#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int sspgst_(integer *itype, char *uplo, integer *n, real *ap, real *bp, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SSPGST reduces a real symmetric-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**T)*A*inv(U) or inv(L)*A*inv(L**T) 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**T or L**T*A*L. B must have been previously factorized as U**T*U or L*L**T by SPPTRF. Arguments ========= ITYPE (input) INTEGER = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); = 2 or 3: compute U*A*U**T or L**T*A*L. UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored and B is factored as U**T*U; = 'L': Lower triangle of A is stored and B is factored as L*L**T. N (input) INTEGER The order of the matrices A and B. N >= 0. AP (input/output) REAL array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric 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) REAL 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 SPPTRF. 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 integer c__1 = 1; static real c_b9 = -1.f; static real c_b11 = 1.f; /* System generated locals */ integer i__1, i__2; real r__1; /* Local variables */ static integer j, k, j1, k1, jj, kk; static real ct, ajj; static integer j1j1; static real akk; static integer k1k1; static real bjj, bkk; extern doublereal sdot_(integer *, real *, integer *, real *, integer *); extern /* Subroutine */ int sspr2_(char *, integer *, real *, real *, integer *, real *, integer *, real *); extern logical lsame_(char *, char *); extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); static logical upper; extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, real *, integer *), sspmv_(char *, integer *, real *, real *, real *, integer *, real *, real *, integer *), stpmv_( char *, char *, char *, integer *, real *, real *, integer *), stpsv_(char *, char *, char *, integer *, real *, real *, integer *), xerbla_(char *, integer *); --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_("SSPGST", &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 */ bjj = bp[jj]; stpsv_(uplo, "Transpose", "Nonunit", &j, &bp[1], &ap[j1], & c__1); i__2 = j - 1; sspmv_(uplo, &i__2, &c_b9, &ap[1], &bp[j1], &c__1, &c_b11, & ap[j1], &c__1); i__2 = j - 1; r__1 = 1.f / bjj; sscal_(&i__2, &r__1, &ap[j1], &c__1); i__2 = j - 1; ap[jj] = (ap[jj] - sdot_(&i__2, &ap[j1], &c__1, &bp[j1], & c__1)) / bjj; /* 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) */ akk = ap[kk]; bkk = bp[kk]; /* Computing 2nd power */ r__1 = bkk; akk /= r__1 * r__1; ap[kk] = akk; if (k < *n) { i__2 = *n - k; r__1 = 1.f / bkk; sscal_(&i__2, &r__1, &ap[kk + 1], &c__1); ct = akk * -.5f; i__2 = *n - k; saxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1) ; i__2 = *n - k; sspr2_(uplo, &i__2, &c_b9, &ap[kk + 1], &c__1, &bp[kk + 1] , &c__1, &ap[k1k1]); i__2 = *n - k; saxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1) ; i__2 = *n - k; stpsv_(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) */ akk = ap[kk]; bkk = bp[kk]; i__2 = k - 1; stpmv_(uplo, "No transpose", "Non-unit", &i__2, &bp[1], &ap[ k1], &c__1); ct = akk * .5f; i__2 = k - 1; saxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1); i__2 = k - 1; sspr2_(uplo, &i__2, &c_b11, &ap[k1], &c__1, &bp[k1], &c__1, & ap[1]); i__2 = k - 1; saxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1); i__2 = k - 1; sscal_(&i__2, &bkk, &ap[k1], &c__1); /* Computing 2nd power */ r__1 = bkk; ap[kk] = akk * (r__1 * r__1); /* 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 */ ajj = ap[jj]; bjj = bp[jj]; i__2 = *n - j; ap[jj] = ajj * bjj + sdot_(&i__2, &ap[jj + 1], &c__1, &bp[jj + 1], &c__1); i__2 = *n - j; sscal_(&i__2, &bjj, &ap[jj + 1], &c__1); i__2 = *n - j; sspmv_(uplo, &i__2, &c_b11, &ap[j1j1], &bp[jj + 1], &c__1, & c_b11, &ap[jj + 1], &c__1); i__2 = *n - j + 1; stpmv_(uplo, "Transpose", "Non-unit", &i__2, &bp[jj], &ap[jj], &c__1); jj = j1j1; /* L40: */ } } } return 0; /* End of SSPGST */ } /* sspgst_ */