/* Subroutine */ int ssygst_(integer *itype, char *uplo, integer *n, real *a,
integer *lda, real *b, integer *ldb, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
integer k, kb, nb;
extern logical lsame_(char *, char *);
logical upper;
extern /* Subroutine */ int strmm_(char *, char *, char *, char *,
integer *, integer *, real *, real *, integer *, real *, integer *
), ssymm_(char *, char *, integer
*, integer *, real *, real *, integer *, real *, integer *, real *
, real *, integer *), strsm_(char *, char *, char
*, char *, integer *, integer *, real *, real *, integer *, real *
, integer *), ssygs2_(integer *,
char *, integer *, real *, integer *, real *, integer *, integer *
), ssyr2k_(char *, char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SSYGST reduces a real symmetric-definite generalized eigenproblem */
/* to standard form. */
/* 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 SPOTRF. */
/* 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. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the symmetric matrix A. If UPLO = 'U', the leading */
/* N-by-N upper triangular part of A contains the upper */
/* triangular part of the matrix A, and the strictly lower */
/* triangular part of A is not referenced. If UPLO = 'L', the */
/* leading N-by-N lower triangular part of A contains the lower */
/* triangular part of the matrix A, and the strictly upper */
/* triangular part of A is not referenced. */
/* On exit, if INFO = 0, the transformed matrix, stored in the */
/* same format as A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (input) REAL array, dimension (LDB,N) */
/* The triangular factor from the Cholesky factorization of B, */
/* as returned by SPOTRF. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* 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;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSYGST", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Determine the block size for this environment. */
nb = ilaenv_(&c__1, "SSYGST", uplo, n, &c_n1, &c_n1, &c_n1);
if (nb <= 1 || nb >= *n) {
/* Use unblocked code */
ssygs2_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
} else {
/* Use blocked code */
if (*itype == 1) {
if (upper) {
/* Compute inv(U')*A*inv(U) */
i__1 = *n;
i__2 = nb;
for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the upper triangle of A(k:n,k:n) */
ssygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k +
k * b_dim1], ldb, info);
if (k + kb <= *n) {
i__3 = *n - k - kb + 1;
strsm_("Left", uplo, "Transpose", "Non-unit", &kb, &
i__3, &c_b14, &b[k + k * b_dim1], ldb, &a[k +
(k + kb) * a_dim1], lda);
i__3 = *n - k - kb + 1;
ssymm_("Left", uplo, &kb, &i__3, &c_b16, &a[k + k *
a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb,
&c_b14, &a[k + (k + kb) * a_dim1], lda);
i__3 = *n - k - kb + 1;
ssyr2k_(uplo, "Transpose", &i__3, &kb, &c_b19, &a[k +
(k + kb) * a_dim1], lda, &b[k + (k + kb) *
b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) *
a_dim1], lda);
i__3 = *n - k - kb + 1;
ssymm_("Left", uplo, &kb, &i__3, &c_b16, &a[k + k *
a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb,
&c_b14, &a[k + (k + kb) * a_dim1], lda);
i__3 = *n - k - kb + 1;
strsm_("Right", uplo, "No transpose", "Non-unit", &kb,
&i__3, &c_b14, &b[k + kb + (k + kb) * b_dim1]
, ldb, &a[k + (k + kb) * a_dim1], lda);
}
/* L10: */
}
} else {
/* Compute inv(L)*A*inv(L') */
i__2 = *n;
i__1 = nb;
for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the lower triangle of A(k:n,k:n) */
ssygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k +
k * b_dim1], ldb, info);
if (k + kb <= *n) {
i__3 = *n - k - kb + 1;
strsm_("Right", uplo, "Transpose", "Non-unit", &i__3,
&kb, &c_b14, &b[k + k * b_dim1], ldb, &a[k +
kb + k * a_dim1], lda);
i__3 = *n - k - kb + 1;
ssymm_("Right", uplo, &i__3, &kb, &c_b16, &a[k + k *
a_dim1], lda, &b[k + kb + k * b_dim1], ldb, &
c_b14, &a[k + kb + k * a_dim1], lda);
i__3 = *n - k - kb + 1;
ssyr2k_(uplo, "No transpose", &i__3, &kb, &c_b19, &a[
k + kb + k * a_dim1], lda, &b[k + kb + k *
b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) *
a_dim1], lda);
i__3 = *n - k - kb + 1;
ssymm_("Right", uplo, &i__3, &kb, &c_b16, &a[k + k *
a_dim1], lda, &b[k + kb + k * b_dim1], ldb, &
c_b14, &a[k + kb + k * a_dim1], lda);
i__3 = *n - k - kb + 1;
strsm_("Left", uplo, "No transpose", "Non-unit", &
i__3, &kb, &c_b14, &b[k + kb + (k + kb) *
b_dim1], ldb, &a[k + kb + k * a_dim1], lda);
}
/* L20: */
}
}
} else {
if (upper) {
/* Compute U*A*U' */
i__1 = *n;
i__2 = nb;
for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */
i__3 = k - 1;
strmm_("Left", uplo, "No transpose", "Non-unit", &i__3, &
kb, &c_b14, &b[b_offset], ldb, &a[k * a_dim1 + 1],
lda)
;
i__3 = k - 1;
ssymm_("Right", uplo, &i__3, &kb, &c_b52, &a[k + k *
a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[
k * a_dim1 + 1], lda);
i__3 = k - 1;
ssyr2k_(uplo, "No transpose", &i__3, &kb, &c_b14, &a[k *
a_dim1 + 1], lda, &b[k * b_dim1 + 1], ldb, &c_b14,
&a[a_offset], lda);
i__3 = k - 1;
ssymm_("Right", uplo, &i__3, &kb, &c_b52, &a[k + k *
a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[
k * a_dim1 + 1], lda);
i__3 = k - 1;
strmm_("Right", uplo, "Transpose", "Non-unit", &i__3, &kb,
&c_b14, &b[k + k * b_dim1], ldb, &a[k * a_dim1 +
1], lda);
ssygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k +
k * b_dim1], ldb, info);
/* L30: */
}
} else {
/* Compute L'*A*L */
i__2 = *n;
i__1 = nb;
for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */
i__3 = k - 1;
strmm_("Right", uplo, "No transpose", "Non-unit", &kb, &
i__3, &c_b14, &b[b_offset], ldb, &a[k + a_dim1],
lda);
i__3 = k - 1;
ssymm_("Left", uplo, &kb, &i__3, &c_b52, &a[k + k *
a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k +
a_dim1], lda);
i__3 = k - 1;
ssyr2k_(uplo, "Transpose", &i__3, &kb, &c_b14, &a[k +
a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[
a_offset], lda);
i__3 = k - 1;
ssymm_("Left", uplo, &kb, &i__3, &c_b52, &a[k + k *
a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k +
a_dim1], lda);
i__3 = k - 1;
strmm_("Left", uplo, "Transpose", "Non-unit", &kb, &i__3,
&c_b14, &b[k + k * b_dim1], ldb, &a[k + a_dim1],
lda);
ssygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k +
k * b_dim1], ldb, info);
/* L40: */
}
}
}
}
return 0;
/* End of SSYGST */
} /* ssygst_ */
/* Subroutine */ int ssygst_(integer *itype, char *uplo, integer *n, real *a,
integer *lda, real *b, integer *ldb, 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
=======
SSYGST reduces a real symmetric-definite generalized eigenproblem
to standard form.
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 SPOTRF.
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
= '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.
A (input/output) REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if INFO = 0, the transformed matrix, stored in the
same format as A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input) REAL array, dimension (LDB,N)
The triangular factor from the Cholesky factorization of B,
as returned by SPOTRF.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
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 integer c_n1 = -1;
static real c_b14 = 1.f;
static real c_b16 = -.5f;
static real c_b19 = -1.f;
static real c_b52 = .5f;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
static integer k;
extern logical lsame_(char *, char *);
static logical upper;
extern /* Subroutine */ int strmm_(char *, char *, char *, char *,
integer *, integer *, real *, real *, integer *, real *, integer *
), ssymm_(char *, char *, integer
*, integer *, real *, real *, integer *, real *, integer *, real *
, real *, integer *), strsm_(char *, char *, char
*, char *, integer *, integer *, real *, real *, integer *, real *
, integer *);
static integer kb, nb;
extern /* Subroutine */ int ssygs2_(integer *, char *, integer *, real *,
integer *, real *, integer *, integer *), ssyr2k_(char *,
char *, integer *, integer *, real *, real *, integer *, real *,
integer *, real *, real *, integer *), xerbla_(
char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* 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;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSYGST", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Determine the block size for this environment. */
nb = ilaenv_(&c__1, "SSYGST", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
if (nb <= 1 || nb >= *n) {
/* Use unblocked code */
ssygs2_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
} else {
/* Use blocked code */
if (*itype == 1) {
if (upper) {
/* Compute inv(U')*A*inv(U) */
i__1 = *n;
i__2 = nb;
for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the upper triangle of A(k:n,k:n) */
ssygs2_(itype, uplo, &kb, &a_ref(k, k), lda, &b_ref(k, k),
ldb, info);
if (k + kb <= *n) {
i__3 = *n - k - kb + 1;
strsm_("Left", uplo, "Transpose", "Non-unit", &kb, &
i__3, &c_b14, &b_ref(k, k), ldb, &a_ref(k, k
+ kb), lda);
i__3 = *n - k - kb + 1;
ssymm_("Left", uplo, &kb, &i__3, &c_b16, &a_ref(k, k),
lda, &b_ref(k, k + kb), ldb, &c_b14, &a_ref(
k, k + kb), lda);
i__3 = *n - k - kb + 1;
ssyr2k_(uplo, "Transpose", &i__3, &kb, &c_b19, &a_ref(
k, k + kb), lda, &b_ref(k, k + kb), ldb, &
c_b14, &a_ref(k + kb, k + kb), lda);
i__3 = *n - k - kb + 1;
ssymm_("Left", uplo, &kb, &i__3, &c_b16, &a_ref(k, k),
lda, &b_ref(k, k + kb), ldb, &c_b14, &a_ref(
k, k + kb), lda);
i__3 = *n - k - kb + 1;
strsm_("Right", uplo, "No transpose", "Non-unit", &kb,
&i__3, &c_b14, &b_ref(k + kb, k + kb), ldb, &
a_ref(k, k + kb), lda);
}
/* L10: */
}
} else {
/* Compute inv(L)*A*inv(L') */
i__2 = *n;
i__1 = nb;
for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the lower triangle of A(k:n,k:n) */
ssygs2_(itype, uplo, &kb, &a_ref(k, k), lda, &b_ref(k, k),
ldb, info);
if (k + kb <= *n) {
i__3 = *n - k - kb + 1;
strsm_("Right", uplo, "Transpose", "Non-unit", &i__3,
&kb, &c_b14, &b_ref(k, k), ldb, &a_ref(k + kb,
k), lda);
i__3 = *n - k - kb + 1;
ssymm_("Right", uplo, &i__3, &kb, &c_b16, &a_ref(k, k)
, lda, &b_ref(k + kb, k), ldb, &c_b14, &a_ref(
k + kb, k), lda);
i__3 = *n - k - kb + 1;
ssyr2k_(uplo, "No transpose", &i__3, &kb, &c_b19, &
a_ref(k + kb, k), lda, &b_ref(k + kb, k), ldb,
&c_b14, &a_ref(k + kb, k + kb), lda);
i__3 = *n - k - kb + 1;
ssymm_("Right", uplo, &i__3, &kb, &c_b16, &a_ref(k, k)
, lda, &b_ref(k + kb, k), ldb, &c_b14, &a_ref(
k + kb, k), lda);
i__3 = *n - k - kb + 1;
strsm_("Left", uplo, "No transpose", "Non-unit", &
i__3, &kb, &c_b14, &b_ref(k + kb, k + kb),
ldb, &a_ref(k + kb, k), lda);
}
/* L20: */
}
}
} else {
if (upper) {
/* Compute U*A*U' */
i__1 = *n;
i__2 = nb;
for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */
i__3 = k - 1;
strmm_("Left", uplo, "No transpose", "Non-unit", &i__3, &
kb, &c_b14, &b[b_offset], ldb, &a_ref(1, k), lda);
i__3 = k - 1;
ssymm_("Right", uplo, &i__3, &kb, &c_b52, &a_ref(k, k),
lda, &b_ref(1, k), ldb, &c_b14, &a_ref(1, k), lda);
i__3 = k - 1;
ssyr2k_(uplo, "No transpose", &i__3, &kb, &c_b14, &a_ref(
1, k), lda, &b_ref(1, k), ldb, &c_b14, &a[
a_offset], lda);
i__3 = k - 1;
ssymm_("Right", uplo, &i__3, &kb, &c_b52, &a_ref(k, k),
lda, &b_ref(1, k), ldb, &c_b14, &a_ref(1, k), lda);
i__3 = k - 1;
strmm_("Right", uplo, "Transpose", "Non-unit", &i__3, &kb,
&c_b14, &b_ref(k, k), ldb, &a_ref(1, k), lda);
ssygs2_(itype, uplo, &kb, &a_ref(k, k), lda, &b_ref(k, k),
ldb, info);
/* L30: */
}
} else {
/* Compute L'*A*L */
i__2 = *n;
i__1 = nb;
for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */
i__3 = k - 1;
strmm_("Right", uplo, "No transpose", "Non-unit", &kb, &
i__3, &c_b14, &b[b_offset], ldb, &a_ref(k, 1),
lda);
i__3 = k - 1;
ssymm_("Left", uplo, &kb, &i__3, &c_b52, &a_ref(k, k),
lda, &b_ref(k, 1), ldb, &c_b14, &a_ref(k, 1), lda);
i__3 = k - 1;
ssyr2k_(uplo, "Transpose", &i__3, &kb, &c_b14, &a_ref(k,
1), lda, &b_ref(k, 1), ldb, &c_b14, &a[a_offset],
lda);
i__3 = k - 1;
ssymm_("Left", uplo, &kb, &i__3, &c_b52, &a_ref(k, k),
lda, &b_ref(k, 1), ldb, &c_b14, &a_ref(k, 1), lda);
i__3 = k - 1;
strmm_("Left", uplo, "Transpose", "Non-unit", &kb, &i__3,
&c_b14, &b_ref(k, k), ldb, &a_ref(k, 1), lda);
ssygs2_(itype, uplo, &kb, &a_ref(k, k), lda, &b_ref(k, k),
ldb, info);
/* L40: */
}
}
}
}
return 0;
/* End of SSYGST */
} /* ssygst_ */
/* Subroutine */ int ssytrd_(char *uplo, integer *n, real *a, integer *lda,
real *d__, real *e, real *tau, real *work, integer *lwork, integer *
info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
integer i__, j, nb, kk, nx, iws;
integer nbmin, iinfo;
logical upper;
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* SSYTRD reduces a real symmetric matrix A to real symmetric */
/* tridiagonal form T by an orthogonal similarity transformation: */
/* Q**T * 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. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the symmetric matrix A. If UPLO = 'U', the leading */
/* N-by-N upper triangular part of A contains the upper */
/* triangular part of the matrix A, and the strictly lower */
/* triangular part of A is not referenced. If UPLO = 'L', the */
/* leading N-by-N lower triangular part of A contains the lower */
/* triangular part of the matrix A, and the strictly upper */
/* triangular part of A is not referenced. */
/* 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 orthogonal */
/* 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 orthogonal matrix Q as a product */
/* of elementary reflectors. See Further Details. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* D (output) REAL array, dimension (N) */
/* The diagonal elements of the tridiagonal matrix T: */
/* D(i) = A(i,i). */
/* E (output) REAL 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) REAL array, dimension (N-1) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= 1. */
/* For optimum performance LWORK >= N*NB, where NB is the */
/* optimal blocksize. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* 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 real scalar, and v is a real vector with */
/* v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */
/* A(1:i-1,i+1), and tau 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 real scalar, and v is a real vector with */
/* v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */
/* and tau in TAU(i). */
/* The contents of A on exit are illustrated by the following examples */
/* with n = 5: */
/* if UPLO = 'U': if UPLO = 'L': */
/* ( d e v2 v3 v4 ) ( d ) */
/* ( d e v3 v4 ) ( e d ) */
/* ( d e v4 ) ( v1 e d ) */
/* ( d e ) ( v1 v2 e d ) */
/* ( d ) ( v1 v2 v3 e d ) */
/* where d and e denote diagonal and off-diagonal elements of T, and vi */
/* denotes an element of the vector defining H(i). */
/* ===================================================================== */
/* Test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--d__;
--e;
--tau;
--work;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
lquery = *lwork == -1;
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else if (*lwork < 1 && ! lquery) {
*info = -9;
}
if (*info == 0) {
/* Determine the block size. */
nb = ilaenv_(&c__1, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1);
lwkopt = *n * nb;
work[1] = (real) lwkopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSYTRD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
work[1] = 1.f;
return 0;
}
nx = *n;
iws = 1;
if (nb > 1 && nb < *n) {
/* Determine when to cross over from blocked to unblocked code */
/* (last block is always handled by unblocked code). */
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__3, "SSYTRD", uplo, n, &c_n1, &c_n1, &
c_n1);
nx = max(i__1,i__2);
if (nx < *n) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: determine the */
/* minimum value of NB, and reduce NB or force use of */
/* unblocked code by setting NX = N. */
/* Computing MAX */
i__1 = *lwork / ldwork;
nb = max(i__1,1);
nbmin = ilaenv_(&c__2, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1);
if (nb < nbmin) {
nx = *n;
}
}
} else {
nx = *n;
}
} else {
nb = 1;
}
if (upper) {
/* Reduce the upper triangle of A. */
/* Columns 1:kk are handled by the unblocked method. */
kk = *n - (*n - nx + nb - 1) / nb * nb;
i__1 = kk + 1;
i__2 = -nb;
for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the */
/* matrix W which is needed to update the unreduced part of */
/* the matrix */
i__3 = i__ + nb - 1;
slatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], &
work[1], &ldwork);
/* Update the unreduced submatrix A(1:i-1,1:i-1), using an */
/* update of the form: A := A - V*W' - W*V' */
i__3 = i__ - 1;
ssyr2k_(uplo, "No transpose", &i__3, &nb, &c_b22, &a[i__ * a_dim1
+ 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda);
/* Copy superdiagonal elements back into A, and diagonal */
/* elements into D */
i__3 = i__ + nb - 1;
for (j = i__; j <= i__3; ++j) {
a[j - 1 + j * a_dim1] = e[j - 1];
d__[j] = a[j + j * a_dim1];
}
}
/* Use unblocked code to reduce the last or only block */
ssytd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo);
} else {
/* Reduce the lower triangle of A */
i__2 = *n - nx;
i__1 = nb;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the */
/* matrix W which is needed to update the unreduced part of */
/* the matrix */
i__3 = *n - i__ + 1;
slatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], &
tau[i__], &work[1], &ldwork);
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using */
/* an update of the form: A := A - V*W' - W*V' */
i__3 = *n - i__ - nb + 1;
ssyr2k_(uplo, "No transpose", &i__3, &nb, &c_b22, &a[i__ + nb +
i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[
i__ + nb + (i__ + nb) * a_dim1], lda);
/* Copy subdiagonal elements back into A, and diagonal */
/* elements into D */
i__3 = i__ + nb - 1;
for (j = i__; j <= i__3; ++j) {
a[j + 1 + j * a_dim1] = e[j];
d__[j] = a[j + j * a_dim1];
}
}
/* Use unblocked code to reduce the last or only block */
i__1 = *n - i__ + 1;
ssytd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__],
&tau[i__], &iinfo);
}
work[1] = (real) lwkopt;
return 0;
/* End of SSYTRD */
} /* ssytrd_ */
void cblas_ssyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE Trans, const integer N, const integer K,
const float alpha, const float *A, const integer lda,
const float *B, const integer ldb, const float beta,
float *C, const integer ldc)
{
char UL, TR;
#ifdef F77_CHAR
F77_CHAR F77_TA, F77_UL;
#else
#define F77_TR &TR
#define F77_UL &UL
#endif
#define F77_N N
#define F77_K K
#define F77_lda lda
#define F77_ldb ldb
#define F77_ldc ldc
extern integer CBLAS_CallFromC;
extern integer RowMajorStrg;
RowMajorStrg = 0;
CBLAS_CallFromC = 1;
if( Order == CblasColMajor )
{
if( Uplo == CblasUpper) UL='U';
else if ( Uplo == CblasLower ) UL='L';
else
{
cblas_xerbla(2, "cblas_ssyr2k",
"Illegal Uplo setting, %d\n", Uplo);
CBLAS_CallFromC = 0;
RowMajorStrg = 0;
return;
}
if( Trans == CblasTrans) TR ='T';
else if ( Trans == CblasConjTrans ) TR='C';
else if ( Trans == CblasNoTrans ) TR='N';
else
{
cblas_xerbla(3, "cblas_ssyr2k",
"Illegal Trans setting, %d\n", Trans);
CBLAS_CallFromC = 0;
RowMajorStrg = 0;
return;
}
#ifdef F77_CHAR
F77_UL = C2F_CHAR(&UL);
F77_TR = C2F_CHAR(&TR);
#endif
ssyr2k_(F77_UL, F77_TR, &F77_N, &F77_K, &alpha, A, &F77_lda, B, &F77_ldb, &beta, C, &F77_ldc);
} else if (Order == CblasRowMajor)
{
RowMajorStrg = 1;
if( Uplo == CblasUpper) UL='L';
else if ( Uplo == CblasLower ) UL='U';
else
{
cblas_xerbla(3, "cblas_ssyr2k",
"Illegal Uplo setting, %d\n", Uplo);
CBLAS_CallFromC = 0;
RowMajorStrg = 0;
return;
}
if( Trans == CblasTrans) TR ='N';
else if ( Trans == CblasConjTrans ) TR='N';
else if ( Trans == CblasNoTrans ) TR='T';
else
{
cblas_xerbla(3, "cblas_ssyr2k",
"Illegal Trans setting, %d\n", Trans);
CBLAS_CallFromC = 0;
RowMajorStrg = 0;
return;
}
#ifdef F77_CHAR
F77_UL = C2F_CHAR(&UL);
F77_TR = C2F_CHAR(&TR);
#endif
ssyr2k_(F77_UL, F77_TR, &F77_N, &F77_K, &alpha, A, &F77_lda, B, &F77_ldb, &beta, C, &F77_ldc);
} else cblas_xerbla(1, "cblas_ssyr2k",
"Illegal Order setting, %d\n", Order);
CBLAS_CallFromC = 0;
RowMajorStrg = 0;
return;
}
/* Subroutine */ int ssytrd_(char *uplo, integer *n, real *a, integer *lda,
real *d, real *e, real *tau, real *work, integer *lwork, integer *
info)
{
/* -- LAPACK routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
SSYTRD reduces a real symmetric matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**T * 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.
A (input/output) REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
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 orthogonal
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 orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
D (output) REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
E (output) REAL 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) REAL array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1.
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
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 real scalar, and v is a real vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau 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 real scalar, and v is a real vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = 'U': if UPLO = 'L':
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
=====================================================================
Test the input parameters
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
static real c_b22 = -1.f;
static real c_b23 = 1.f;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
static integer i, j;
extern logical lsame_(char *, char *);
static integer nbmin, iinfo;
static logical upper;
static integer nb, kk;
extern /* Subroutine */ int ssytd2_(char *, integer *, real *, integer *,
real *, real *, real *, integer *), ssyr2k_(char *, char *
, integer *, integer *, real *, real *, integer *, real *,
integer *, real *, real *, integer *);
static integer nx;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int slatrd_(char *, integer *, integer *, real *,
integer *, real *, real *, real *, integer *);
static integer ldwork, iws;
#define D(I) d[(I)-1]
#define E(I) e[(I)-1]
#define TAU(I) tau[(I)-1]
#define WORK(I) work[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else if (*lwork < 1) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSYTRD", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
WORK(1) = 1.f;
return 0;
}
/* Determine the block size. */
nb = ilaenv_(&c__1, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, 6L, 1L);
nx = *n;
iws = 1;
if (nb > 1 && nb < *n) {
/* Determine when to cross over from blocked to unblocked code
(last block is always handled by unblocked code).
Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__3, "SSYTRD", uplo, n, &c_n1, &c_n1, &
c_n1, 6L, 1L);
nx = max(i__1,i__2);
if (nx < *n) {
/* Determine if workspace is large enough for blocked co
de. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: deter
mine the
minimum value of NB, and reduce NB or force us
e of
unblocked code by setting NX = N.
Computing MAX */
i__1 = *lwork / ldwork;
nb = max(i__1,1);
nbmin = ilaenv_(&c__2, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1,
6L, 1L);
if (nb < nbmin) {
nx = *n;
}
}
} else {
nx = *n;
}
} else {
nb = 1;
}
if (upper) {
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
kk = *n - (*n - nx + nb - 1) / nb * nb;
i__1 = kk + 1;
i__2 = -nb;
for (i = *n - nb + 1; -nb < 0 ? i >= kk+1 : i <= kk+1; i += -nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form
the
matrix W which is needed to update the unreduced part
of
the matrix */
i__3 = i + nb - 1;
slatrd_(uplo, &i__3, &nb, &A(1,1), lda, &E(1), &TAU(1), &
WORK(1), &ldwork);
/* Update the unreduced submatrix A(1:i-1,1:i-1), using
an
update of the form: A := A - V*W' - W*V' */
i__3 = i - 1;
ssyr2k_(uplo, "No transpose", &i__3, &nb, &c_b22, &A(1,i), lda, &WORK(1), &ldwork, &c_b23, &A(1,1), lda);
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
i__3 = i + nb - 1;
for (j = i; j <= i+nb-1; ++j) {
A(j-1,j) = E(j - 1);
D(j) = A(j,j);
/* L10: */
}
/* L20: */
}
/* Use unblocked code to reduce the last or only block */
ssytd2_(uplo, &kk, &A(1,1), lda, &D(1), &E(1), &TAU(1), &iinfo);
} else {
/* Reduce the lower triangle of A */
i__2 = *n - nx;
i__1 = nb;
for (i = 1; nb < 0 ? i >= *n-nx : i <= *n-nx; i += nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form
the
matrix W which is needed to update the unreduced part
of
the matrix */
i__3 = *n - i + 1;
slatrd_(uplo, &i__3, &nb, &A(i,i), lda, &E(i), &TAU(i),
&WORK(1), &ldwork);
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), usin
g
an update of the form: A := A - V*W' - W*V' */
i__3 = *n - i - nb + 1;
ssyr2k_(uplo, "No transpose", &i__3, &nb, &c_b22, &A(i+nb,i), lda, &WORK(nb + 1), &ldwork, &c_b23, &A(i+nb,i+nb), lda);
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
i__3 = i + nb - 1;
for (j = i; j <= i+nb-1; ++j) {
A(j+1,j) = E(j);
D(j) = A(j,j);
/* L30: */
}
/* L40: */
}
/* Use unblocked code to reduce the last or only block */
i__1 = *n - i + 1;
ssytd2_(uplo, &i__1, &A(i,i), lda, &D(i), &E(i), &TAU(i), &
iinfo);
}
WORK(1) = (real) iws;
return 0;
/* End of SSYTRD */
} /* ssytrd_ */
