// Copyright (C) 2010 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_MATRiX_TRSM_Hh_
#define DLIB_MATRiX_TRSM_Hh_
#include "lapack/fortran_id.h"
#include "cblas_constants.h"
namespace dlib
{
namespace blas_bindings
{
#ifndef CBLAS_H
extern "C"
{
void cblas_strsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag, const int M, const int N,
const float alpha, const float *A, const int lda,
float *B, const int ldb);
void cblas_dtrsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag, const int M, const int N,
const double alpha, const double *A, const int lda,
double *B, const int ldb);
}
#endif // if not CBLAS_H
// ------------------------------------------------------------------------------------
/* Purpose */
/* ======= */
/* DTRSM solves one of the matrix equations */
/* op( A )*X = alpha*B, or X*op( A ) = alpha*B, */
/* where alpha is a scalar, X and B are m by n matrices, A is a unit, or */
/* non-unit, upper or lower triangular matrix and op( A ) is one of */
/* op( A ) = A or op( A ) = A'. */
/* The matrix X is overwritten on B. */
/* Arguments */
/* ========== */
/* SIDE - CHARACTER*1. */
/* On entry, SIDE specifies whether op( A ) appears on the left */
/* or right of X as follows: */
/* SIDE = 'L' or 'l' op( A )*X = alpha*B. */
/* SIDE = 'R' or 'r' X*op( A ) = alpha*B. */
/* Unchanged on exit. */
/* UPLO - CHARACTER*1. */
/* On entry, UPLO specifies whether the matrix A is an upper or */
/* lower triangular matrix as follows: */
/* UPLO = 'U' or 'u' A is an upper triangular matrix. */
/* UPLO = 'L' or 'l' A is a lower triangular matrix. */
/* Unchanged on exit. */
/* TRANSA - CHARACTER*1. */
/* On entry, TRANSA specifies the form of op( A ) to be used in */
/* the matrix multiplication as follows: */
/* TRANSA = 'N' or 'n' op( A ) = A. */
/* TRANSA = 'T' or 't' op( A ) = A'. */
/* TRANSA = 'C' or 'c' op( A ) = A'. */
/* Unchanged on exit. */
/* DIAG - CHARACTER*1. */
/* On entry, DIAG specifies whether or not A is unit triangular */
/* as follows: */
/* DIAG = 'U' or 'u' A is assumed to be unit triangular. */
/* DIAG = 'N' or 'n' A is not assumed to be unit */
/* triangular. */
/* Unchanged on exit. */
/* M - INTEGER. */
/* On entry, M specifies the number of rows of B. M must be at */
/* least zero. */
/* Unchanged on exit. */
/* N - INTEGER. */
/* On entry, N specifies the number of columns of B. N must be */
/* at least zero. */
/* Unchanged on exit. */
/* ALPHA - DOUBLE PRECISION. */
/* On entry, ALPHA specifies the scalar alpha. When alpha is */
/* zero then A is not referenced and B need not be set before */
/* entry. */
/* Unchanged on exit. */
/* A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m */
/* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. */
/* Before entry with UPLO = 'U' or 'u', the leading k by k */
/* upper triangular part of the array A must contain the upper */
/* triangular matrix and the strictly lower triangular part of */
/* A is not referenced. */
/* Before entry with UPLO = 'L' or 'l', the leading k by k */
/* lower triangular part of the array A must contain the lower */
/* triangular matrix and the strictly upper triangular part of */
/* A is not referenced. */
/* Note that when DIAG = 'U' or 'u', the diagonal elements of */
/* A are not referenced either, but are assumed to be unity. */
/* Unchanged on exit. */
/* LDA - INTEGER. */
/* On entry, LDA specifies the first dimension of A as declared */
/* in the calling (sub) program. When SIDE = 'L' or 'l' then */
/* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' */
/* then LDA must be at least max( 1, n ). */
/* Unchanged on exit. */
/* B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). */
/* Before entry, the leading m by n part of the array B must */
/* contain the right-hand side matrix B, and on exit is */
/* overwritten by the solution matrix X. */
/* LDB - INTEGER. */
/* On entry, LDB specifies the first dimension of B as declared */
/* in the calling (sub) program. LDB must be at least */
/* max( 1, m ). */
/* Unchanged on exit. */
/* Level 3 Blas routine. */
/* -- Written on 8-February-1989. */
/* Jack Dongarra, Argonne National Laboratory. */
/* Iain Duff, AERE Harwell. */
/* Jeremy Du Croz, Numerical Algorithms Group Ltd. */
/* Sven Hammarling, Numerical Algorithms Group Ltd. */
template <typename T>
void local_trsm(
const enum CBLAS_ORDER Order,
enum CBLAS_SIDE Side,
enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
long m,
long n,
T alpha,
const T *a,
long lda,
T *b,
long ldb
)
/*!
This is a copy of the dtrsm routine from the netlib.org BLAS which was run though
f2c and converted into this form for use when a BLAS library is not available.
!*/
{
if (Order == CblasRowMajor)
{
// since row major ordering looks like transposition to FORTRAN we need to flip a
// few things.
if (Side == CblasLeft)
Side = CblasRight;
else
Side = CblasLeft;
if (Uplo == CblasUpper)
Uplo = CblasLower;
else
Uplo = CblasUpper;
std::swap(m,n);
}
/* System generated locals */
long a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
long i__, j, k, info;
T temp;
bool lside;
long nrowa;
bool upper;
bool nounit;
/* 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 */
lside = (Side == CblasLeft);
if (lside)
{
nrowa = m;
} else
{
nrowa = n;
}
nounit = (Diag == CblasNonUnit);
upper = (Uplo == CblasUpper);
info = 0;
if (! lside && ! (Side == CblasRight)) {
info = 1;
} else if (! upper && !(Uplo == CblasLower) ) {
info = 2;
} else if (!(TransA == CblasNoTrans) &&
!(TransA == CblasTrans) &&
!(TransA == CblasConjTrans)) {
info = 3;
} else if (!(Diag == CblasUnit) &&
!(Diag == CblasNonUnit) ) {
info = 4;
} else if (m < 0) {
info = 5;
} else if (n < 0) {
info = 6;
} else if (lda < std::max<long>(1,nrowa)) {
info = 9;
} else if (ldb < std::max<long>(1,m)) {
info = 11;
}
DLIB_CASSERT( info == 0, "Invalid inputs given to local_trsm");
/* Quick return if possible. */
if (m == 0 || n == 0) {
return;
}
/* And when alpha.eq.zero. */
if (alpha == 0.) {
i__1 = n;
for (j = 1; j <= i__1; ++j) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = 0.;
/* L10: */
}
/* L20: */
}
return;
}
/* Start the operations. */
if (lside) {
if (TransA == CblasNoTrans) {
/* Form B := alpha*inv( A )*B. */
if (upper) {
i__1 = n;
for (j = 1; j <= i__1; ++j) {
if (alpha != 1.) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
;
/* L30: */
}
}
for (k = m; k >= 1; --k) {
if (b[k + j * b_dim1] != 0.) {
if (nounit) {
b[k + j * b_dim1] /= a[k + k * a_dim1];
}
i__2 = k - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
i__ + k * a_dim1];
/* L40: */
}
}
/* L50: */
}
/* L60: */
}
} else {
i__1 = n;
for (j = 1; j <= i__1; ++j) {
if (alpha != 1.) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
;
/* L70: */
}
}
i__2 = m;
for (k = 1; k <= i__2; ++k) {
if (b[k + j * b_dim1] != 0.) {
if (nounit) {
b[k + j * b_dim1] /= a[k + k * a_dim1];
}
i__3 = m;
for (i__ = k + 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
i__ + k * a_dim1];
/* L80: */
}
}
/* L90: */
}
/* L100: */
}
}
} else {
/* Form B := alpha*inv( A' )*B. */
if (upper) {
i__1 = n;
for (j = 1; j <= i__1; ++j) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = alpha * b[i__ + j * b_dim1];
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L110: */
}
if (nounit) {
temp /= a[i__ + i__ * a_dim1];
}
b[i__ + j * b_dim1] = temp;
/* L120: */
}
/* L130: */
}
} else {
i__1 = n;
for (j = 1; j <= i__1; ++j) {
for (i__ = m; i__ >= 1; --i__) {
temp = alpha * b[i__ + j * b_dim1];
i__2 = m;
for (k = i__ + 1; k <= i__2; ++k) {
temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L140: */
}
if (nounit) {
temp /= a[i__ + i__ * a_dim1];
}
b[i__ + j * b_dim1] = temp;
/* L150: */
}
/* L160: */
}
}
}
} else {
if (TransA == CblasNoTrans) {
/* Form B := alpha*B*inv( A ). */
if (upper) {
i__1 = n;
for (j = 1; j <= i__1; ++j) {
if (alpha != 1.) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
;
/* L170: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
if (a[k + j * a_dim1] != 0.) {
i__3 = m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
i__ + k * b_dim1];
/* L180: */
}
}
/* L190: */
}
if (nounit) {
temp = 1. / a[j + j * a_dim1];
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L200: */
}
}
/* L210: */
}
} else {
for (j = n; j >= 1; --j) {
if (alpha != 1.) {
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + j * b_dim1] = alpha * b[i__ + j * b_dim1]
;
/* L220: */
}
}
i__1 = n;
for (k = j + 1; k <= i__1; ++k) {
if (a[k + j * a_dim1] != 0.) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
i__ + k * b_dim1];
/* L230: */
}
}
/* L240: */
}
if (nounit) {
temp = 1. / a[j + j * a_dim1];
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L250: */
}
}
/* L260: */
}
}
} else {
/* Form B := alpha*B*inv( A' ). */
if (upper) {
for (k = n; k >= 1; --k) {
if (nounit) {
temp = 1. / a[k + k * a_dim1];
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L270: */
}
}
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
if (a[j + k * a_dim1] != 0.) {
temp = a[j + k * a_dim1];
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= temp * b[i__ + k *
b_dim1];
/* L280: */
}
}
/* L290: */
}
if (alpha != 1.) {
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + k * b_dim1] = alpha * b[i__ + k * b_dim1]
;
/* L300: */
}
}
/* L310: */
}
} else {
i__1 = n;
for (k = 1; k <= i__1; ++k) {
if (nounit) {
temp = 1. / a[k + k * a_dim1];
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L320: */
}
}
i__2 = n;
for (j = k + 1; j <= i__2; ++j) {
if (a[j + k * a_dim1] != 0.) {
temp = a[j + k * a_dim1];
i__3 = m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= temp * b[i__ + k *
b_dim1];
/* L330: */
}
}
/* L340: */
}
if (alpha != 1.) {
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + k * b_dim1] = alpha * b[i__ + k * b_dim1]
;
/* L350: */
}
}
/* L360: */
}
}
}
}
}
// ------------------------------------------------------------------------------------
inline void cblas_trsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag, const int M, const int N,
const float alpha, const float *A, const int lda,
float *B, const int ldb)
{
#ifdef DLIB_USE_BLAS
if (M > 4)
{
cblas_strsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
return;
}
#endif
local_trsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
}
inline void cblas_trsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag, const int M, const int N,
const double alpha, const double *A, const int lda,
double *B, const int ldb)
{
#ifdef DLIB_USE_BLAS
if (M > 4)
{
cblas_dtrsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
return;
}
#endif
local_trsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
}
inline void cblas_trsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag, const int M, const int N,
const long double alpha, const long double *A, const int lda,
long double *B, const int ldb)
{
local_trsm(Order, Side, Uplo, TransA, Diag, M, N, alpha, A, lda, B, ldb);
}
// ------------------------------------------------------------------------------------
template <
typename T,
long NR1, long NR2,
long NC1, long NC2,
typename MM
>
inline void triangular_solver (
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const matrix<T,NR1,NC1,MM,row_major_layout>& A,
const T alpha,
matrix<T,NR2,NC2,MM,row_major_layout>& B
)
{
cblas_trsm(CblasRowMajor, Side, Uplo, TransA, Diag, B.nr(), B.nc(),
alpha, &A(0,0), A.nc(), &B(0,0), B.nc());
}
// ------------------------------------------------------------------------------------
template <
typename T,
long NR1, long NR2,
long NC1, long NC2,
typename MM
>
inline void triangular_solver (
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const matrix<T,NR1,NC1,MM,column_major_layout>& A,
const T alpha,
matrix<T,NR2,NC2,MM,column_major_layout>& B
)
{
cblas_trsm(CblasColMajor, Side, Uplo, TransA, Diag, B.nr(), B.nc(),
alpha, &A(0,0), A.nr(), &B(0,0), B.nr());
}
// ------------------------------------------------------------------------------------
template <
typename T,
long NR1, long NR2,
long NC1, long NC2,
typename MM
>
inline void triangular_solver (
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const matrix<T,NR1,NC1,MM,column_major_layout>& A,
matrix<T,NR2,NC2,MM,column_major_layout>& B,
long rows_of_B
)
{
const T alpha = 1;
cblas_trsm(CblasColMajor, Side, Uplo, TransA, Diag, rows_of_B, B.nc(),
alpha, &A(0,0), A.nr(), &B(0,0), B.nr());
}
// ------------------------------------------------------------------------------------
template <
typename T,
long NR1, long NR2,
long NC1, long NC2,
typename MM,
typename layout
>
inline void triangular_solver (
const enum CBLAS_SIDE Side,
const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA,
const enum CBLAS_DIAG Diag,
const matrix<T,NR1,NC1,MM,layout>& A,
matrix<T,NR2,NC2,MM,layout>& B
)
{
const T alpha = 1;
triangular_solver(Side, Uplo, TransA, Diag, A, alpha, B);
}
// ------------------------------------------------------------------------------------
}
}
#endif // DLIB_MATRiX_TRSM_Hh_