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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,334 @@ | ||
| package native | ||
|
|
||
| import ( | ||
| "math" | ||
|
|
||
| "github.com/gonum/blas" | ||
| "github.com/gonum/blas/blas64" | ||
| ) | ||
|
|
||
| // Dlatrs solves a triangular system of equations scaled to prevent overflow. It | ||
| // solves | ||
| // A * x = scale * b if trans == blas.NoTrans | ||
| // A^T * x = scale * b if trans == blas.Trans | ||
| // where the scale s is set for numeric stability. | ||
| // | ||
| // A is an n×n triangular matrix. On entry, the slice x contains the values of | ||
| // of b, and on exit it contains the solution vector x. | ||
| // | ||
| // If normin == true, cnorm is an input and cnorm[j] contains the norm of the off-diagonal | ||
| // part of the j^th column of A. If trans == blas.NoTrans, cnorm[j] must be greater | ||
| // than or equal to the infinity norm, and greater than or equal to the one-norm | ||
| // otherwise. If normin == false, then cnorm is treated as an output, and is set | ||
| // to contain the 1-norm of the off-diagonal part of the j^th column of A. | ||
| func (impl Implementation) Dlatrs(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, normin bool, n int, a []float64, lda int, x []float64, cnorm []float64) (scale float64) { | ||
| if uplo != blas.Upper && uplo != blas.Lower { | ||
| panic(badUplo) | ||
| } | ||
| if trans != blas.Trans && trans != blas.NoTrans { | ||
| panic(badTrans) | ||
| } | ||
| if diag != blas.Unit && diag != blas.NonUnit { | ||
| panic(badDiag) | ||
| } | ||
| upper := uplo == blas.Upper | ||
| noTrans := trans == blas.NoTrans | ||
| nonUnit := diag == blas.NonUnit | ||
|
|
||
| if n < 0 { | ||
| panic(nLT0) | ||
| } | ||
| checkMatrix(n, n, a, lda) | ||
| checkVector(n, x, 1) | ||
| checkVector(n, cnorm, 1) | ||
|
|
||
| if n == 0 { | ||
| return | ||
| } | ||
| scale = 1 | ||
| bi := blas64.Implementation() | ||
| if !normin { | ||
| if upper { | ||
| for j := 0; j < n; j++ { | ||
| cnorm[j] = bi.Dasum(j, a[j:], lda) | ||
| } | ||
| } else { | ||
| for j := 0; j < n-1; j++ { | ||
| cnorm[j] = bi.Dasum(n-j-1, a[(j+1)*lda+j:], lda) | ||
| } | ||
| cnorm[n-1] = 0 | ||
| } | ||
| } | ||
| // Scale the column norms by tscal if the maximum element in cnorm is greater than bignum. | ||
| imax := bi.Idamax(n, cnorm, 1) | ||
| tmax := cnorm[imax] | ||
| var tscal float64 | ||
| if tmax <= bignum { | ||
| tscal = 1 | ||
| } else { | ||
| tscal = 1 / (smlnum * tmax) | ||
| bi.Dscal(n, tscal, cnorm, 1) | ||
| } | ||
|
|
||
| // Compute a bound on the computed solution vector to see if bi.Dtrsv can be used. | ||
| j := bi.Idamax(n, x, 1) | ||
| xmax := math.Abs(x[j]) | ||
| xbnd := xmax | ||
| var grow float64 | ||
| var jfirst, jlast, jinc int | ||
| if noTrans { | ||
| if upper { | ||
| jfirst = n - 1 | ||
| jlast = 0 | ||
| jinc = -1 | ||
| } else { | ||
| jfirst = 0 | ||
| jlast = n - 1 | ||
| jinc = 1 | ||
| } | ||
| // Compute the growth in A * x = b. | ||
| if tscal != 1 { | ||
| grow = 0 | ||
| goto Finish | ||
| } | ||
| if nonUnit { | ||
| grow = 1 / math.Max(xbnd, smlnum) | ||
| xbnd = grow | ||
| for j := jfirst; j != jlast; j += jinc { | ||
| if grow <= smlnum { | ||
| goto Finish | ||
| } | ||
| tjj := math.Abs(a[j*lda+j]) | ||
| xbnd = math.Min(xbnd, math.Min(1, tjj)*grow) | ||
| if tjj+cnorm[j] >= smlnum { | ||
| grow *= tjj / (tjj + cnorm[j]) | ||
| } else { | ||
| grow = 0 | ||
| } | ||
| } | ||
| grow = xbnd | ||
| } else { | ||
| grow = math.Min(1, 1/math.Max(xbnd, smlnum)) | ||
| for j := jfirst; j != jlast; j += jinc { | ||
| if grow <= smlnum { | ||
| goto Finish | ||
| } | ||
| grow *= 1 / (1 + cnorm[j]) | ||
| } | ||
| } | ||
| } else { | ||
| if upper { | ||
| jfirst = 0 | ||
| jlast = n - 1 | ||
| jinc = 1 | ||
| } else { | ||
| jfirst = n - 1 | ||
| jlast = 0 | ||
| jinc = -1 | ||
| } | ||
| if tscal != 1 { | ||
| grow = 0 | ||
| goto Finish | ||
| } | ||
| if nonUnit { | ||
| grow = 1 / (math.Max(xbnd, smlnum)) | ||
| xbnd = grow | ||
| for j := jfirst; j != jlast; j += jinc { | ||
| if grow <= smlnum { | ||
| goto Finish | ||
| } | ||
| xj := 1 + cnorm[j] | ||
| grow = math.Min(grow, xbnd/xj) | ||
| tjj := math.Abs(a[j*lda+j]) | ||
| if xj > tjj { | ||
| xbnd *= tjj / xj | ||
| } | ||
| } | ||
| grow = math.Min(grow, xbnd) | ||
| } else { | ||
| grow = math.Min(1, 1/math.Max(xbnd, smlnum)) | ||
| for j := jfirst; j != jlast; j += jinc { | ||
| if grow <= smlnum { | ||
| goto Finish | ||
| } | ||
| xj := 1 + cnorm[j] | ||
| grow /= xj | ||
| } | ||
| } | ||
| } | ||
|
|
||
| Finish: | ||
| if grow*tscal > smlnum { | ||
| bi.Dtrsv(uplo, trans, diag, n, a, lda, x, 1) | ||
| // TODO(btracey): check if this else is everything | ||
| } else { | ||
| if xmax > bignum { | ||
| scale = bignum / xmax | ||
| bi.Dscal(n, scale, x, 1) | ||
| xmax = bignum | ||
| } | ||
| if noTrans { | ||
| for j := jfirst; j != jlast; j += jinc { | ||
| xj := math.Abs(x[j]) | ||
| var tjjs float64 | ||
| if nonUnit { | ||
| tjjs = a[j*lda+j] * tscal | ||
| } else { | ||
| tjjs = tscal | ||
| if tscal == 1 { | ||
| break | ||
| } | ||
| } | ||
| tjj := math.Abs(tjjs) | ||
| if tjj > smlnum { | ||
| if tjj < 1 { | ||
| if xj > tjj*bignum { | ||
| rec := 1 / xj | ||
| bi.Dscal(n, rec, x, 1) | ||
| scale *= rec | ||
| xmax *= rec | ||
| } | ||
| } | ||
| x[j] /= tjjs | ||
| xj = math.Abs(x[j]) | ||
| } else if tjj > 0 { | ||
| if xj > tjj*bignum { | ||
| rec := (tjj * bignum) / xj | ||
| if cnorm[j] > 1 { | ||
| rec /= cnorm[j] | ||
| } | ||
| bi.Dscal(n, rec, x, 1) | ||
| scale *= rec | ||
| xmax *= rec | ||
| } | ||
| x[j] /= tjjs | ||
| xj = math.Abs(x[j]) | ||
| } else { | ||
| for i := 0; i < n; i++ { | ||
| x[i] = 0 | ||
| } | ||
| x[j] = 1 | ||
| xj = 1 | ||
| scale = 0 | ||
| xmax = 0 | ||
| } | ||
| if xj > 1 { | ||
| rec := 1 / xj | ||
| if cnorm[j] > (bignum-xmax)*rec { | ||
| rec *= 0.5 | ||
| bi.Dscal(n, rec, x, 1) | ||
| scale *= rec | ||
| } | ||
| } else if xj*cnorm[j] > bignum-xmax { | ||
| bi.Dscal(n, 0.5, x, 1) | ||
| scale *= 0.5 | ||
| } | ||
| if upper { | ||
| if j > 0 { | ||
| bi.Daxpy(j, -x[j]*tscal, a[j:], lda, x, 1) | ||
| i := bi.Idamax(j, x, 1) | ||
| xmax = math.Abs(x[i]) | ||
| } | ||
| } else { | ||
| if j < n-1 { | ||
| bi.Daxpy(n-j-1, -x[j]*tscal, a[(j+1)*lda+j:], lda, x[j+1:], 1) | ||
| i := j + bi.Idamax(n-j-1, x[j+1:], 1) | ||
| xmax = math.Abs(x[i]) | ||
| } | ||
| } | ||
| } | ||
| } else { | ||
| for j := jfirst; j != jlast; j += jinc { | ||
| xj := math.Abs(x[j]) | ||
| uscal := tscal | ||
| rec := 1 / math.Max(xmax, 1) | ||
| var tjjs float64 | ||
| if cnorm[j] > (bignum-xj)*rec { | ||
| rec *= 0.5 | ||
| if nonUnit { | ||
| tjjs = a[j*lda+j] * tscal | ||
| } else { | ||
| tjjs = tscal | ||
| } | ||
| tjj := math.Abs(tjjs) | ||
| if tjj > 1 { | ||
| rec = math.Min(1, rec*tjj) | ||
| uscal /= tjjs | ||
| } | ||
| if rec < 1 { | ||
| bi.Dscal(n, rec, x, 1) | ||
| scale *= rec | ||
| xmax *= rec | ||
| } | ||
| } | ||
| var sumj float64 | ||
| if uscal == 1 { | ||
| if upper { | ||
| sumj = bi.Ddot(j, a[j:], lda, x, 1) | ||
| } else if j < n-1 { | ||
| sumj = bi.Ddot(n-j-1, a[(j+1)*lda+j:], lda, x[j+1:], 1) | ||
| } | ||
| } else { | ||
| if upper { | ||
| for i := 0; i < j; i++ { | ||
| sumj += (a[i*lda+j] * uscal) * x[i] | ||
| } | ||
| } else if j < n { | ||
| for i := j + 1; i < n; i++ { | ||
| sumj += (a[i*lda+j] * uscal) * x[i] | ||
| } | ||
| } | ||
| } | ||
| if uscal == tscal { | ||
| x[j] -= sumj | ||
| xj := math.Abs(x[j]) | ||
| var tjjs float64 | ||
| if nonUnit { | ||
| tjjs = a[j*lda+j] * tscal | ||
| } else { | ||
| tjjs = tscal | ||
| if tscal == 1 { | ||
| goto Out2 | ||
| } | ||
| } | ||
| tjj := math.Abs(tjjs) | ||
| if tjj > smlnum { | ||
| if tjj < 1 { | ||
| if xj > tjj*bignum { | ||
| rec = 1 / xj | ||
| bi.Dscal(n, rec, x, 1) | ||
| scale *= rec | ||
| xmax *= rec | ||
| } | ||
| } | ||
| x[j] /= tjjs | ||
| } else if tjj > 0 { | ||
| if xj > tjj*bignum { | ||
| rec = (tjj * bignum) / xj | ||
| bi.Dscal(n, rec, x, 1) | ||
| scale *= rec | ||
| xmax *= rec | ||
| } | ||
| x[j] /= tjjs | ||
| } else { | ||
| for i := 0; i < n; i++ { | ||
| x[i] = 0 | ||
| } | ||
| x[j] = 1 | ||
| scale = 0 | ||
| xmax = 0 | ||
| } | ||
| } else { | ||
| x[j] = x[j]/tjjs - sumj | ||
| } | ||
| Out2: | ||
| xmax = math.Max(xmax, math.Abs(x[j])) | ||
| } | ||
| } | ||
| scale /= tscal | ||
| } | ||
| if tscal != 1 { | ||
| bi.Dscal(n, 1/tscal, cnorm, 1) | ||
| } | ||
| return scale | ||
| } | ||
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I take it the lda here is because we are row major.
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Yep. It's computing the sum over the column.