#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int chpgst_(integer *itype, char *uplo, integer *n, complex * ap, complex *bp, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= CHPGST reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage. If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. B must have been previously factorized as U**H*U or L*L**H by CPPTRF. Arguments ========= ITYPE (input) INTEGER = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); = 2 or 3: compute U*A*U**H or L**H*A*L. UPLO (input) CHARACTER = 'U': Upper triangle of A is stored and B is factored as U**H*U; = 'L': Lower triangle of A is stored and B is factored as L*L**H. N (input) INTEGER The order of the matrices A and B. N >= 0. AP (input/output) COMPLEX 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)*(2n-j)/2) = A(i,j) for j<=i<=n. On exit, if INFO = 0, the transformed matrix, stored in the same format as A. BP (input) COMPLEX array, dimension (N*(N+1)/2) The triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by CPPTRF. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static complex c_b1 = {1.f,0.f}; static integer c__1 = 1; /* System generated locals */ integer i__1, i__2, i__3, i__4; real r__1, r__2; complex q__1, q__2, q__3; /* Local variables */ extern /* Subroutine */ int chpr2_(char *, integer *, complex *, complex * , integer *, complex *, integer *, complex *); static integer j, k; extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer *, complex *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int chpmv_(char *, integer *, complex *, complex * , complex *, integer *, complex *, complex *, integer *), caxpy_(integer *, complex *, complex *, integer *, complex *, integer *), ctpmv_(char *, char *, char *, integer *, complex *, complex *, integer *); static logical upper; static integer j1, k1; extern /* Subroutine */ int ctpsv_(char *, char *, char *, integer *, complex *, complex *, integer *); static integer jj, kk; static complex ct; extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer *), xerbla_(char *, integer *); static real ajj; static integer j1j1; static real akk; static integer k1k1; static real bjj, bkk; --bp; --ap; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (*itype < 1 || *itype > 3) { *info = -1; } else if (! upper && ! lsame_(uplo, "L")) { *info = -2; } else if (*n < 0) { *info = -3; } if (*info != 0) { i__1 = -(*info); xerbla_("CHPGST", &i__1); return 0; } if (*itype == 1) { if (upper) { /* Compute inv(U')*A*inv(U) J1 and JJ are the indices of A(1,j) and A(j,j) */ jj = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { j1 = jj + 1; jj += j; /* Compute the j-th column of the upper triangle of A */ i__2 = jj; i__3 = jj; r__1 = ap[i__3].r; ap[i__2].r = r__1, ap[i__2].i = 0.f; i__2 = jj; bjj = bp[i__2].r; ctpsv_(uplo, "Conjugate transpose", "Non-unit", &j, &bp[1], & ap[j1], &c__1); i__2 = j - 1; q__1.r = -1.f, q__1.i = 0.f; chpmv_(uplo, &i__2, &q__1, &ap[1], &bp[j1], &c__1, &c_b1, &ap[ j1], &c__1); i__2 = j - 1; r__1 = 1.f / bjj; csscal_(&i__2, &r__1, &ap[j1], &c__1); i__2 = jj; i__3 = jj; i__4 = j - 1; cdotc_(&q__3, &i__4, &ap[j1], &c__1, &bp[j1], &c__1); q__2.r = ap[i__3].r - q__3.r, q__2.i = ap[i__3].i - q__3.i; q__1.r = q__2.r / bjj, q__1.i = q__2.i / bjj; ap[i__2].r = q__1.r, ap[i__2].i = q__1.i; /* L10: */ } } else { /* Compute inv(L)*A*inv(L') KK and K1K1 are the indices of A(k,k) and A(k+1,k+1) */ kk = 1; i__1 = *n; for (k = 1; k <= i__1; ++k) { k1k1 = kk + *n - k + 1; /* Update the lower triangle of A(k:n,k:n) */ i__2 = kk; akk = ap[i__2].r; i__2 = kk; bkk = bp[i__2].r; /* Computing 2nd power */ r__1 = bkk; akk /= r__1 * r__1; i__2 = kk; ap[i__2].r = akk, ap[i__2].i = 0.f; if (k < *n) { i__2 = *n - k; r__1 = 1.f / bkk; csscal_(&i__2, &r__1, &ap[kk + 1], &c__1); r__1 = akk * -.5f; ct.r = r__1, ct.i = 0.f; i__2 = *n - k; caxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1) ; i__2 = *n - k; q__1.r = -1.f, q__1.i = 0.f; chpr2_(uplo, &i__2, &q__1, &ap[kk + 1], &c__1, &bp[kk + 1] , &c__1, &ap[k1k1]); i__2 = *n - k; caxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1) ; i__2 = *n - k; ctpsv_(uplo, "No transpose", "Non-unit", &i__2, &bp[k1k1], &ap[kk + 1], &c__1); } kk = k1k1; /* L20: */ } } } else { if (upper) { /* Compute U*A*U' K1 and KK are the indices of A(1,k) and A(k,k) */ kk = 0; i__1 = *n; for (k = 1; k <= i__1; ++k) { k1 = kk + 1; kk += k; /* Update the upper triangle of A(1:k,1:k) */ i__2 = kk; akk = ap[i__2].r; i__2 = kk; bkk = bp[i__2].r; i__2 = k - 1; ctpmv_(uplo, "No transpose", "Non-unit", &i__2, &bp[1], &ap[ k1], &c__1); r__1 = akk * .5f; ct.r = r__1, ct.i = 0.f; i__2 = k - 1; caxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1); i__2 = k - 1; chpr2_(uplo, &i__2, &c_b1, &ap[k1], &c__1, &bp[k1], &c__1, & ap[1]); i__2 = k - 1; caxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1); i__2 = k - 1; csscal_(&i__2, &bkk, &ap[k1], &c__1); i__2 = kk; /* Computing 2nd power */ r__2 = bkk; r__1 = akk * (r__2 * r__2); ap[i__2].r = r__1, ap[i__2].i = 0.f; /* L30: */ } } else { /* Compute L'*A*L JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1) */ jj = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { j1j1 = jj + *n - j + 1; /* Compute the j-th column of the lower triangle of A */ i__2 = jj; ajj = ap[i__2].r; i__2 = jj; bjj = bp[i__2].r; i__2 = jj; r__1 = ajj * bjj; i__3 = *n - j; cdotc_(&q__2, &i__3, &ap[jj + 1], &c__1, &bp[jj + 1], &c__1); q__1.r = r__1 + q__2.r, q__1.i = q__2.i; ap[i__2].r = q__1.r, ap[i__2].i = q__1.i; i__2 = *n - j; csscal_(&i__2, &bjj, &ap[jj + 1], &c__1); i__2 = *n - j; chpmv_(uplo, &i__2, &c_b1, &ap[j1j1], &bp[jj + 1], &c__1, & c_b1, &ap[jj + 1], &c__1); i__2 = *n - j + 1; ctpmv_(uplo, "Conjugate transpose", "Non-unit", &i__2, &bp[jj] , &ap[jj], &c__1); jj = j1j1; /* L40: */ } } } return 0; /* End of CHPGST */ } /* chpgst_ */