangular matrix A, in Schur canonical form. > \endverbatim > > \param[in] LDA > \verbatim > LDA is INTEGER > The leading dimension of the array A. LDA >= max(1,M). > \endverbatim > > \param[in] B > \verbatim > B is DOUBLE PRECISION array, dimension (LDB,N) > The upper quasi-triangular matrix B, in Schur canonical form. > \endverbatim > > \param[in] LDB > \verbatim > LDB is INTEGER > The leading dimension of the array B. LDB >= max(1,N). > \endverbatim > > \param[in,out] C > \verbatim > C is DOUBLE PRECISION array, dimension (LDC,N) > On entry, the M-by-N right hand side matrix C. > On exit, C is overwritten by the solution matrix X. > \endverbatim > > \param[in] LDC > \verbatim > LDC is INTEGER > The leading dimension of the array C. LDC >= max(1,M) > \endverbatim > > \param[out] SCALE > \verbatim > SCALE is DOUBLE PRECISION > The scale factor, scale, set <= 1 to avoid overflow in X. > \endverbatim > > \param[out] INFO > \verbatim > INFO is INTEGER > = 0: successful exit > < 0: if INFO = -i, the i-th argument had an illegal value > = 1: A and B have common or very close eigenvalues; perturbed > values were used to solve the equation (but the matrices > A and B are unchanged). > \endverbatim Authors: ======== > \author Univ. of Tennessee > \author Univ. of California Berkeley > \author Univ. of Colorado Denver > \author NAG Ltd. > \date November 2011 > \ingroup doubleSYcomputational ===================================================================== Subroutine */ int igraphdtrsyl_(char *trana, char *tranb, integer *isgn, integer *m, integer *n, doublereal *a, integer *lda, doublereal *b, integer * ldb, doublereal *c__, integer *ldc, doublereal *scale, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2; /* Local variables */ integer j, k, l; doublereal x[4] /* was [2][2] */; integer k1, k2, l1, l2; doublereal a11, db, da11, vec[4] /* was [2][2] */, dum[1], eps, sgn; extern doublereal igraphddot_(integer *, doublereal *, integer *, doublereal *, integer *); integer ierr; doublereal smin, suml, sumr; extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *, integer *); extern logical igraphlsame_(char *, char *); integer knext, lnext; doublereal xnorm; extern /* Subroutine */ int igraphdlaln2_(logical *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal * , doublereal *, integer *, doublereal *, doublereal *, integer *), igraphdlasy2_(logical *, logical *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *), igraphdlabad_(doublereal *, doublereal *); extern doublereal igraphdlamch_(char *), igraphdlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); doublereal scaloc; extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen); doublereal bignum; logical notrna, notrnb; doublereal smlnum; /* -- LAPACK computational routine (version 3.4.0) -- -- LAPACK is a software package provided by Univ. of Tennessee, -- -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- November 2011 ===================================================================== Decode and Test input parameters Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; /* Function Body */ notrna = igraphlsame_(trana, "N"); notrnb = igraphlsame_(tranb, "N"); *info = 0; if (! notrna && ! igraphlsame_(trana, "T") && ! igraphlsame_( trana, "C")) { *info = -1; } else if (! notrnb && ! igraphlsame_(tranb, "T") && ! igraphlsame_(tranb, "C")) { *info = -2; } else if (*isgn != 1 && *isgn != -1) { *info = -3; } else if (*m < 0) { *info = -4; } else if (*n < 0) { *info = -5; } else if (*lda < max(1,*m)) { *info = -7; } else if (*ldb < max(1,*n)) { *info = -9; } else if (*ldc < max(1,*m)) { *info = -11; } if (*info != 0) { i__1 = -(*info); igraphxerbla_("DTRSYL", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ *scale = 1.; if (*m == 0 || *n == 0) { return 0; } /* Set constants to control overflow */ eps = igraphdlamch_("P"); smlnum = igraphdlamch_("S"); bignum = 1. / smlnum; igraphdlabad_(&smlnum, &bignum); smlnum = smlnum * (doublereal) (*m * *n) / eps; bignum = 1. / smlnum; /* Computing MAX */ d__1 = smlnum, d__2 = eps * igraphdlange_("M", m, m, &a[a_offset], lda, dum), d__1 = max(d__1,d__2), d__2 = eps * igraphdlange_("M", n, n, &b[b_offset], ldb, dum); smin = max(d__1,d__2); sgn = (doublereal) (*isgn); if (notrna && notrnb) { /* Solve A*X + ISGN*X*B = scale*C. The (K,L)th block of X is determined starting from bottom-left corner column by column by A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L) Where M L-1 R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]. I=K+1 J=1 Start column loop (index = L) L1 (L2) : column index of the first (first) row of X(K,L). */ lnext = 1; i__1 = *n; for (l = 1; l <= i__1; ++l) { if (l < lnext) { goto L60; } if (l == *n) { l1 = l; l2 = l; } else { if (b[l + 1 + l * b_dim1] != 0.) { l1 = l; l2 = l + 1; lnext = l + 2; } else { l1 = l; l2 = l; lnext = l + 1; } } /* Start row loop (index = K) K1 (K2): row index of the first (last) row of X(K,L). */ knext = *m; for (k = *m; k >= 1; --k) { if (k > knext) { goto L50; } if (k == 1) { k1 = k; k2 = k; } else { if (a[k + (k - 1) * a_dim1] != 0.) { k1 = k - 1; k2 = k; knext = k - 2; } else { k1 = k; k2 = k; knext = k - 1; } } if (l1 == l2 && k1 == k2) { i__2 = *m - k1; /* Computing MIN */ i__3 = k1 + 1; /* Computing MIN */ i__4 = k1 + 1; suml = igraphddot_(&i__2, &a[k1 + min(i__3,*m) * a_dim1], lda, & c__[min(i__4,*m) + l1 * c_dim1], &c__1); i__2 = l1 - 1; sumr = igraphddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); scaloc = 1.; a11 = a[k1 + k1 * a_dim1] + sgn * b[l1 + l1 * b_dim1]; da11 = abs(a11); if (da11 <= smin) { a11 = smin; da11 = smin; *info = 1; } db = abs(vec[0]); if (da11 < 1. && db > 1.) { if (db > bignum * da11) { scaloc = 1. / db; } } x[0] = vec[0] * scaloc / a11; if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L10: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; } else if (l1 == l2 && k1 != k2) { i__2 = *m - k2; /* Computing MIN */ i__3 = k2 + 1; /* Computing MIN */ i__4 = k2 + 1; suml = igraphddot_(&i__2, &a[k1 + min(i__3,*m) * a_dim1], lda, & c__[min(i__4,*m) + l1 * c_dim1], &c__1); i__2 = l1 - 1; sumr = igraphddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__2 = *m - k2; /* Computing MIN */ i__3 = k2 + 1; /* Computing MIN */ i__4 = k2 + 1; suml = igraphddot_(&i__2, &a[k2 + min(i__3,*m) * a_dim1], lda, & c__[min(i__4,*m) + l1 * c_dim1], &c__1); i__2 = l1 - 1; sumr = igraphddot_(&i__2, &c__[k2 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); d__1 = -sgn * b[l1 + l1 * b_dim1]; igraphdlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &a[k1 + k1 * a_dim1], lda, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L20: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k2 + l1 * c_dim1] = x[1]; } else if (l1 != l2 && k1 == k2) { i__2 = *m - k1; /* Computing MIN */ i__3 = k1 + 1; /* Computing MIN */ i__4 = k1 + 1; suml = igraphddot_(&i__2, &a[k1 + min(i__3,*m) * a_dim1], lda, & c__[min(i__4,*m) + l1 * c_dim1], &c__1); i__2 = l1 - 1; sumr = igraphddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = sgn * (c__[k1 + l1 * c_dim1] - (suml + sgn * sumr)); i__2 = *m - k1; /* Computing MIN */ i__3 = k1 + 1; /* Computing MIN */ i__4 = k1 + 1; suml = igraphddot_(&i__2, &a[k1 + min(i__3,*m) * a_dim1], lda, & c__[min(i__4,*m) + l2 * c_dim1], &c__1); i__2 = l1 - 1; sumr = igraphddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l2 * b_dim1 + 1], &c__1); vec[1] = sgn * (c__[k1 + l2 * c_dim1] - (suml + sgn * sumr)); d__1 = -sgn * a[k1 + k1 * a_dim1]; igraphdlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &b[l1 + l1 * b_dim1], ldb, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L30: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[1]; } else if (l1 != l2 && k1 != k2) { i__2 = *m - k2; /* Computing MIN */ i__3 = k2 + 1; /* Computing MIN */ i__4 = k2 + 1; suml = igraphddot_(&i__2, &a[k1 + min(i__3,*m) * a_dim1], lda, & c__[min(i__4,*m) + l1 * c_dim1], &c__1); i__2 = l1 - 1; sumr = igraphddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__2 = *m - k2; /* Computing MIN */ i__3 = k2 + 1; /* Computing MIN */ i__4 = k2 + 1; suml = igraphddot_(&i__2, &a[k1 + min(i__3,*m) * a_dim1], lda, & c__[min(i__4,*m) + l2 * c_dim1], &c__1); i__2 = l1 - 1; sumr = igraphddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l2 * b_dim1 + 1], &c__1); vec[2] = c__[k1 + l2 * c_dim1] - (suml + sgn * sumr); i__2 = *m - k2; /* Computing MIN */ i__3 = k2 + 1; /* Computing MIN */ i__4 = k2 + 1; suml = igraphddot_(&i__2, &a[k2 + min(i__3,*m) * a_dim1], lda, & c__[min(i__4,*m) + l1 * c_dim1], &c__1); i__2 = l1 - 1; sumr = igraphddot_(&i__2, &c__[k2 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); i__2 = *m - k2; /* Computing MIN */ i__3 = k2 + 1; /* Computing MIN */ i__4 = k2 + 1; suml = igraphddot_(&i__2, &a[k2 + min(i__3,*m) * a_dim1], lda, & c__[min(i__4,*m) + l2 * c_dim1], &c__1); i__2 = l1 - 1; sumr = igraphddot_(&i__2, &c__[k2 + c_dim1], ldc, &b[l2 * b_dim1 + 1], &c__1); vec[3] = c__[k2 + l2 * c_dim1] - (suml + sgn * sumr); igraphdlasy2_(&c_false, &c_false, isgn, &c__2, &c__2, &a[k1 + k1 * a_dim1], lda, &b[l1 + l1 * b_dim1], ldb, vec, &c__2, &scaloc, x, &c__2, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L40: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[2]; c__[k2 + l1 * c_dim1] = x[1]; c__[k2 + l2 * c_dim1] = x[3]; } L50: ; } L60: ; } } else if (! notrna && notrnb) { /* Solve A**T *X + ISGN*X*B = scale*C. The (K,L)th block of X is determined starting from upper-left corner column by column by A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L) Where K-1 T L-1 R(K,L) = SUM [A(I,K)**T*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)] I=1 J=1 Start column loop (index = L) L1 (L2): column index of the first (last) row of X(K,L) */ lnext = 1; i__1 = *n; for (l = 1; l <= i__1; ++l) { if (l < lnext) { goto L120; } if (l == *n) { l1 = l; l2 = l; } else { if (b[l + 1 + l * b_dim1] != 0.) { l1 = l; l2 = l + 1; lnext = l + 2; } else { l1 = l; l2 = l; lnext = l + 1; } } /* Start row loop (index = K) K1 (K2): row index of the first (last) row of X(K,L) */ knext = 1; i__2 = *m; for (k = 1; k <= i__2; ++k) { if (k < knext) { goto L110; } if (k == *m) { k1 = k; k2 = k; } else { if (a[k + 1 + k * a_dim1] != 0.) { k1 = k; k2 = k + 1; knext = k + 2; } else { k1 = k; k2 = k; knext = k + 1; } } if (l1 == l2 && k1 == k2) { i__3 = k1 - 1; suml = igraphddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = igraphddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); scaloc = 1.; a11 = a[k1 + k1 * a_dim1] + sgn * b[l1 + l1 * b_dim1]; da11 = abs(a11); if (da11 <= smin) { a11 = smin; da11 = smin; *info = 1; } db = abs(vec[0]); if (da11 < 1. && db > 1.) { if (db > bignum * da11) { scaloc = 1. / db; } } x[0] = vec[0] * scaloc / a11; if (scaloc != 1.) { i__3 = *n; for (j = 1; j <= i__3; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L70: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; } else if (l1 == l2 && k1 != k2) { i__3 = k1 - 1; suml = igraphddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = igraphddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__3 = k1 - 1; suml = igraphddot_(&i__3, &a[k2 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = igraphddot_(&i__3, &c__[k2 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); d__1 = -sgn * b[l1 + l1 * b_dim1]; igraphdlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &a[k1 + k1 * a_dim1], lda, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__3 = *n; for (j = 1; j <= i__3; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L80: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k2 + l1 * c_dim1] = x[1]; } else if (l1 != l2 && k1 == k2) { i__3 = k1 - 1; suml = igraphddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = igraphddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = sgn * (c__[k1 + l1 * c_dim1] - (suml + sgn * sumr)); i__3 = k1 - 1; suml = igraphddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l2 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = igraphddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l2 * b_dim1 + 1], &c__1); vec[1] = sgn * (c__[k1 + l2 * c_dim1] - (suml + sgn * sumr)); d__1 = -sgn * a[k1 + k1 * a_dim1]; igraphdlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &b[l1 + l1 * b_dim1], ldb, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__3 = *n; for (j = 1; j <= i__3; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L90: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[1]; } else if (l1 != l2 && k1 != k2) { i__3 = k1 - 1; suml = igraphddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = igraphddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__3 = k1 - 1; suml = igraphddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l2 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = igraphddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l2 * b_dim1 + 1], &c__1); vec[2] = c__[k1 + l2 * c_dim1] - (suml + sgn * sumr); i__3 = k1 - 1; suml = igraphddot_(&i__3, &a[k2 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = igraphddot_(&i__3, &c__[k2 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); i__3 = k1 - 1; suml = igraphddot_(&i__3, &a[k2 * a_dim1 + 1], &c__1, &c__[l2 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = igraphddot_(&i__3, &c__[k2 + c_dim1], ldc, &b[l2 * b_dim1 + 1], &c__1); vec[3] = c__[k2 + l2 * c_dim1] - (suml + sgn * sumr); igraphdlasy2_(&c_true, &c_false, isgn, &c__2, &c__2, &a[k1 + k1 * a_dim1], lda, &b[l1 + l1 * b_dim1], ldb, vec, & c__2, &scaloc, x, &c__2, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__3 = *n; for (j = 1; j <= i__3; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L100: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[2]; c__[k2 + l1 * c_dim1] = x[1]; c__[k2 + l2 * c_dim1] = x[3]; } L110: ; } L120: ; } } else if (! notrna && ! notrnb) { /* Solve A**T*X + ISGN*X*B**T = scale*C. The (K,L)th block of X is determined starting from top-right corner column by column by A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L)**T = C(K,L) - R(K,L) Where K-1 N R(K,L) = SUM [A(I,K)**T*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)**T]. I=1 J=L+1 Start column loop (index = L) L1 (L2): column index of the first (last) row of X(K,L) */ lnext = *n; for (l = *n; l >= 1; --l) { if (l > lnext) { goto L180; } if (l == 1) { l1 = l; l2 = l; } else { if (b[l + (l - 1) * b_dim1] != 0.) { l1 = l - 1; l2 = l; lnext = l - 2; } else { l1 = l; l2 = l; lnext = l - 1; } } /* Start row loop (index = K) K1 (K2): row index of the first (last) row of X(K,L) */ knext = 1; i__1 = *m; for (k = 1; k <= i__1; ++k) { if (k < knext) { goto L170; } if (k == *m) { k1 = k; k2 = k; } else { if (a[k + 1 + k * a_dim1] != 0.) { k1 = k; k2 = k + 1; knext = k + 2; } else { k1 = k; k2 = k; knext = k + 1; } } if (l1 == l2 && k1 == k2) { i__2 = k1 - 1; suml = igraphddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__2 = *n - l1; /* Computing MIN */ i__3 = l1 + 1; /* Computing MIN */ i__4 = l1 + 1; sumr = igraphddot_(&i__2, &c__[k1 + min(i__3,*n) * c_dim1], ldc, &b[l1 + min(i__4,*n) * b_dim1], ldb); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); scaloc = 1.; a11 = a[k1 + k1 * a_dim1] + sgn * b[l1 + l1 * b_dim1]; da11 = abs(a11); if (da11 <= smin) { a11 = smin; da11 = smin; *info = 1; } db = abs(vec[0]); if (da11 < 1. && db > 1.) { if (db > bignum * da11) { scaloc = 1. / db; } } x[0] = vec[0] * scaloc / a11; if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L130: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; } else if (l1 == l2 && k1 != k2) { i__2 = k1 - 1; suml = igraphddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = igraphddot_(&i__2, &c__[k1 + min(i__3,*n) * c_dim1], ldc, &b[l1 + min(i__4,*n) * b_dim1], ldb); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__2 = k1 - 1; suml = igraphddot_(&i__2, &a[k2 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = igraphddot_(&i__2, &c__[k2 + min(i__3,*n) * c_dim1], ldc, &b[l1 + min(i__4,*n) * b_dim1], ldb); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); d__1 = -sgn * b[l1 + l1 * b_dim1]; igraphdlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &a[k1 + k1 * a_dim1], lda, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L140: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k2 + l1 * c_dim1] = x[1]; } else if (l1 != l2 && k1 == k2) { i__2 = k1 - 1; suml = igraphddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = igraphddot_(&i__2, &c__[k1 + min(i__3,*n) * c_dim1], ldc, &b[l1 + min(i__4,*n) * b_dim1], ldb); vec[0] = sgn * (c__[k1 + l1 * c_dim1] - (suml + sgn * sumr)); i__2 = k1 - 1; suml = igraphddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l2 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = igraphddot_(&i__2, &c__[k1 + min(i__3,*n) * c_dim1], ldc, &b[l2 + min(i__4,*n) * b_dim1], ldb); vec[1] = sgn * (c__[k1 + l2 * c_dim1] - (suml + sgn * sumr)); d__1 = -sgn * a[k1 + k1 * a_dim1]; igraphdlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &b[l1 + l1 * b_dim1], ldb, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L150: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[1]; } else if (l1 != l2 && k1 != k2) { i__2 = k1 - 1; suml = igraphddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = igraphddot_(&i__2, &c__[k1 + min(i__3,*n) * c_dim1], ldc, &b[l1 + min(i__4,*n) * b_dim1], ldb); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__2 = k1 - 1; suml = igraphddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l2 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = igraphddot_(&i__2, &c__[k1 + min(i__3,*n) * c_dim1], ldc, &b[l2 + min(i__4,*n) * b_dim1], ldb); vec[2] = c__[k1 + l2 * c_dim1] - (suml + sgn * sumr); i__2 = k1 - 1; suml = igraphddot_(&i__2, &a[k2 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = igraphddot_(&i__2, &c__[k2 + min(i__3,*n) * c_dim1], ldc, &b[l1 + min(i__4,*n) * b_dim1], ldb); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); i__2 = k1 - 1; suml = igraphddot_(&i__2, &a[k2 * a_dim1 + 1], &c__1, &c__[l2 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = igraphddot_(&i__2, &c__[k2 + min(i__3,*n) * c_dim1], ldc, &b[l2 + min(i__4,*n) * b_dim1], ldb); vec[3] = c__[k2 + l2 * c_dim1] - (suml + sgn * sumr); igraphdlasy2_(&c_true, &c_true, isgn, &c__2, &c__2, &a[k1 + k1 * a_dim1], lda, &b[l1 + l1 * b_dim1], ldb, vec, & c__2, &scaloc, x, &c__2, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L160: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[2]; c__[k2 + l1 * c_dim1] = x[1]; c__[k2 + l2 * c_dim1] = x[3]; } L170: ; } L180: ; } } else if (notrna && ! notrnb) { /* Solve A*X + ISGN*X*B**T = scale*C. The (K,L)th block of X is determined starting from bottom-right corner column by column by A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L)**T = C(K,L) - R(K,L) Where M N R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)**T]. I=K+1 J=L+1 Start column loop (index = L) L1 (L2): column index of the first (last) row of X(K,L) */ lnext = *n; for (l = *n; l >= 1; --l) { if (l > lnext) { goto L240; } if (l == 1) { l1 = l; l2 = l; } else { if (b[l + (l - 1) * b_dim1] != 0.) { l1 = l - 1; l2 = l; lnext = l - 2; } else { l1 = l; l2 = l; lnext = l - 1; } } /* Start row loop (index = K) K1 (K2): row index of the first (last) row of X(K,L) */ knext = *m; for (k = *m; k >= 1; --k) { if (k > knext) { goto L230; } if (k == 1) { k1 = k; k2 = k; } else { if (a[k + (k - 1) * a_dim1] != 0.) { k1 = k - 1; k2 = k; knext = k - 2; } else { k1 = k; k2 = k; knext = k - 1; } } if (l1 == l2 && k1 == k2) { i__1 = *m - k1; /* Computing MIN */ i__2 = k1 + 1; /* Computing MIN */ i__3 = k1 + 1; suml = igraphddot_(&i__1, &a[k1 + min(i__2,*m) * a_dim1], lda, & c__[min(i__3,*m) + l1 * c_dim1], &c__1); i__1 = *n - l1; /* Computing MIN */ i__2 = l1 + 1; /* Computing MIN */ i__3 = l1 + 1; sumr = igraphddot_(&i__1, &c__[k1 + min(i__2,*n) * c_dim1], ldc, &b[l1 + min(i__3,*n) * b_dim1], ldb); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); scaloc = 1.; a11 = a[k1 + k1 * a_dim1] + sgn * b[l1 + l1 * b_dim1]; da11 = abs(a11); if (da11 <= smin) { a11 = smin; da11 = smin; *info = 1; } db = abs(vec[0]); if (da11 < 1. && db > 1.) { if (db > bignum * da11) { scaloc = 1. / db; } } x[0] = vec[0] * scaloc / a11; if (scaloc != 1.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L190: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; } else if (l1 == l2 && k1 != k2) { i__1 = *m - k2; /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; suml = igraphddot_(&i__1, &a[k1 + min(i__2,*m) * a_dim1], lda, & c__[min(i__3,*m) + l1 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = igraphddot_(&i__1, &c__[k1 + min(i__2,*n) * c_dim1], ldc, &b[l1 + min(i__3,*n) * b_dim1], ldb); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__1 = *m - k2; /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; suml = igraphddot_(&i__1, &a[k2 + min(i__2,*m) * a_dim1], lda, & c__[min(i__3,*m) + l1 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = igraphddot_(&i__1, &c__[k2 + min(i__2,*n) * c_dim1], ldc, &b[l1 + min(i__3,*n) * b_dim1], ldb); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); d__1 = -sgn * b[l1 + l1 * b_dim1]; igraphdlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &a[k1 + k1 * a_dim1], lda, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L200: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k2 + l1 * c_dim1] = x[1]; } else if (l1 != l2 && k1 == k2) { i__1 = *m - k1; /* Computing MIN */ i__2 = k1 + 1; /* Computing MIN */ i__3 = k1 + 1; suml = igraphddot_(&i__1, &a[k1 + min(i__2,*m) * a_dim1], lda, & c__[min(i__3,*m) + l1 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = igraphddot_(&i__1, &c__[k1 + min(i__2,*n) * c_dim1], ldc, &b[l1 + min(i__3,*n) * b_dim1], ldb); vec[0] = sgn * (c__[k1 + l1 * c_dim1] - (suml + sgn * sumr)); i__1 = *m - k1; /* Computing MIN */ i__2 = k1 + 1; /* Computing MIN */ i__3 = k1 + 1; suml = igraphddot_(&i__1, &a[k1 + min(i__2,*m) * a_dim1], lda, & c__[min(i__3,*m) + l2 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = igraphddot_(&i__1, &c__[k1 + min(i__2,*n) * c_dim1], ldc, &b[l2 + min(i__3,*n) * b_dim1], ldb); vec[1] = sgn * (c__[k1 + l2 * c_dim1] - (suml + sgn * sumr)); d__1 = -sgn * a[k1 + k1 * a_dim1]; igraphdlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &b[l1 + l1 * b_dim1], ldb, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L210: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[1]; } else if (l1 != l2 && k1 != k2) { i__1 = *m - k2; /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; suml = igraphddot_(&i__1, &a[k1 + min(i__2,*m) * a_dim1], lda, & c__[min(i__3,*m) + l1 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = igraphddot_(&i__1, &c__[k1 + min(i__2,*n) * c_dim1], ldc, &b[l1 + min(i__3,*n) * b_dim1], ldb); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__1 = *m - k2; /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; suml = igraphddot_(&i__1, &a[k1 + min(i__2,*m) * a_dim1], lda, & c__[min(i__3,*m) + l2 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = igraphddot_(&i__1, &c__[k1 + min(i__2,*n) * c_dim1], ldc, &b[l2 + min(i__3,*n) * b_dim1], ldb); vec[2] = c__[k1 + l2 * c_dim1] - (suml + sgn * sumr); i__1 = *m - k2; /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; suml = igraphddot_(&i__1, &a[k2 + min(i__2,*m) * a_dim1], lda, & c__[min(i__3,*m) + l1 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = igraphddot_(&i__1, &c__[k2 + min(i__2,*n) * c_dim1], ldc, &b[l1 + min(i__3,*n) * b_dim1], ldb); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); i__1 = *m - k2; /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; suml = igraphddot_(&i__1, &a[k2 + min(i__2,*m) * a_dim1], lda, & c__[min(i__3,*m) + l2 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = igraphddot_(&i__1, &c__[k2 + min(i__2,*n) * c_dim1], ldc, &b[l2 + min(i__3,*n) * b_dim1], ldb); vec[3] = c__[k2 + l2 * c_dim1] - (suml + sgn * sumr); igraphdlasy2_(&c_false, &c_true, isgn, &c__2, &c__2, &a[k1 + k1 * a_dim1], lda, &b[l1 + l1 * b_dim1], ldb, vec, & c__2, &scaloc, x, &c__2, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { igraphdscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L220: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[2]; c__[k2 + l1 * c_dim1] = x[1]; c__[k2 + l2 * c_dim1] = x[3]; } L230: ; } L240: ; } } return 0; /* End of DTRSYL */ } /* igraphdtrsyl_ */