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 // Copyright ©2015 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 ( "math" "gonum.org/v1/gonum/lapack" ) // Dlange returns the value of the specified norm of a general m×n matrix A: // lapack.MaxAbs: the maximum absolute value of any element. // lapack.MaxColumnSum: the maximum column sum of the absolute values of the elements (1-norm). // lapack.MaxRowSum: the maximum row sum of the absolute values of the elements (infinity-norm). // lapack.Frobenius: the square root of the sum of the squares of the elements (Frobenius norm). // If norm == lapack.MaxColumnSum, work must be of length n, and this function will // panic otherwise. There are no restrictions on work for the other matrix norms. func (impl Implementation) Dlange(norm lapack.MatrixNorm, m, n int, a []float64, lda int, work []float64) float64 { // TODO(btracey): These should probably be refactored to use BLAS calls. switch { case norm != lapack.MaxRowSum && norm != lapack.MaxColumnSum && norm != lapack.Frobenius && norm != lapack.MaxAbs: panic(badNorm) case m < 0: panic(mLT0) case n < 0: panic(nLT0) case lda < max(1, n): panic(badLdA) } // Quick return if possible. if m == 0 || n == 0 { return 0 } switch { case len(a) < (m-1)*lda+n: panic(badLdA) case norm == lapack.MaxColumnSum && len(work) < n: panic(shortWork) } switch norm { case lapack.MaxAbs: var value float64 for i := 0; i < m; i++ { for j := 0; j < n; j++ { value = math.Max(value, math.Abs(a[i*lda+j])) } } return value case lapack.MaxColumnSum: for i := 0; i < n; i++ { work[i] = 0 } for i := 0; i < m; i++ { for j := 0; j < n; j++ { work[j] += math.Abs(a[i*lda+j]) } } var value float64 for i := 0; i < n; i++ { value = math.Max(value, work[i]) } return value case lapack.MaxRowSum: var value float64 for i := 0; i < m; i++ { var sum float64 for j := 0; j < n; j++ { sum += math.Abs(a[i*lda+j]) } value = math.Max(value, sum) } return value default: // lapack.Frobenius scale := 0.0 sum := 1.0 for i := 0; i < m; i++ { rowscale, rowsum := impl.Dlassq(n, a[i*lda:], 1, 0, 1) scale, sum = impl.Dcombssq(scale, sum, rowscale, rowsum) } return scale * math.Sqrt(sum) } }