#include "blaswrap.h" /* -- translated by f2c (version 19990503). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Table of constant values */ static doublereal c_b29 = 1.; static doublereal c_b30 = 0.; static doublereal c_b33 = -1.; /* Subroutine */ int dlatm5_(integer *prtype, integer *m, integer *n, doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * c__, integer *ldc, doublereal *d__, integer *ldd, doublereal *e, integer *lde, doublereal *f, integer *ldf, doublereal *r__, integer * ldr, doublereal *l, integer *ldl, doublereal *alpha, integer *qblcka, integer *qblckb) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1, d_offset, e_dim1, e_offset, f_dim1, f_offset, l_dim1, l_offset, r_dim1, r_offset, i__1, i__2; /* Builtin functions */ double sin(doublereal); /* Local variables */ static integer i__, j, k; extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); static doublereal imeps, reeps; #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] #define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1] #define d___ref(a_1,a_2) d__[(a_2)*d_dim1 + a_1] #define e_ref(a_1,a_2) e[(a_2)*e_dim1 + a_1] #define l_ref(a_1,a_2) l[(a_2)*l_dim1 + a_1] #define r___ref(a_1,a_2) r__[(a_2)*r_dim1 + a_1] /* -- LAPACK test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 Purpose ======= DLATM5 generates matrices involved in the Generalized Sylvester equation: A * R - L * B = C D * R - L * E = F They also satisfy (the diagonalization condition) [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] ) [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] ) Arguments ========= PRTYPE (input) INTEGER "Points" to a certian type of the matrices to generate (see futher details). M (input) INTEGER Specifies the order of A and D and the number of rows in C, F, R and L. N (input) INTEGER Specifies the order of B and E and the number of columns in C, F, R and L. A (output) DOUBLE PRECISION array, dimension (LDA, M). On exit A M-by-M is initialized according to PRTYPE. LDA (input) INTEGER The leading dimension of A. B (output) DOUBLE PRECISION array, dimension (LDB, N). On exit B N-by-N is initialized according to PRTYPE. LDB (input) INTEGER The leading dimension of B. C (output) DOUBLE PRECISION array, dimension (LDC, N). On exit C M-by-N is initialized according to PRTYPE. LDC (input) INTEGER The leading dimension of C. D (output) DOUBLE PRECISION array, dimension (LDD, M). On exit D M-by-M is initialized according to PRTYPE. LDD (input) INTEGER The leading dimension of D. E (output) DOUBLE PRECISION array, dimension (LDE, N). On exit E N-by-N is initialized according to PRTYPE. LDE (input) INTEGER The leading dimension of E. F (output) DOUBLE PRECISION array, dimension (LDF, N). On exit F M-by-N is initialized according to PRTYPE. LDF (input) INTEGER The leading dimension of F. R (output) DOUBLE PRECISION array, dimension (LDR, N). On exit R M-by-N is initialized according to PRTYPE. LDR (input) INTEGER The leading dimension of R. L (output) DOUBLE PRECISION array, dimension (LDL, N). On exit L M-by-N is initialized according to PRTYPE. LDL (input) INTEGER The leading dimension of L. ALPHA (input) DOUBLE PRECISION Parameter used in generating PRTYPE = 1 and 5 matrices. QBLCKA (input) INTEGER When PRTYPE = 3, specifies the distance between 2-by-2 blocks on the diagonal in A. Otherwise, QBLCKA is not referenced. QBLCKA > 1. QBLCKB (input) INTEGER When PRTYPE = 3, specifies the distance between 2-by-2 blocks on the diagonal in B. Otherwise, QBLCKB is not referenced. QBLCKB > 1. Further Details =============== PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices A : if (i == j) then A(i, j) = 1.0 if (j == i + 1) then A(i, j) = -1.0 else A(i, j) = 0.0, i, j = 1...M B : if (i == j) then B(i, j) = 1.0 - ALPHA if (j == i + 1) then B(i, j) = 1.0 else B(i, j) = 0.0, i, j = 1...N D : if (i == j) then D(i, j) = 1.0 else D(i, j) = 0.0, i, j = 1...M E : if (i == j) then E(i, j) = 1.0 else E(i, j) = 0.0, i, j = 1...N L = R are chosen from [-10...10], which specifies the right hand sides (C, F). PRTYPE = 2 or 3: Triangular and/or quasi- triangular. A : if (i <= j) then A(i, j) = [-1...1] else A(i, j) = 0.0, i, j = 1...M if (PRTYPE = 3) then A(k + 1, k + 1) = A(k, k) A(k + 1, k) = [-1...1] sign(A(k, k + 1) = -(sin(A(k + 1, k)) k = 1, M - 1, QBLCKA B : if (i <= j) then B(i, j) = [-1...1] else B(i, j) = 0.0, i, j = 1...N if (PRTYPE = 3) then B(k + 1, k + 1) = B(k, k) B(k + 1, k) = [-1...1] sign(B(k, k + 1) = -(sign(B(k + 1, k)) k = 1, N - 1, QBLCKB D : if (i <= j) then D(i, j) = [-1...1]. else D(i, j) = 0.0, i, j = 1...M E : if (i <= j) then D(i, j) = [-1...1] else E(i, j) = 0.0, i, j = 1...N L, R are chosen from [-10...10], which specifies the right hand sides (C, F). PRTYPE = 4 Full A(i, j) = [-10...10] D(i, j) = [-1...1] i,j = 1...M B(i, j) = [-10...10] E(i, j) = [-1...1] i,j = 1...N R(i, j) = [-10...10] L(i, j) = [-1...1] i = 1..M ,j = 1...N L, R specifies the right hand sides (C, F). PRTYPE = 5 special case common and/or close eigs. ===================================================================== Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; d_dim1 = *ldd; d_offset = 1 + d_dim1 * 1; d__ -= d_offset; e_dim1 = *lde; e_offset = 1 + e_dim1 * 1; e -= e_offset; f_dim1 = *ldf; f_offset = 1 + f_dim1 * 1; f -= f_offset; r_dim1 = *ldr; r_offset = 1 + r_dim1 * 1; r__ -= r_offset; l_dim1 = *ldl; l_offset = 1 + l_dim1 * 1; l -= l_offset; /* Function Body */ if (*prtype == 1) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *m; for (j = 1; j <= i__2; ++j) { if (i__ == j) { a_ref(i__, j) = 1.; d___ref(i__, j) = 1.; } else if (i__ == j - 1) { a_ref(i__, j) = -1.; d___ref(i__, j) = 0.; } else { a_ref(i__, j) = 0.; d___ref(i__, j) = 0.; } /* L10: */ } /* L20: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n; for (j = 1; j <= i__2; ++j) { if (i__ == j) { b_ref(i__, j) = 1. - *alpha; e_ref(i__, j) = 1.; } else if (i__ == j - 1) { b_ref(i__, j) = 1.; e_ref(i__, j) = 0.; } else { b_ref(i__, j) = 0.; e_ref(i__, j) = 0.; } /* L30: */ } /* L40: */ } i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n; for (j = 1; j <= i__2; ++j) { r___ref(i__, j) = (.5 - sin((doublereal) (i__ / j))) * 20.; l_ref(i__, j) = r___ref(i__, j); /* L50: */ } /* L60: */ } } else if (*prtype == 2 || *prtype == 3) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *m; for (j = 1; j <= i__2; ++j) { if (i__ <= j) { a_ref(i__, j) = (.5 - sin((doublereal) i__)) * 2.; d___ref(i__, j) = (.5 - sin((doublereal) (i__ * j))) * 2.; } else { a_ref(i__, j) = 0.; d___ref(i__, j) = 0.; } /* L70: */ } /* L80: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n; for (j = 1; j <= i__2; ++j) { if (i__ <= j) { b_ref(i__, j) = (.5 - sin((doublereal) (i__ + j))) * 2.; e_ref(i__, j) = (.5 - sin((doublereal) j)) * 2.; } else { b_ref(i__, j) = 0.; e_ref(i__, j) = 0.; } /* L90: */ } /* L100: */ } i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n; for (j = 1; j <= i__2; ++j) { r___ref(i__, j) = (.5 - sin((doublereal) (i__ * j))) * 20.; l_ref(i__, j) = (.5 - sin((doublereal) (i__ + j))) * 20.; /* L110: */ } /* L120: */ } if (*prtype == 3) { if (*qblcka <= 1) { *qblcka = 2; } i__1 = *m - 1; i__2 = *qblcka; for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) { a_ref(k + 1, k + 1) = a_ref(k, k); a_ref(k + 1, k) = -sin(a_ref(k, k + 1)); /* L130: */ } if (*qblckb <= 1) { *qblckb = 2; } i__2 = *n - 1; i__1 = *qblckb; for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) { b_ref(k + 1, k + 1) = b_ref(k, k); b_ref(k + 1, k) = -sin(b_ref(k, k + 1)); /* L140: */ } } } else if (*prtype == 4) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *m; for (j = 1; j <= i__2; ++j) { a_ref(i__, j) = (.5 - sin((doublereal) (i__ * j))) * 20.; d___ref(i__, j) = (.5 - sin((doublereal) (i__ + j))) * 2.; /* L150: */ } /* L160: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n; for (j = 1; j <= i__2; ++j) { b_ref(i__, j) = (.5 - sin((doublereal) (i__ + j))) * 20.; e_ref(i__, j) = (.5 - sin((doublereal) (i__ * j))) * 2.; /* L170: */ } /* L180: */ } i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n; for (j = 1; j <= i__2; ++j) { r___ref(i__, j) = (.5 - sin((doublereal) (j / i__))) * 20.; l_ref(i__, j) = (.5 - sin((doublereal) (i__ * j))) * 2.; /* L190: */ } /* L200: */ } } else if (*prtype >= 5) { reeps = 20. / *alpha; imeps = -1.5 / *alpha; i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *n; for (j = 1; j <= i__2; ++j) { r___ref(i__, j) = (.5 - sin((doublereal) (i__ * j))) * *alpha / 20.; l_ref(i__, j) = (.5 - sin((doublereal) (i__ + j))) * *alpha / 20.; /* L210: */ } /* L220: */ } i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { d___ref(i__, i__) = 1.; /* L230: */ } i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { if (i__ <= 4) { a_ref(i__, i__) = 1.; if (i__ > 2) { a_ref(i__, i__) = reeps + 1.; } if (i__ % 2 != 0 && i__ < *m) { a_ref(i__, i__ + 1) = imeps; } else if (i__ > 1) { a_ref(i__, i__ - 1) = -imeps; } } else if (i__ <= 8) { if (i__ <= 6) { a_ref(i__, i__) = reeps; } else { a_ref(i__, i__) = -reeps; } if (i__ % 2 != 0 && i__ < *m) { a_ref(i__, i__ + 1) = 1.; } else if (i__ > 1) { a_ref(i__, i__ - 1) = -1.; } } else { a_ref(i__, i__) = 1.; if (i__ % 2 != 0 && i__ < *m) { a_ref(i__, i__ + 1) = imeps * 2; } else if (i__ > 1) { a_ref(i__, i__ - 1) = -imeps * 2; } } /* L240: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { e_ref(i__, i__) = 1.; if (i__ <= 4) { b_ref(i__, i__) = -1.; if (i__ > 2) { b_ref(i__, i__) = 1. - reeps; } if (i__ % 2 != 0 && i__ < *n) { b_ref(i__, i__ + 1) = imeps; } else if (i__ > 1) { b_ref(i__, i__ - 1) = -imeps; } } else if (i__ <= 8) { if (i__ <= 6) { b_ref(i__, i__) = reeps; } else { b_ref(i__, i__) = -reeps; } if (i__ % 2 != 0 && i__ < *n) { b_ref(i__, i__ + 1) = imeps + 1.; } else if (i__ > 1) { b_ref(i__, i__ - 1) = -1. - imeps; } } else { b_ref(i__, i__) = 1. - reeps; if (i__ % 2 != 0 && i__ < *n) { b_ref(i__, i__ + 1) = imeps * 2; } else if (i__ > 1) { b_ref(i__, i__ - 1) = -imeps * 2; } } /* L250: */ } } /* Compute rhs (C, F) */ dgemm_("N", "N", m, n, m, &c_b29, &a[a_offset], lda, &r__[r_offset], ldr, &c_b30, &c__[c_offset], ldc); dgemm_("N", "N", m, n, n, &c_b33, &l[l_offset], ldl, &b[b_offset], ldb, & c_b29, &c__[c_offset], ldc); dgemm_("N", "N", m, n, m, &c_b29, &d__[d_offset], ldd, &r__[r_offset], ldr, &c_b30, &f[f_offset], ldf); dgemm_("N", "N", m, n, n, &c_b33, &l[l_offset], ldl, &e[e_offset], lde, & c_b29, &f[f_offset], ldf); /* End of DLATM5 */ return 0; } /* dlatm5_ */ #undef r___ref #undef l_ref #undef e_ref #undef d___ref #undef b_ref #undef a_ref .