#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int sspgvd_(integer *itype, char *jobz, char *uplo, integer * n, real *ap, real *bp, real *w, real *z__, integer *ldz, real *work, integer *lwork, integer *iwork, integer *liwork, integer *info) { /* -- LAPACK driver routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SSPGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be symmetric, stored in packed format, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. Arguments ========= ITYPE (input) INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x JOBZ (input) CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO (input) CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored. 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)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, the contents of AP are destroyed. BP (input/output) REAL array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix B, packed columnwise in a linear array. The j-th column of B is stored in the array BP as follows: if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. On exit, the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T, in the same storage format as B. W (output) REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. Z (output) REAL array, dimension (LDZ, N) If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I. If JOBZ = 'N', then Z is not referenced. LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the required LWORK. LWORK (input) INTEGER The dimension of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= 2*N. If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. If LWORK = -1, then a workspace query is assumed; the routine only calculates the required sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the required LIWORK. LIWORK (input) INTEGER The dimension of the array IWORK. If JOBZ = 'N' or N <= 1, LIWORK >= 1. If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the required sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: SPPTRF or SSPEVD returned an error code: <= N: if INFO = i, SSPEVD failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; > N: if INFO = N + i, for 1 <= i <= N, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. Further Details =============== Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; /* System generated locals */ integer z_dim1, z_offset, i__1; real r__1, r__2; /* Local variables */ static integer j, neig; extern logical lsame_(char *, char *); static integer lwmin; static char trans[1]; static logical upper, wantz; extern /* Subroutine */ int stpmv_(char *, char *, char *, integer *, real *, real *, integer *), stpsv_(char *, char *, char *, integer *, real *, real *, integer *), xerbla_(char *, integer *); static integer liwmin; extern /* Subroutine */ int sspevd_(char *, char *, integer *, real *, real *, real *, integer *, real *, integer *, integer *, integer * , integer *), spptrf_(char *, integer *, real *, integer *); static logical lquery; extern /* Subroutine */ int sspgst_(integer *, char *, integer *, real *, real *, integer *); --ap; --bp; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; --iwork; /* Function Body */ wantz = lsame_(jobz, "V"); upper = lsame_(uplo, "U"); lquery = *lwork == -1 || *liwork == -1; *info = 0; if (*itype < 1 || *itype > 3) { *info = -1; } else if (! (wantz || lsame_(jobz, "N"))) { *info = -2; } else if (! (upper || lsame_(uplo, "L"))) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -9; } if (*info == 0) { if (*n <= 1) { liwmin = 1; lwmin = 1; } else { if (wantz) { liwmin = *n * 5 + 3; /* Computing 2nd power */ i__1 = *n; lwmin = *n * 6 + 1 + (i__1 * i__1 << 1); } else { liwmin = 1; lwmin = *n << 1; } } work[1] = (real) lwmin; iwork[1] = liwmin; if (*lwork < lwmin && ! lquery) { *info = -11; } else if (*liwork < liwmin && ! lquery) { *info = -13; } } if (*info != 0) { i__1 = -(*info); xerbla_("SSPGVD", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Form a Cholesky factorization of BP. */ spptrf_(uplo, n, &bp[1], info); if (*info != 0) { *info = *n + *info; return 0; } /* Transform problem to standard eigenvalue problem and solve. */ sspgst_(itype, uplo, n, &ap[1], &bp[1], info); sspevd_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], lwork, &iwork[1], liwork, info); /* Computing MAX */ r__1 = (real) lwmin; lwmin = dmax(r__1,work[1]); /* Computing MAX */ r__1 = (real) liwmin, r__2 = (real) iwork[1]; liwmin = dmax(r__1,r__2); if (wantz) { /* Backtransform eigenvectors to the original problem. */ neig = *n; if (*info > 0) { neig = *info - 1; } if (*itype == 1 || *itype == 2) { /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */ if (upper) { *(unsigned char *)trans = 'N'; } else { *(unsigned char *)trans = 'T'; } i__1 = neig; for (j = 1; j <= i__1; ++j) { stpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 1], &c__1); /* L10: */ } } else if (*itype == 3) { /* For B*A*x=(lambda)*x; backtransform eigenvectors: x = L*y or U'*y */ if (upper) { *(unsigned char *)trans = 'T'; } else { *(unsigned char *)trans = 'N'; } i__1 = neig; for (j = 1; j <= i__1; ++j) { stpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 1], &c__1); /* L20: */ } } } work[1] = (real) lwmin; iwork[1] = liwmin; return 0; /* End of SSPGVD */ } /* sspgvd_ */