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#include "relapack.h"
#if XSYGST_ALLOW_MALLOC
#include "stdlib.h"
#endif
static void RELAPACK_dsygst_rec(const int *, const char *, const int *,
double *, const int *, const double *, const int *,
double *, const int *, int *);
/** DSYGST reduces a real symmetric-definite generalized eigenproblem to standard form.
*
* This routine is functionally equivalent to LAPACK's dsygst.
* For details on its interface, see
* http://www.netlib.org/lapack/explore-html/dc/d04/dsygst_8f.html
* */
void RELAPACK_dsygst(
const int *itype, const char *uplo, const int *n,
double *A, const int *ldA, const double *B, const int *ldB,
int *info
) {
// Check arguments
const int lower = LAPACK(lsame)(uplo, "L");
const int upper = LAPACK(lsame)(uplo, "U");
*info = 0;
if (*itype < 1 || *itype > 3)
*info = -1;
else if (!lower && !upper)
*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) {
const int minfo = -*info;
LAPACK(xerbla)("DSYGST", &minfo);
return;
}
// Clean char * arguments
const char cleanuplo = lower ? 'L' : 'U';
// Allocate work space
double *Work = NULL;
int lWork = 0;
#if XSYGST_ALLOW_MALLOC
const int n1 = DREC_SPLIT(*n);
lWork = n1 * (*n - n1);
Work = malloc(lWork * sizeof(double));
if (!Work)
lWork = 0;
#endif
// recursive kernel
RELAPACK_dsygst_rec(itype, &cleanuplo, n, A, ldA, B, ldB, Work, &lWork, info);
// Free work space
#if XSYGST_ALLOW_MALLOC
if (Work)
free(Work);
#endif
}
/** dsygst's recursive compute kernel */
static void RELAPACK_dsygst_rec(
const int *itype, const char *uplo, const int *n,
double *A, const int *ldA, const double *B, const int *ldB,
double *Work, const int *lWork, int *info
) {
if (*n <= MAX(CROSSOVER_SSYGST, 1)) {
// Unblocked
LAPACK(dsygs2)(itype, uplo, n, A, ldA, B, ldB, info);
return;
}
// Constants
const double ZERO[] = { 0. };
const double ONE[] = { 1. };
const double MONE[] = { -1. };
const double HALF[] = { .5 };
const double MHALF[] = { -.5 };
const int iONE[] = { 1 };
// Loop iterator
int i;
// Splitting
const int n1 = DREC_SPLIT(*n);
const int n2 = *n - n1;
// A_TL A_TR
// A_BL A_BR
double *const A_TL = A;
double *const A_TR = A + *ldA * n1;
double *const A_BL = A + n1;
double *const A_BR = A + *ldA * n1 + n1;
// B_TL B_TR
// B_BL B_BR
const double *const B_TL = B;
const double *const B_TR = B + *ldB * n1;
const double *const B_BL = B + n1;
const double *const B_BR = B + *ldB * n1 + n1;
// recursion(A_TL, B_TL)
RELAPACK_dsygst_rec(itype, uplo, &n1, A_TL, ldA, B_TL, ldB, Work, lWork, info);
if (*itype == 1)
if (*uplo == 'L') {
// A_BL = A_BL / B_TL'
BLAS(dtrsm)("R", "L", "T", "N", &n2, &n1, ONE, B_TL, ldB, A_BL, ldA);
if (*lWork > n2 * n1) {
// T = -1/2 * B_BL * A_TL
BLAS(dsymm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ZERO, Work, &n2);
// A_BL = A_BL + T
for (i = 0; i < n1; i++)
BLAS(daxpy)(&n2, ONE, Work + n2 * i, iONE, A_BL + *ldA * i, iONE);
} else
// A_BL = A_BL - 1/2 B_BL * A_TL
BLAS(dsymm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ONE, A_BL, ldA);
// A_BR = A_BR - A_BL * B_BL' - B_BL * A_BL'
BLAS(dsyr2k)("L", "N", &n2, &n1, MONE, A_BL, ldA, B_BL, ldB, ONE, A_BR, ldA);
if (*lWork > n2 * n1)
// A_BL = A_BL + T
for (i = 0; i < n1; i++)
BLAS(daxpy)(&n2, ONE, Work + n2 * i, iONE, A_BL + *ldA * i, iONE);
else
// A_BL = A_BL - 1/2 B_BL * A_TL
BLAS(dsymm)("R", "L", &n2, &n1, MHALF, A_TL, ldA, B_BL, ldB, ONE, A_BL, ldA);
// A_BL = B_BR \ A_BL
BLAS(dtrsm)("L", "L", "N", "N", &n2, &n1, ONE, B_BR, ldB, A_BL, ldA);
} else {
// A_TR = B_TL' \ A_TR
BLAS(dtrsm)("L", "U", "T", "N", &n1, &n2, ONE, B_TL, ldB, A_TR, ldA);
if (*lWork > n2 * n1) {
// T = -1/2 * A_TL * B_TR
BLAS(dsymm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ZERO, Work, &n1);
// A_TR = A_BL + T
for (i = 0; i < n2; i++)
BLAS(daxpy)(&n1, ONE, Work + n1 * i, iONE, A_TR + *ldA * i, iONE);
} else
// A_TR = A_TR - 1/2 A_TL * B_TR
BLAS(dsymm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ONE, A_TR, ldA);
// A_BR = A_BR - A_TR' * B_TR - B_TR' * A_TR
BLAS(dsyr2k)("U", "T", &n2, &n1, MONE, A_TR, ldA, B_TR, ldB, ONE, A_BR, ldA);
if (*lWork > n2 * n1)
// A_TR = A_BL + T
for (i = 0; i < n2; i++)
BLAS(daxpy)(&n1, ONE, Work + n1 * i, iONE, A_TR + *ldA * i, iONE);
else
// A_TR = A_TR - 1/2 A_TL * B_TR
BLAS(dsymm)("L", "U", &n1, &n2, MHALF, A_TL, ldA, B_TR, ldB, ONE, A_TR, ldA);
// A_TR = A_TR / B_BR
BLAS(dtrsm)("R", "U", "N", "N", &n1, &n2, ONE, B_BR, ldB, A_TR, ldA);
}
else
if (*uplo == 'L') {
// A_BL = A_BL * B_TL
BLAS(dtrmm)("R", "L", "N", "N", &n2, &n1, ONE, B_TL, ldB, A_BL, ldA);
if (*lWork > n2 * n1) {
// T = 1/2 * A_BR * B_BL
BLAS(dsymm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ZERO, Work, &n2);
// A_BL = A_BL + T
for (i = 0; i < n1; i++)
BLAS(daxpy)(&n2, ONE, Work + n2 * i, iONE, A_BL + *ldA * i, iONE);
} else
// A_BL = A_BL + 1/2 A_BR * B_BL
BLAS(dsymm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ONE, A_BL, ldA);
// A_TL = A_TL + A_BL' * B_BL + B_BL' * A_BL
BLAS(dsyr2k)("L", "T", &n1, &n2, ONE, A_BL, ldA, B_BL, ldB, ONE, A_TL, ldA);
if (*lWork > n2 * n1)
// A_BL = A_BL + T
for (i = 0; i < n1; i++)
BLAS(daxpy)(&n2, ONE, Work + n2 * i, iONE, A_BL + *ldA * i, iONE);
else
// A_BL = A_BL + 1/2 A_BR * B_BL
BLAS(dsymm)("L", "L", &n2, &n1, HALF, A_BR, ldA, B_BL, ldB, ONE, A_BL, ldA);
// A_BL = B_BR * A_BL
BLAS(dtrmm)("L", "L", "T", "N", &n2, &n1, ONE, B_BR, ldB, A_BL, ldA);
} else {
// A_TR = B_TL * A_TR
BLAS(dtrmm)("L", "U", "N", "N", &n1, &n2, ONE, B_TL, ldB, A_TR, ldA);
if (*lWork > n2 * n1) {
// T = 1/2 * B_TR * A_BR
BLAS(dsymm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ZERO, Work, &n1);
// A_TR = A_TR + T
for (i = 0; i < n2; i++)
BLAS(daxpy)(&n1, ONE, Work + n1 * i, iONE, A_TR + *ldA * i, iONE);
} else
// A_TR = A_TR + 1/2 B_TR A_BR
BLAS(dsymm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ONE, A_TR, ldA);
// A_TL = A_TL + A_TR * B_TR' + B_TR * A_TR'
BLAS(dsyr2k)("U", "N", &n1, &n2, ONE, A_TR, ldA, B_TR, ldB, ONE, A_TL, ldA);
if (*lWork > n2 * n1)
// A_TR = A_TR + T
for (i = 0; i < n2; i++)
BLAS(daxpy)(&n1, ONE, Work + n1 * i, iONE, A_TR + *ldA * i, iONE);
else
// A_TR = A_TR + 1/2 B_TR * A_BR
BLAS(dsymm)("R", "U", &n1, &n2, HALF, A_BR, ldA, B_TR, ldB, ONE, A_TR, ldA);
// A_TR = A_TR * B_BR
BLAS(dtrmm)("R", "U", "T", "N", &n1, &n2, ONE, B_BR, ldB, A_TR, ldA);
}
// recursion(A_BR, B_BR)
RELAPACK_dsygst_rec(itype, uplo, &n2, A_BR, ldA, B_BR, ldB, Work, lWork, info);
}
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