Portuguesai

I
[iˈɾɔjʒ du ˈmaɾ ǀ ˈnobɾɨ ˈpovu ǀ]
[nɐˈsɐ̃w vɐˈɫẽtɨ imuɾˈtaɫ ǀ]
[ɫɨvɐ̃ˈtaj ˈoʒɨ dɨ ˈnovu]
[u ʃpɫẽˈdoɾ dɨ puɾtuˈgaɫ ‖]
[ˈẽtɾɨ ɐʒ ˈbɾumɐʒ dɐ mɨˈmɔɾiɐ ǀ]
[ˈɔ ˈpatɾiɐ ǀ ˈsẽtɨsɨ ɐ ˈvoʃ]
[duʃ ˈtewz iˈgɾɛʒiuz ɐˈvɔʃ ǀ]
[kɨ ˈadɨ giˈaɾtɨ à viˈtɔɾiɐ ‖]
[ˈkoɾu]
[à ˈaɾmɐʃ ǀ à ˈaɾmɐʃ ‖]
[ˈsobɾɨ ɐ ˈteʁɐ ǀ ˈsobɾɨ u ˈmaɾ ǀ]
[à ˈaɾmɐʃ ǀ à ˈaɾmɐʃ ‖]
[ˈpeɫɐ ˈpatɾiɐ ɫuˈtaɾ ‖]
[ˈkõtɾɐ uʃ kɐˈɲõjʃ ǀ maɾˈʃaɾ ǀ maɾˈʃaɾ ‖]
II
[dɨʃˈfɾaɫdɐ ɐ ĩˈviktɐ bɐ̃wˈdɐjɾɐ ǀ]
[à ˈɫuʒ ˈvivɐ du ˈtew ˈsɛw ‖]
[ˈbɾadɨ ɐ iwˈɾopɐ à ˈteʁɐ ĩˈtɐjɾɐ ǀ]
[puɾtuˈgaɫ ˈnɐ̃w pɨɾɨˈsew]
[ˈbɐjʒɐ u ˈsoɫu ˈtew ʒuˈkũdu]
[u osiˈɐnu ǀ ɐ ʁuˈʒiɾ ɐˈmoɾ ǀ]
[i ˈtew ˈbɾasu vẽsɨˈdoɾ]
[ˈdew ˈmũduʒ ˈnovuz ˈau ˈmũdu ‖]
[ˈkoɾu]
III
[sawˈdaj u ˈsɔɫ kɨ dɨʃˈpõtɐ]
[ˈsobɾɨ ˈũ ʁiˈdẽtɨ puɾˈviɾ ǀ]
[ˈsɐjʒɐ u ˈeku dɨ ˈumɐ ɐˈfɾõtɐ]
[u siˈnaɫ du ʁɨsuɾˈʒiɾ ‖]
[ˈʁajuʒ ˈdesɐ awˈɾoɾɐ ˈfoɾtɨ]
[ˈsɐ̃w ˈkomu ˈbɐjʒuʒ dɨ ˈmɐ̃j ǀ]
[kɨ nuʒ ˈgwaɾdɐ̃w ǀ nuʃ suʃˈtɐ̃jɐ̃j ǀ]
[ˈkõtɾɐ ɐz ĩˈʒuɾiɐʒ dɐ ˈsoɾtɨ ‖]
[ˈkoɾu]^[2]

I
Heroes of the sea, noble people,
Valiant and immortal nation,
Raise once again today
The splendor of Portugal!
Among the haze of memory,
Oh Fatherland, one feels the voice
Of your distinguished forefathers,
Chorus:
To arms, to arms!
Over land, over sea,
To arms, to arms!
For the Fatherland, fight!
Against the cannons, march on, march on!
II
Hoist the undefeated flag,
In the lively light of your sky!
May Europe cry out to the whole Earth:
Portugal has not perished
Kiss your merry ground
The ocean, roaring with love,
And your victorious arm
Gave new worlds to the world!
Chorus
III
Salute the Sun that rises
Over a gleeful future;
Let the echo of an offense
Be the sign for a comeback.
Rays of this strong dawn
Are like a mother's kisses,
That keep us, sustain us,
Against the injuries of fate.
Chorus

Householder QR Householder transformations are simple orthogonal transformations corre- sponding to re ection through a plane. Householder transformation and QR decomposition A Householder transformation of a vector is its reflection with respect a plane (or hyperplane) through the origin represented by its normal vector of unit length, which can be found as where is the projection of onto. In general, the projection of onto any vector is. The Householder Algorithm. Compute the factor Rof a QRfactorization of m × n matrix A(m ≥ n). Leave result in place of A, store reflection vectors vkfor later. Qr householder method validation. Householder reflector LVF pp.161. Like LU decomposition, Householder transformation zeros out elements A(i + 1: n,i) column by column. X x x x x x x x x x x x ⇒ x x x 0 x x 0 x x 0 x x ⇒ x x x 0 x x 0 0 x 0 0 x ⇒ x x x 0 x x 0 0 x 0 0 0. The householderDecomposition method is a member of the cMatrix object. The cMatrix object is a rather simple object to perform a few matrix operations. It has a few operator overloads and the ability to transpose a matrix. Download the project at the end of this post to see the details. Here is the Householder decomposition.

I
[iˈɾɔjʒ du ˈmaɾ ǀ ˈnobɾɨ ˈpovu ǀ]
[nɐˈsɐ̃w vɐˈɫẽtɨ imuɾˈtaɫ ǀ]
[ɫɨvɐ̃ˈtaj ˈoʒɨ dɨ ˈnovu]
[u ʃpɫẽˈdoɾ dɨ puɾtuˈgaɫ ‖]
[ˈẽtɾɨ ɐʒ ˈbɾumɐʒ dɐ mɨˈmɔɾiɐ ǀ]
[ˈɔ ˈpatɾiɐ ǀ ˈsẽtɨsɨ ɐ ˈvoʃ]
[duʃ ˈtewz iˈgɾɛʒiuz ɐˈvɔʃ ǀ]
[kɨ ˈadɨ giˈaɾtɨ à viˈtɔɾiɐ ‖]
[ˈkoɾu]
[à ˈaɾmɐʃ ǀ à ˈaɾmɐʃ ‖]
[ˈsobɾɨ ɐ ˈteʁɐ ǀ ˈsobɾɨ u ˈmaɾ ǀ]
[à ˈaɾmɐʃ ǀ à ˈaɾmɐʃ ‖]
[ˈpeɫɐ ˈpatɾiɐ ɫuˈtaɾ ‖]
[ˈkõtɾɐ uʃ kɐˈɲõjʃ ǀ maɾˈʃaɾ ǀ maɾˈʃaɾ ‖]
II
[dɨʃˈfɾaɫdɐ ɐ ĩˈviktɐ bɐ̃wˈdɐjɾɐ ǀ]
[à ˈɫuʒ ˈvivɐ du ˈtew ˈsɛw ‖]
[ˈbɾadɨ ɐ iwˈɾopɐ à ˈteʁɐ ĩˈtɐjɾɐ ǀ]
[puɾtuˈgaɫ ˈnɐ̃w pɨɾɨˈsew]
[ˈbɐjʒɐ u ˈsoɫu ˈtew ʒuˈkũdu]
[u osiˈɐnu ǀ ɐ ʁuˈʒiɾ ɐˈmoɾ ǀ]
[i ˈtew ˈbɾasu vẽsɨˈdoɾ]
[ˈdew ˈmũduʒ ˈnovuz ˈau ˈmũdu ‖]
[ˈkoɾu]
III
[sawˈdaj u ˈsɔɫ kɨ dɨʃˈpõtɐ]
[ˈsobɾɨ ˈũ ʁiˈdẽtɨ puɾˈviɾ ǀ]
[ˈsɐjʒɐ u ˈeku dɨ ˈumɐ ɐˈfɾõtɐ]
[u siˈnaɫ du ʁɨsuɾˈʒiɾ ‖]
[ˈʁajuʒ ˈdesɐ awˈɾoɾɐ ˈfoɾtɨ]
[ˈsɐ̃w ˈkomu ˈbɐjʒuʒ dɨ ˈmɐ̃j ǀ]
[kɨ nuʒ ˈgwaɾdɐ̃w ǀ nuʃ suʃˈtɐ̃jɐ̃j ǀ]
[ˈkõtɾɐ ɐz ĩˈʒuɾiɐʒ dɐ ˈsoɾtɨ ‖]
[ˈkoɾu]^[2]

I
Heroes of the sea, noble people,
Valiant and immortal nation,
Raise once again today
The splendor of Portugal!
Among the haze of memory,
Oh Fatherland, one feels the voice
Of your distinguished forefathers,
Chorus:
To arms, to arms!
Over land, over sea,
To arms, to arms!
For the Fatherland, fight!
Against the cannons, march on, march on!
II
Hoist the undefeated flag,
In the lively light of your sky!
May Europe cry out to the whole Earth:
Portugal has not perished
Kiss your merry ground
The ocean, roaring with love,
And your victorious arm
Gave new worlds to the world!
Chorus
III
Salute the Sun that rises
Over a gleeful future;
Let the echo of an offense
Be the sign for a comeback.
Rays of this strong dawn
Are like a mother's kisses,
That keep us, sustain us,
Against the injuries of fate.
Chorus

Householder QR Householder transformations are simple orthogonal transformations corre- sponding to re ection through a plane. Householder transformation and QR decomposition A Householder transformation of a vector is its reflection with respect a plane (or hyperplane) through the origin represented by its normal vector of unit length, which can be found as where is the projection of onto. In general, the projection of onto any vector is. The Householder Algorithm. Compute the factor Rof a QRfactorization of m × n matrix A(m ≥ n). Leave result in place of A, store reflection vectors vkfor later. Qr householder method validation. Householder reflector LVF pp.161. Like LU decomposition, Householder transformation zeros out elements A(i + 1: n,i) column by column. X x x x x x x x x x x x ⇒ x x x 0 x x 0 x x 0 x x ⇒ x x x 0 x x 0 0 x 0 0 x ⇒ x x x 0 x x 0 0 x 0 0 0. The householderDecomposition method is a member of the cMatrix object. The cMatrix object is a rather simple object to perform a few matrix operations. It has a few operator overloads and the ability to transpose a matrix. Download the project at the end of this post to see the details. Here is the Householder decomposition.