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// Copyright ©2018 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package gonum
import (
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
)
// Dpotrs solves a system of n linear equations A*X = B where A is an n×n
// symmetric positive definite matrix and B is an n×nrhs matrix. The matrix A is
// represented by its Cholesky factorization
// A = Uᵀ*U if uplo == blas.Upper
// A = L*Lᵀ if uplo == blas.Lower
// as computed by Dpotrf. On entry, B contains the right-hand side matrix B, on
// return it contains the solution matrix X.
func (Implementation) Dpotrs(uplo blas.Uplo, n, nrhs int, a []float64, lda int, b []float64, ldb int) {
switch {
case uplo != blas.Upper && uplo != blas.Lower:
panic(badUplo)
case n < 0:
panic(nLT0)
case nrhs < 0:
panic(nrhsLT0)
case lda < max(1, n):
panic(badLdA)
case ldb < max(1, nrhs):
panic(badLdB)
}
// Quick return if possible.
if n == 0 || nrhs == 0 {
return
}
switch {
case len(a) < (n-1)*lda+n:
panic(shortA)
case len(b) < (n-1)*ldb+nrhs:
panic(shortB)
}
bi := blas64.Implementation()
if uplo == blas.Upper {
// Solve Uᵀ * U * X = B where U is stored in the upper triangle of A.
// Solve Uᵀ * X = B, overwriting B with X.
bi.Dtrsm(blas.Left, blas.Upper, blas.Trans, blas.NonUnit, n, nrhs, 1, a, lda, b, ldb)
// Solve U * X = B, overwriting B with X.
bi.Dtrsm(blas.Left, blas.Upper, blas.NoTrans, blas.NonUnit, n, nrhs, 1, a, lda, b, ldb)
} else {
// Solve L * Lᵀ * X = B where L is stored in the lower triangle of A.
// Solve L * X = B, overwriting B with X.
bi.Dtrsm(blas.Left, blas.Lower, blas.NoTrans, blas.NonUnit, n, nrhs, 1, a, lda, b, ldb)
// Solve Lᵀ * X = B, overwriting B with X.
bi.Dtrsm(blas.Left, blas.Lower, blas.Trans, blas.NonUnit, n, nrhs, 1, a, lda, b, ldb)
}
}