#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zhptrd_(char *uplo, integer *n, doublecomplex *ap, doublereal *d__, doublereal *e, doublecomplex *tau, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZHPTRD reduces a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T. Arguments ========= UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, if UPLO = 'U', the diagonal and first superdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors; if UPLO = 'L', the diagonal and first subdiagonal of A are over- written by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors. See Further Details. D (output) DOUBLE PRECISION array, dimension (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i). E (output) DOUBLE PRECISION array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. TAU (output) COMPLEX*16 array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Further Details =============== If UPLO = 'U', the matrix Q is represented as a product of elementary reflectors Q = H(n-1) . . . H(2) H(1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a complex scalar, and v is a complex vector with v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP, overwriting A(1:i-1,i+1), and tau is stored in TAU(i). If UPLO = 'L', the matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(n-1). Each H(i) has the form H(i) = I - tau * v * v' where tau is a complex scalar, and v is a complex vector with v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP, overwriting A(i+2:n,i), and tau is stored in TAU(i). ===================================================================== Test the input parameters Parameter adjustments */ /* Table of constant values */ static doublecomplex c_b2 = {0.,0.}; static integer c__1 = 1; /* System generated locals */ integer i__1, i__2, i__3; doublereal d__1; doublecomplex z__1, z__2, z__3, z__4; /* Local variables */ static integer i__, i1, ii, i1i1; static doublecomplex taui; extern /* Subroutine */ int zhpr2_(char *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *); static doublecomplex alpha; extern logical lsame_(char *, char *); extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); static logical upper; extern /* Subroutine */ int zhpmv_(char *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(char *, integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *); --tau; --e; --d__; --ap; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } if (*info != 0) { i__1 = -(*info); xerbla_("ZHPTRD", &i__1); return 0; } /* Quick return if possible */ if (*n <= 0) { return 0; } if (upper) { /* Reduce the upper triangle of A. I1 is the index in AP of A(1,I+1). */ i1 = *n * (*n - 1) / 2 + 1; i__1 = i1 + *n - 1; i__2 = i1 + *n - 1; d__1 = ap[i__2].r; ap[i__1].r = d__1, ap[i__1].i = 0.; for (i__ = *n - 1; i__ >= 1; --i__) { /* Generate elementary reflector H(i) = I - tau * v * v' to annihilate A(1:i-1,i+1) */ i__1 = i1 + i__ - 1; alpha.r = ap[i__1].r, alpha.i = ap[i__1].i; zlarfg_(&i__, &alpha, &ap[i1], &c__1, &taui); i__1 = i__; e[i__1] = alpha.r; if (taui.r != 0. || taui.i != 0.) { /* Apply H(i) from both sides to A(1:i,1:i) */ i__1 = i1 + i__ - 1; ap[i__1].r = 1., ap[i__1].i = 0.; /* Compute y := tau * A * v storing y in TAU(1:i) */ zhpmv_(uplo, &i__, &taui, &ap[1], &ap[i1], &c__1, &c_b2, &tau[ 1], &c__1); /* Compute w := y - 1/2 * tau * (y'*v) * v */ z__3.r = -.5, z__3.i = -0.; z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r * taui.i + z__3.i * taui.r; zdotc_(&z__4, &i__, &tau[1], &c__1, &ap[i1], &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; zaxpy_(&i__, &alpha, &ap[i1], &c__1, &tau[1], &c__1); /* Apply the transformation as a rank-2 update: A := A - v * w' - w * v' */ z__1.r = -1., z__1.i = -0.; zhpr2_(uplo, &i__, &z__1, &ap[i1], &c__1, &tau[1], &c__1, &ap[ 1]); } i__1 = i1 + i__ - 1; i__2 = i__; ap[i__1].r = e[i__2], ap[i__1].i = 0.; i__1 = i__ + 1; i__2 = i1 + i__; d__[i__1] = ap[i__2].r; i__1 = i__; tau[i__1].r = taui.r, tau[i__1].i = taui.i; i1 -= i__; /* L10: */ } d__[1] = ap[1].r; } else { /* Reduce the lower triangle of A. II is the index in AP of A(i,i) and I1I1 is the index of A(i+1,i+1). */ ii = 1; d__1 = ap[1].r; ap[1].r = d__1, ap[1].i = 0.; i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { i1i1 = ii + *n - i__ + 1; /* Generate elementary reflector H(i) = I - tau * v * v' to annihilate A(i+2:n,i) */ i__2 = ii + 1; alpha.r = ap[i__2].r, alpha.i = ap[i__2].i; i__2 = *n - i__; zlarfg_(&i__2, &alpha, &ap[ii + 2], &c__1, &taui); i__2 = i__; e[i__2] = alpha.r; if (taui.r != 0. || taui.i != 0.) { /* Apply H(i) from both sides to A(i+1:n,i+1:n) */ i__2 = ii + 1; ap[i__2].r = 1., ap[i__2].i = 0.; /* Compute y := tau * A * v storing y in TAU(i:n-1) */ i__2 = *n - i__; zhpmv_(uplo, &i__2, &taui, &ap[i1i1], &ap[ii + 1], &c__1, & c_b2, &tau[i__], &c__1); /* Compute w := y - 1/2 * tau * (y'*v) * v */ z__3.r = -.5, z__3.i = -0.; z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r * taui.i + z__3.i * taui.r; i__2 = *n - i__; zdotc_(&z__4, &i__2, &tau[i__], &c__1, &ap[ii + 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__2 = *n - i__; zaxpy_(&i__2, &alpha, &ap[ii + 1], &c__1, &tau[i__], &c__1); /* Apply the transformation as a rank-2 update: A := A - v * w' - w * v' */ i__2 = *n - i__; z__1.r = -1., z__1.i = -0.; zhpr2_(uplo, &i__2, &z__1, &ap[ii + 1], &c__1, &tau[i__], & c__1, &ap[i1i1]); } i__2 = ii + 1; i__3 = i__; ap[i__2].r = e[i__3], ap[i__2].i = 0.; i__2 = i__; i__3 = ii; d__[i__2] = ap[i__3].r; i__2 = i__; tau[i__2].r = taui.r, tau[i__2].i = taui.i; ii = i1i1; /* L20: */ } i__1 = *n; i__2 = ii; d__[i__1] = ap[i__2].r; } return 0; /* End of ZHPTRD */ } /* zhptrd_ */