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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++ {
scale, sum = impl.Dlassq(n, a[i*lda:], 1, scale, sum)
}
return scale * math.Sqrt(sum)
}
}
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