int sspgv_(int *itype, char *jobz, char *uplo, int *
n, float *ap, float *bp, float *w, float *z__, int *ldz, float *work,
int *info)
{
/* System generated locals */
int z_dim1, z_offset, i__1;
/* Local variables */
int j, neig;
extern int lsame_(char *, char *);
char trans[1];
int upper;
extern int sspev_(char *, char *, int *, float *,
float *, float *, int *, float *, int *);
int wantz;
extern int stpmv_(char *, char *, char *, int *,
float *, float *, int *), stpsv_(char *,
char *, char *, int *, float *, float *, int *), xerbla_(char *, int *), spptrf_(char
*, int *, float *, int *), sspgst_(int *, char
*, int *, float *, float *, int *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SSPGV computes all the eigenvalues and, optionally, the eigenvectors */
/* of a float 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. */
/* 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) REAL array, dimension (3*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: SPPTRF or SSPEV returned an error code: */
/* <= N: if INFO = i, SSPEV 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. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
--bp;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
/* Function Body */
wantz = lsame_(jobz, "V");
upper = lsame_(uplo, "U");
*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) {
i__1 = -(*info);
xerbla_("SSPGV ", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form a Cholesky factorization of B. */
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);
sspev_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], info);
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: */
}
}
}
return 0;
/* End of SSPGV */
} /* sspgv_ */
/* Subroutine */ int sspgv_(integer *itype, char *jobz, char *uplo, integer *
n, real *ap, real *bp, real *w, real *z__, integer *ldz, real *work,
integer *info)
{
/* -- LAPACK driver 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
=======
SSPGV 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.
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) REAL array, dimension (3*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: SPPTRF or SSPEV returned an error code:
<= N: if INFO = i, SSPEV 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.
=====================================================================
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;
/* Local variables */
static integer neig, j;
extern logical lsame_(char *, char *);
static char trans[1];
static logical upper;
extern /* Subroutine */ int sspev_(char *, char *, integer *, real *,
real *, real *, integer *, real *, integer *);
static logical wantz;
extern /* Subroutine */ int stpmv_(char *, char *, char *, integer *,
real *, real *, integer *), stpsv_(char *,
char *, char *, integer *, real *, real *, integer *), xerbla_(char *, integer *), spptrf_(char
*, integer *, real *, integer *), sspgst_(integer *, char
*, integer *, real *, real *, integer *);
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]
--ap;
--bp;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--work;
/* Function Body */
wantz = lsame_(jobz, "V");
upper = lsame_(uplo, "U");
*info = 0;
if (*itype < 0 || *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) {
i__1 = -(*info);
xerbla_("SSPGV ", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form a Cholesky factorization of B. */
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);
sspev_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], info);
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___ref(1, j), &
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___ref(1, j), &
c__1);
/* L20: */
}
}
}
return 0;
/* End of SSPGV */
} /* sspgv_ */
