/* -- 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 doublecomplex c_b1 = {0.,0.}; static doublecomplex c_b2 = {1.,0.}; static integer c__3 = 3; static integer c__1 = 1; /* Subroutine */ int zlaghe_(integer *n, integer *k, doublereal *d, doublecomplex *a, integer *lda, integer *iseed, doublecomplex *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; doublereal d__1; doublecomplex z__1, z__2, z__3, z__4; /* Builtin functions */ double z_abs(doublecomplex *); void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg( doublecomplex *, doublecomplex *); /* Local variables */ extern /* Subroutine */ int zher2_(char *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); static integer i, j; static doublecomplex alpha; extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zscal_(integer *, doublecomplex *, doublecomplex *, integer *); extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); extern /* Subroutine */ int zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *), zhemv_(char *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *); extern doublereal dznrm2_(integer *, doublecomplex *, integer *); static doublecomplex wa, wb; static doublereal wn; extern /* Subroutine */ int xerbla_(char *, integer *), zlarnv_( integer *, integer *, integer *, doublecomplex *); static doublecomplex 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 September 30, 1994 Purpose ======= ZLAGHE generates a complex hermitian matrix A, by pre- and post- multiplying a real diagonal matrix D with a random unitary matrix: A = U*D*U'. The semi-bandwidth may then be reduced to k by additional unitary 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) COMPLEX*16 array, dimension (LDA,N) The generated n by n hermitian 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) COMPLEX*16 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); xerbla_("ZLAGHE", &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) { i__3 = i + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; /* L10: */ } /* L20: */ } i__1 = *n; for (i = 1; i <= i__1; ++i) { i__2 = i + i * a_dim1; i__3 = i; a[i__2].r = d[i__3], a[i__2].i = 0.; /* L30: */ } /* Generate lower triangle of hermitian matrix */ for (i = *n - 1; i >= 1; --i) { /* generate random reflection */ i__1 = *n - i + 1; zlarnv_(&c__3, &iseed[1], &i__1, &work[1]); i__1 = *n - i + 1; wn = dznrm2_(&i__1, &work[1], &c__1); d__1 = wn / z_abs(&work[1]); z__1.r = d__1 * work[1].r, z__1.i = d__1 * work[1].i; wa.r = z__1.r, wa.i = z__1.i; if (wn == 0.) { tau.r = 0., tau.i = 0.; } else { z__1.r = work[1].r + wa.r, z__1.i = work[1].i + wa.i; wb.r = z__1.r, wb.i = z__1.i; i__1 = *n - i; z_div(&z__1, &c_b2, &wb); zscal_(&i__1, &z__1, &work[2], &c__1); work[1].r = 1., work[1].i = 0.; z_div(&z__1, &wb, &wa); d__1 = z__1.r; tau.r = d__1, tau.i = 0.; } /* 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; zhemv_("Lower", &i__1, &tau, &a[i + i * a_dim1], lda, &work[1], &c__1, &c_b1, &work[*n + 1], &c__1); /* compute v := y - 1/2 * tau * ( y, u ) * u */ z__3.r = -.5, z__3.i = 0.; z__2.r = z__3.r * tau.r - z__3.i * tau.i, z__2.i = z__3.r * tau.i + z__3.i * tau.r; i__1 = *n - i + 1; zdotc_(&z__4, &i__1, &work[*n + 1], &c__1, &work[1], &c__1); z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * z__4.i + z__2.i * z__4.r; alpha.r = z__1.r, alpha.i = z__1.i; i__1 = *n - i + 1; zaxpy_(&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; z__1.r = -1., z__1.i = 0.; zher2_("Lower", &i__1, &z__1, &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 = dznrm2_(&i__2, &a[*k + i + i * a_dim1], &c__1); d__1 = wn / z_abs(&a[*k + i + i * a_dim1]); i__2 = *k + i + i * a_dim1; z__1.r = d__1 * a[i__2].r, z__1.i = d__1 * a[i__2].i; wa.r = z__1.r, wa.i = z__1.i; if (wn == 0.) { tau.r = 0., tau.i = 0.; } else { i__2 = *k + i + i * a_dim1; z__1.r = a[i__2].r + wa.r, z__1.i = a[i__2].i + wa.i; wb.r = z__1.r, wb.i = z__1.i; i__2 = *n - *k - i; z_div(&z__1, &c_b2, &wb); zscal_(&i__2, &z__1, &a[*k + i + 1 + i * a_dim1], &c__1); i__2 = *k + i + i * a_dim1; a[i__2].r = 1., a[i__2].i = 0.; z_div(&z__1, &wb, &wa); d__1 = z__1.r; tau.r = d__1, tau.i = 0.; } /* 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; zgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*k + i + (i + 1) * a_dim1], lda, &a[*k + i + i * a_dim1], &c__1, &c_b1, &work[ 1], &c__1); i__2 = *n - *k - i + 1; i__3 = *k - 1; z__1.r = -tau.r, z__1.i = -tau.i; zgerc_(&i__2, &i__3, &z__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; zhemv_("Lower", &i__2, &tau, &a[*k + i + (*k + i) * a_dim1], lda, &a[* k + i + i * a_dim1], &c__1, &c_b1, &work[1], &c__1); /* compute v := y - 1/2 * tau * ( y, u ) * u */ z__3.r = -.5, z__3.i = 0.; z__2.r = z__3.r * tau.r - z__3.i * tau.i, z__2.i = z__3.r * tau.i + z__3.i * tau.r; i__2 = *n - *k - i + 1; zdotc_(&z__4, &i__2, &work[1], &c__1, &a[*k + i + i * a_dim1], &c__1); z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * z__4.i + z__2.i * z__4.r; alpha.r = z__1.r, alpha.i = z__1.i; i__2 = *n - *k - i + 1; zaxpy_(&i__2, &alpha, &a[*k + i + i * a_dim1], &c__1, &work[1], &c__1) ; /* apply hermitian rank-2 update to A(k+i:n,k+i:n) */ i__2 = *n - *k - i + 1; z__1.r = -1., z__1.i = 0.; zher2_("Lower", &i__2, &z__1, &a[*k + i + i * a_dim1], &c__1, &work[1] , &c__1, &a[*k + i + (*k + i) * a_dim1], lda); i__2 = *k + i + i * a_dim1; z__1.r = -wa.r, z__1.i = -wa.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; i__2 = *n; for (j = *k + i + 1; j <= i__2; ++j) { i__3 = j + i * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; /* L50: */ } /* L60: */ } /* Store full hermitian matrix */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i = j + 1; i <= i__2; ++i) { i__3 = j + i * a_dim1; d_cnjg(&z__1, &a[i + j * a_dim1]); a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L70: */ } /* L80: */ } return 0; /* End of ZLAGHE */ } /* zlaghe_ */