/* -- translated by f2c (version 19940927). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Table of constant values */ static integer c__3 = 3; static integer c__1 = 1; static doublereal c_b12 = 0.; static doublereal c_b19 = -1.; static doublereal c_b26 = 1.; /* Subroutine */ int dlagsy_slu(integer *n, integer *k, doublereal *d, doublereal *a, integer *lda, integer *iseed, doublereal *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; doublereal d__1; /* Builtin functions */ double d_sign(doublereal *, doublereal *); /* Local variables */ extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *); extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *), dnrm2_(integer *, doublereal *, integer *); extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *); static integer i, j; static doublereal alpha; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *), dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *), daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *), dsymv_(char *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); static doublereal wa, wb, wn; extern /* Subroutine */ int dlarnv_slu(integer *, integer *, integer *, doublereal *); extern int input_error(char *, int *); static doublereal tau; /* -- LAPACK auxiliary test routine (version 2.0) Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University February 29, 1992 Purpose ======= DLAGSY generates a real symmetric matrix A, by pre- and post- multiplying a real diagonal matrix D with a random orthogonal matrix: A = U*D*U'. The semi-bandwidth may then be reduced to k by additional orthogonal transformations. Arguments ========= N (input) INTEGER The order of the matrix A. N >= 0. K (input) INTEGER The number of nonzero subdiagonals within the band of A. 0 <= K <= N-1. D (input) DOUBLE PRECISION array, dimension (N) The diagonal elements of the diagonal matrix D. A (output) DOUBLE PRECISION array, dimension (LDA,N) The generated n by n symmetric matrix A (the full matrix is stored). LDA (input) INTEGER The leading dimension of the array A. LDA >= N. ISEED (input/output) INTEGER array, dimension (4) On entry, the seed of the random number generator; the array elements must be between 0 and 4095, and ISEED(4) must be odd. On exit, the seed is updated. WORK (workspace) DOUBLE PRECISION array, dimension (2*N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== Test the input arguments Parameter adjustments */ --d; a_dim1 = *lda; a_offset = a_dim1 + 1; a -= a_offset; --iseed; --work; /* Function Body */ *info = 0; if (*n < 0) { *info = -1; } else if (*k < 0 || *k > *n - 1) { *info = -2; } else if (*lda < max(1,*n)) { *info = -5; } if (*info < 0) { i__1 = -(*info); input_error("DLAGSY", &i__1); return 0; } /* initialize lower triangle of A to diagonal matrix */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i = j + 1; i <= i__2; ++i) { a[i + j * a_dim1] = 0.; /* L10: */ } /* L20: */ } i__1 = *n; for (i = 1; i <= i__1; ++i) { a[i + i * a_dim1] = d[i]; /* L30: */ } /* Generate lower triangle of symmetric matrix */ for (i = *n - 1; i >= 1; --i) { /* generate random reflection */ i__1 = *n - i + 1; dlarnv_slu(&c__3, &iseed[1], &i__1, &work[1]); i__1 = *n - i + 1; wn = dnrm2_(&i__1, &work[1], &c__1); wa = d_sign(&wn, &work[1]); if (wn == 0.) { tau = 0.; } else { wb = work[1] + wa; i__1 = *n - i; d__1 = 1. / wb; dscal_(&i__1, &d__1, &work[2], &c__1); work[1] = 1.; tau = wb / wa; } /* apply random reflection to A(i:n,i:n) from the left and the right compute y := tau * A * u */ i__1 = *n - i + 1; dsymv_("Lower", &i__1, &tau, &a[i + i * a_dim1], lda, &work[1], &c__1, &c_b12, &work[*n + 1], &c__1); /* compute v := y - 1/2 * tau * ( y, u ) * u */ i__1 = *n - i + 1; alpha = tau * -.5 * ddot_(&i__1, &work[*n + 1], &c__1, &work[1], & c__1); i__1 = *n - i + 1; daxpy_(&i__1, &alpha, &work[1], &c__1, &work[*n + 1], &c__1); /* apply the transformation as a rank-2 update to A(i:n,i:n) */ i__1 = *n - i + 1; dsyr2_("Lower", &i__1, &c_b19, &work[1], &c__1, &work[*n + 1], &c__1, &a[i + i * a_dim1], lda); /* L40: */ } /* Reduce number of subdiagonals to K */ i__1 = *n - 1 - *k; for (i = 1; i <= i__1; ++i) { /* generate reflection to annihilate A(k+i+1:n,i) */ i__2 = *n - *k - i + 1; wn = dnrm2_(&i__2, &a[*k + i + i * a_dim1], &c__1); wa = d_sign(&wn, &a[*k + i + i * a_dim1]); if (wn == 0.) { tau = 0.; } else { wb = a[*k + i + i * a_dim1] + wa; i__2 = *n - *k - i; d__1 = 1. / wb; dscal_(&i__2, &d__1, &a[*k + i + 1 + i * a_dim1], &c__1); a[*k + i + i * a_dim1] = 1.; tau = wb / wa; } /* apply reflection to A(k+i:n,i+1:k+i-1) from the left */ i__2 = *n - *k - i + 1; i__3 = *k - 1; dgemv_("Transpose", &i__2, &i__3, &c_b26, &a[*k + i + (i + 1) * a_dim1], lda, &a[*k + i + i * a_dim1], &c__1, &c_b12, &work[1] , &c__1); i__2 = *n - *k - i + 1; i__3 = *k - 1; d__1 = -tau; dger_(&i__2, &i__3, &d__1, &a[*k + i + i * a_dim1], &c__1, &work[1], & c__1, &a[*k + i + (i + 1) * a_dim1], lda); /* apply reflection to A(k+i:n,k+i:n) from the left and the rig ht compute y := tau * A * u */ i__2 = *n - *k - i + 1; dsymv_("Lower", &i__2, &tau, &a[*k + i + (*k + i) * a_dim1], lda, &a[* k + i + i * a_dim1], &c__1, &c_b12, &work[1], &c__1); /* compute v := y - 1/2 * tau * ( y, u ) * u */ i__2 = *n - *k - i + 1; alpha = tau * -.5 * ddot_(&i__2, &work[1], &c__1, &a[*k + i + i * a_dim1], &c__1); i__2 = *n - *k - i + 1; daxpy_(&i__2, &alpha, &a[*k + i + i * a_dim1], &c__1, &work[1], &c__1) ; /* apply symmetric rank-2 update to A(k+i:n,k+i:n) */ i__2 = *n - *k - i + 1; dsyr2_("Lower", &i__2, &c_b19, &a[*k + i + i * a_dim1], &c__1, &work[ 1], &c__1, &a[*k + i + (*k + i) * a_dim1], lda); a[*k + i + i * a_dim1] = -wa; i__2 = *n; for (j = *k + i + 1; j <= i__2; ++j) { a[j + i * a_dim1] = 0.; /* L50: */ } /* L60: */ } /* Store full symmetric matrix */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i = j + 1; i <= i__2; ++i) { a[j + i * a_dim1] = a[i + j * a_dim1]; /* L70: */ } /* L80: */ } return 0; /* End of DLAGSY */ } /* dlagsy_slu */