Underground.[233]
To dream of being in an underground habitation, you are in danger of losing reputation and fortune.
To dream of riding on an underground railway, foretells that you will engage in some peculiar speculation which will contribute to your distress and anxiety.
[233] See Cars, etc.
Undress.
To dream that you are undressing, foretells, scandalous gossip will overshadow you.
For a woman to dream that she sees the ruler of her country undressed, signifies sadness will overtake anticipated pleasures. She will suffer pain through the apprehension of evil to those dear to her.
To see others undressed, is an omen of stolen pleasures, which will rebound with grief.
Unfortunate.
To dream that you are unfortunate, is significant of loss to yourself, and trouble for others.
Uniform.
To see a uniform in your dream, denotes that you will have influential friends to aid you in obtaining your desires.
For a young woman to dream that she wears a uniform, foretells that she will luckily confer her favors upon a man who appreciated them, and returns love for passion. If she discards it, she will be in danger of public scandal by her notorious love for adventure.
To see people arrayed in strange uniforms, foretells the disruption of friendly relations with some other Power by your own government. This may also apply to families or friends. To see a friend or relative looking sad while dressed in uniform, or as a soldier, predicts ill fortune or continued absence.
United States Mail Box.
To see a United States mail box, in a dream, denotes that you are about to enter into transactions which will be claimed to be illegal.
To put a letter in one, denotes you will be held responsible for some irregularity of another.
Unknown.[234]
To dream of meeting unknown persons, foretells change for good, or bad as the person is good looking, or ugly, or deformed.
To feel that you are unknown, denotes that strange things will cast a shadow of ill luck over you.
[234] See Mystery.
Urgent.
To dream that you are supporting an urgent petition, is a sign that you will engage in some affair which will need fine financiering to carry it through successfully.
Urinal.
To dream of a urinal, disorder will predominate in your home.
Urine.
To dream of seeing urine, denotes ill health will make you disagreeable and unpleasant with your friends.
To dream that you are urinating, is an omen of bad luck, and trying seasons to love.
Urn.
To dream of an urn, foretells you will prosper in some respects, and in others disfavor will be apparent. To see broken urns, unhappiness will confront you.
Usurer.
To find yourself a usurer in your dreams, foretells that you will be treated with coldness by your associates, and your business will decline to your consternation.
If others are usurers, you will discard some former friend on account of treachery.
Usurper.
To dream that you are a usurper, foretells you will have trouble in establishing a good title to property.
If others are trying to usurp your rights, there will be a struggle between you and your competitors, but you will eventually win.
For a young woman to have this dream, she will be a party to a spicy rivalry, in which she will win.
``Where there is no vision, the people perish; but he that keepeth the law, happy is he.''—Prov. xxix., 18.
Vaccinate.
To dream of being vaccinated, foretells that your susceptibility to female charms will be played upon to your sorrow.
To dream that others are vaccinated, shows you will fail to find contentment where it is sought, and your affairs will suffer decline in consequence.
For a young woman to be vaccinated on her leg, foreshadows her undoing through treachery.
Vagrant.
To dream that you are a vagrant, portends poverty and misery.
To see vagrants is a sign of contagion invading your community.
To give to a vagrant, denotes that your generosity will be applauded.
Valentine.
To dream that you are sending valentines, foretells that you will lose opportunities of enriching yourself.
For a young woman to receive one, denotes that she will marry a weak, but ardent lover against the counsels of her guardians.
Valley.
To find yourself walking through green and pleasant valleys, foretells great improvements in business, and lovers will be happy and congenial. If the valley is barren, the reverse is predicted. If marshy, illness or vexations may follow.
Vapor Bath.
To dream of a vapor bath, you will have fretful people for companions, unless you dream of emerging from one, and then you will find that your cares will be temporary.
Varnishing.
To dream of varnishing anything, denotes that you will seek to win distinction by fraudulent means.
To see others varnishing, foretells that you are threatened with danger from the endeavor of friends to add to their own possessions.
Vase.
To dream of a vase, denotes that you will enjoy sweetest pleasure and contentment in the home life.
To drink from a vase, you will soon thrill with the delights of stolen love.
To see a broken vase, foretells early sorrow. For a young woman to receive one, signifies that she will soon obtain her dearest wish.
Vat.
To see a vat in your dreams, foretells anguish and suffering from the hands of cruel persons, into which you have unwittingly fallen.
Vatican.
To dream of the vatican, signifies unexpected favors will fall within your grasp. You will form the acquaintance of distinguished people, if you see royal personages speaking to the Pope.
Vault.
To dream of a vault, denotes bereavement and other misfortune. To see a vault for valuables, signifies your fortune will surprise many, as your circumstances will appear to be meagre. To see the doors of a vault open, implies loss and treachery of people whom you trust.
Vegetables.
To dream of eating vegetables, is an omen of strange luck. You will think for a time that you are tremendously successful, but will find to your sorrow that you have been grossly imposed upon.
Withered, or decayed vegetables, bring unmitigated woe and sadness.
For a young woman to dream that she is preparing vegetables for dinner, foretells that she will lose the man she desired through pique, but she will win a well-meaning and faithful husband. Her engagements will be somewhat disappointing.
Vehicle.
To ride in a vehicle while dreaming, foretells threatened loss, or illness.
To be thrown from one, foretells hasty and unpleasant news.
To see a broken one, signals failure in important affairs.
To buy one, you will reinstate yourself in your former position.
To sell one, denotes unfavorable change in affairs.
Veil.
To dream that you wear a veil, denotes that you will not be perfectly sincere with your lover, and you will be forced to use stratagem to retain him.
To see others wearing veils, you will be maligned and defamed by apparent friends.
An old, or torn veil, warns you that deceit is being thrown around you with sinister design.
For a young woman to dream that she loses her veil, denotes that her lover sees through her deceitful ways and is likely to retaliate with the same.
To dream of seeing a bridal veil, foretells that you will make a successful change in the immediate future, and much happiness in your position.
For a young woman to dream that she wears a bridal veil, denotes that she will engage in some affair which will afford her lasting profit and enjoyment. If it gets loose, or any accident befalls it, she will be burdened with sadness and pain.
To throw a veil aside, indicates separation or disgrace.
To see mourning veils in your dreams, signifies distress and trouble, and embarrassment in business.
Vein.
To see your veins in a dream, insures you against slander, if they are normal.
To see them bleeding, denotes that you will have a great sorrow from which there will be no escape.
To see them swollen, you will rise hastily to distinction and places of trust.
Velvet.
To dream of velvet, portends very successful enterprises.
If you wear it, some distinction will be conferred upon you.
To see old velvet, means your prosperity will suffer from your extreme pride.
If a young woman dreams that she is clothed in velvet garments, it denotes that she will have honors bestowed upon her, and the choice between several wealthy lovers.
Veneer.
To dream that you are veneering, denotes that you will systematically deceive your friends, your speculations will be of a misleading nature.
Ventriloquist.
To dream of a ventriloquist, denotes that some treasonable affair is going to prove detrimental to your interest.
If you think yourself one, you will not conduct yourself honorably towards people who trust you.
For a young woman to dream she is mystified by the voice of a ventriloquist, foretells that she will be deceived into illicit adventures.
Veranda.
To dream of being on a veranda, denotes that you are to be successful in some affair which is giving you anxiety.
For a young woman to be with her lover on a veranda, denotes her early and happy marriage.
To see an old veranda, denotes the decline of hopes, and disappointment in business and love.
Vermin.[235]
Vermin crawling in your dreams, signifies sickness and much trouble. See Locust.
Vertigo.
To dream that you have vertigo, foretells you will have loss in domestic happiness, and your affairs will be under gloomy outlooks.
Vessels.[236]
To dream of vessels, denotes labor and activity.
[236] See Ships and similar words.
Vexed.
If you are vexed in your dreams, you will find many worries scattered through your early awakening.

Vicar.
To dream of a vicar, foretells that you will do foolish things while furious with jealousy and envy.
For a young woman to dream she marries a vicar, foretells that she will fail to awake reciprocal affection in the man she desires, and will live a spinster, or marry to keep from being one.
Vice.
To dream that you are favoring any vice, signifies you are about to endanger your reputation, by letting evil persuasions entice you.
If you see others indulging in vice, some ill fortune will engulf the interest of some relative or associate.
Victim.
To dream that you are the victim of any scheme, foretells that you will be oppressed and over-powered by your enemies. Your family relations will also be strained.
To victimize others, denotes that you will amass wealth dishonorably and prefer illicit relations, to the sorrow of your companions.
Victory.
To dream that you win a victory, foretells that you will successfully resist the attacks of enemies, and will have the love of women for the asking.
Village.
To dream that you are in a village, denotes that you will enjoy good health and find yourself fortunately provided for.
To revisit the village home of your youth, denotes that you will have pleasant surprises in store and favorable news from absent friends.
If the village looks dilapidated, or the dream indistinct, it foretells that trouble and sadness will soon come to you.
Vine.
To dream of vines, is propitious of success and happiness.
Good health is in store for those who see flowering vines.
If they are dead, you will fail in some momentous enterprise.
To see poisonous vines, foretells that you will be the victim of a plausible scheme and you will impair your health.
Vinegar.
To dream of drinking vinegar, denotes that you will be exasperated and worried into assenting to some engagement which will fill you with evil foreboding.
To use vinegar on vegetables, foretells a deepening of already distressing affairs.
To dream of vinegar at all times, denotes inharmonious and unfavorable aspects.
Vineyard.
To dream of a vineyard, denotes favorable speculations and auspicious love-making.
To visit a vineyard which is not well-kept and filled with bad odors, denotes disappointment will overshadow your most sanguine anticipations.
Violence.
To dream that any person does you violence, denotes that you will be overcome by enemies.
If you do some other persons violence, you will lose fortune and favor by your reprehensible way of conducting your affairs.
Violets.
To see violets in your dreams, or gather them, brings joyous occasions in which you will find favor with some superior person.
For a young woman to gather them, denotes that she will soon meet her future husband.
To see them dry, or withered, denotes that her love will be scorned and thrown aside.
Violin.
To see, or hear a violin in dreams, foretells harmony and peace in the family, and financial affairs will cause no apprehension.
For a young woman to play on one in her dreams, denotes that she will be honored and receive lavish gifts.
If her attempt to play is unsuccessful, she will lose favor, and aspire to things she never can possess.
A broken one, indicates sad bereavement and separation.
Viper.
To dream of a viper, foretells that calamities are threatening you. To dream that a many-hued viper, and capable of throwing itself into many pieces, or unjointing itself, attacks you, denotes that your enemies are bent on your ruin and will work unitedly, yet apart, to displace you.
Virgin.
To dream of a virgin, denotes that you will have comparative luck in your speculations. For a married woman to dream that she is a virgin, foretells that she will suffer remorse over her past, and the future will hold no promise of better things.
For a young woman to dream that she is no longer a virgin, foretells that she will run great risk of losing her reputation by being indiscreet with her male friends.
For a man to dream of illicit association with a virgin, denotes that he will fail to accomplish an enterprise, and much worry will be caused him by the appeals of people. His aspirations will be foiled through unwarranted associations.
Visit.
If you visit in your dreams, you will shortly have some pleasant occasion in your life.

For a friend to visit you, denotes that news of a favorable nature will soon reach you. If the friend appears sad and travel-worn, there will be a note of displeasure growing out of the visit, or other slight disappointments may follow. If she is dressed in black or white and looks pale or ghastly, serious illness or accidents are predicted.
Visions.
To dream that you have a strange vision, denotes that you will be unfortunate in your dealings and sickness will unfit you for pleasant duties.
If persons appear to you in visions, it foretells uprising and strife of families or state.
If your friend is near dissolution and you are warned in a vision, he will appear suddenly before you, usually in white garments. Visions of death and trouble have such close resemblance, that they are sometimes mistaken one for the other.
To see visions of any order in your dreams, you may look for unusual developments in your business, and a different atmosphere and surroundings in private life. Things will be reversed for a while with you. You will have changes in your business and private life seemingly bad, but eventually good for all concerned.
The Supreme Will is always directed toward the ultimate good of the race.
Vitriol.
If you see vitriol in your dreams, it is a token of some innocent person being censured by you.
To throw it on people, shows you will bear malice towards parties who seek to favor you.
 This dream for a business man, denotes enemies and much persecution.
Voice.
To dream of hearing voices, denotes pleasant reconciliations, if they are calm and pleasing; high-pitched and angry voices, signify disappointments and unfavorable situations.
To hear weeping voices, shows that sudden anger will cause you to inflict injury upon a friend.
If you hear the voice of God, you will make a noble effort to rise higher in unselfish and honorable principles, and will justly hold the admiration of high-minded people.
For a mother to hear the voice of her child, is a sign of approaching misery, perplexity and grievous doubts.
To hear the voice of distress, or a warning one calling to you, implies your own serious misfortune or that of some one close to you. If the voice is recognized, it is often ominous of accident or illness, which may eliminate death or loss.
Volcano.
To see a volcano in your dreams, signifies that you will be in violent disputes, which threaten your reputation as a fair dealing and honest citizen.
For a young woman, it means that her selfishness and greed will lead her into intricate adventures.
Vomit.
To dream of vomiting, is a sign that you will be afflicted with a malady which will threaten invalidism, or you will be connected with a racy scandal.
To see others vomiting, denotes that you will be made aware of the false pretenses of persons who are trying to engage your aid.
For a woman to dream that she vomits a chicken, and it hops off, denotes she will be disappointed in some pleasure by the illness of some relative. Unfavorable business and discontent are also predicted.
 You will be cast down with gloomy forebodings, and children and domesticity in general will ally to work you discomfort.
Vote.
If you dream of casting a vote on any measure, you will be engulfed in a commotion which will affect your community.
To vote fraudulently, foretells that your dishonesty will overcome your better inclinations.
Voucher.
To dream of vouchers, foretells that patient toil will defeat idle scheming to arrest fortune from you.
To sign one, denotes that you have the aid and confidence of those around you, despite the evil workings of enemies.
To lose one, signifies that you will have a struggle for your rights with relatives.
Vow.
To dream that you are making or listening to vows, foretells complaint will be made against you of unfaithfulness in business, or some love contract. To take the vows of a church, denotes you will bear yourself with unswerving integrity through some difficulty.
To break or ignore a vow, foretells disastrous consequences will attend your dealings.
Voyage.
To make a voyage in your dreams, foretells that you will receive some inheritance besides that which your labors win for you.
A disastrous voyage brings incompetence, and false loves.
Vultures.
To dream of vultures, signifies that some scheming person is bent on injuring you, and will not succeed unless you see the vulture wounded, or dead.

Wading.[237]
If you wade in clear water while dreaming, you will partake of evanescent, but exquisite joys. If the water is muddy, you are in danger of illness, or some sorrowful experiences.
To see children wading in clear water is a happy prognostication, as you will be favored in your enterprises.
For a young woman to dream of wading in clear foaming water, she will soon gain the desire nearest her heart.
[237] See Bathing.
Wadding.
Wadding, if seen in a dream, brings consolation to the sorrowing, and indifference to unfriendly criticism.
Wafer.
Wafer, if seen in a dream, purports an encounter with enemies.
To eat one, suggests impoverished fortune.
For a young woman to bake them, denotes that she will be tormented and distressed by fears of remaining in the unmarried state.
Wager.
To dream of making a wager, signifies that you will resort to dishonest means to forward your schemes.
If you lose a wager, you will sustain injury from base connections with those out of your social sphere.
To win one, reinstates you in favor with fortune.
If you are not able to put up a wager, you will be discouraged and prostrated by the adverseness of circumstances.
Wages.
Wages, if received in dreams, brings unlooked for good to persons engaging in new enterprises.
To pay out wages, denotes that you will be confounded by dissatisfaction.
To have your wages reduced, warns you of unfriendly interest that is being taken against you.
An increase of wages, suggests unusual profit in any undertaking.
Wagon.
To dream of a wagon, denotes that you will be unhappily mated, and many troubles will prematurely age you.
To drive one down a hill, is ominous of proceedings which will fill you with disquiet, and will cause you loss.
To drive one up hill, improves your worldly affairs.
To drive a heavily loaded wagon, denotes that duty will hold you in a moral position, despite your efforts to throw her off.
To drive into muddy water, is a gruesome prognostication, bringing you into a vortex of unhappiness and fearful foreboding.
To see a covered wagon, foretells that you will be encompassed by mysterious treachery, which will retard your advancement.
For a young woman to dream that she drives a wagon near a dangerous embankment, portends that she will be driven into an illicit entanglement, which will fill her with terror, lest she be openly discovered and ostracised. If she drives across a clear stream of water, she will enjoy adventure without bringing opprobrium upon herself.
A broken wagon represents distress and failure.
Wagtail.
To see a wagtail in a dream, foretells that you will be the victim of unpleasant gossip, and your affairs will develop unmistakable loss.
Waif.
To dream of a waif, denotes personal difficulties, and especial ill-luck in business.
Wail.[238]
A wail falling upon your ear while in the midst of a dream, brings fearful news of disaster and woe.
For a young woman to hear a wail, foretells that she will be deserted and left alone in distress, and perchance disgrace.
[238] See Weeping.
Waist and Shirt-Waist.
To dream of a round full waist, denotes that you will be favored by an agreeable dispensation of fortune.
A small, unnatural waist, foretells displeasing success and recriminating disputes.
For a young woman to dream of a nice, ready-made shirt-waist, denotes that she will win admiration through her ingenuity and pleasing manners.
To dream that her shirt-waist is torn, she will be censured for her illicit engagements. If she is trying on a shirt-waist, she will encounter rivalry in love, but if she succeeds in adjusting the waist to her person, she will successfully combat the rivalry and win the object of her love.
Waiter.
To dream of a waiter, signifies you will be pleasantly entertained by a friend. To see one cross or disorderly, means offensive people will thrust themselves upon your hospitality.
Wake.
To dream that you attend a wake, denotes that you will sacrifice some important engagement to enjoy some ill-favored assignation.
For a young woman to see her lover at a wake, foretells that she will listen to the entreaties of passion, and will be persuaded to hazard honor for love.
Walking.[239]
To dream of walking through rough brier, entangled paths, denotes that you will be much distressed over your business complications, and disagreeable misunderstandings will produce coldness and indifference.
To walk in pleasant places, you will be the possessor of fortune and favor.
To walk in the night brings misadventure, and unavailing struggle for contentment.
For a young woman to find herself walking rapidly in her dreams, denotes that she will inherit some property, and will possess a much desired object.
[239] See Wading.
Walking Stick.
To see a walking stick in a dream, foretells you will enter into contracts without proper deliberation, and will consequently suffer reverses. If you use one in walking, you will be dependent upon the advice of others. To admire handsome ones, you will entrust your interest to others, but they will be faithful.
Wallet.
To see wallets in a dream, foretells burdens of a pleasant nature will await your discretion as to assuming them. An old or soiled one, implies unfavorable results from your labors.
Walls.
To dream that you find a wall obstructing your progress, you will surely succumb to ill-favored influences and lose important victories in your affairs.
To jump over it, you will overcome obstacles and win your desires. To force a breach in a wall, you will succeed in the attainment of your wishes by sheer tenacity of purpose.
To demolish one, you will overthrow your enemies. To build one, foretells that you will carefully lay plans and will solidify your fortune to the exclusion of failure, or designing enemies.
For a young woman to walk on top of a wall, shows that her future happiness will soon be made secure. For her to hide behind a wall, denotes that she will form connections that she will be ashamed to acknowledge. If she walks beside a base wall. she will soon have run the gamut of her attractions, and will likely be deserted at a precarious time.
Walnut.
To dream of walnuts, is an omen significant of prolific joys and favors.
To dream that you crack a decayed walnut, denotes that your expectations will end in bitterness and regretable collapse.
For a young woman to dream that she has walnut stain on her hands, foretells that she will see her lover turn his attention to another, and she will entertain only regrets for her past indiscreet conduct.
Waltz.
To see the waltz danced, foretells that you will have pleasant relations with a cheerful and adventuresome person.
For a young woman to waltz with her lover, denotes that she will be the object of much admiration, but none will seek her for a wife. If she sees her lover waltzing with a rival, she will overcome obstacles to her desires with strategy. If she waltzes with a woman, she will be loved for her virtues and winning ways. If she sees persons whirling in the waltz as if intoxicated, she will be engulfed so deeply in desire and pleasure that it will be a miracle if she resists the impassioned advances of her lover and male acquaintances.
Want.
To dream that you are in want, denotes that you have unfortunately ignored the realities of life, and chased folly to her stronghold of sorrow and adversity.
If you find yourself contented in a state of want, you will bear the misfortune which threatens you with heroism, and will see the clouds of misery disperse.
To relieve want, signifies that you will be esteemed for your disinterested kindness, but you will feel no pleasure in well doing.
War.
To dream of war, foretells unfortunate conditions in business, and much disorder and strife in domestic affairs.
For a young woman to dream that her lover goes to war, denotes that she will hear of something detrimental to her lover's character.
To dream that your country is defeated in war, is a sign that it will suffer revolution of a business and political nature. Personal interest will sustain a blow either way.
If of victory you dream, there will be brisk activity along business lines, and domesticity will be harmonious.
Wardrobe.
To dream of your wardrobe, denotes that your fortune will be endangered by your attempts to appear richer than you are.
If you imagine you have a scant wardrobe, you will seek association with strangers.
Warehouse.
To dream of a warehouse, denotes for you a successful enterprise. To see an empty one, is a sign that you will be cheated and foiled in some plan which you have given much thought and maneuvering.
Warrant.
To dream that a warrant is being served on you, denotes that you will engage in some important work which will give you great uneasiness as to its standing and profits.
To see a warrant served on some one else, there will be danger of your actions bringing you into fatal quarrels or misunderstandings. You are likely to be justly indignant with the wantonness of some friend.
Warts.
If you are troubled with warts on your person, in dreams, you will be unable to successfully parry the thrusts made at your honor.
To see them leaving your hands, foretells that you will overcome disagreeable obstructions to fortune.
To see them on others, shows that you have bitter enemies near you. If you doctor them, you will struggle with energy to ward off threatened danger to you and yours.
Washboard.
To see a washboard in your dreams, is indicative of embarrassment. If you see a woman using one, it predicts that you will let women rob you of energy and fortune.
A broken one, portends that you will come to grief and disgraceful deeds through fast living.
Wash-bowl.
To dream of a wash-bowl, signifies that new cares will interest you, and afford much enjoyment to others.
To bathe your face and hands in a bowl of clear water, denotes that you will soon consummate passionate wishes which will bind you closely to some one who interested you, but before passion enveloped you.
If the bowl is soiled, or broken, you will rue an illicit engagement, which will give others pain, and afford you small pleasure.
Washer Woman.
A washer woman seen in dreams, represents infidelity and a strange adventure. For the business man, or farmer, this dream indicates expanding trade and fine crops. For a woman to dream that she is a washer woman, denotes that she will throw decorum aside in her persistent effort to hold the illegal favor of men.
Washing.[240]
To dream that you are washing yourself, signifies that you pride yourself on the numberless liaisons you maintain.
[240] See Wash Bowl or Bathing.
Wasp.
Wasps, if seen in dreams, denotes that enemies will scourge and spitefully villify you.
If one stings you, you will feel the effect of envy and hatred.
Waste.
To dream of wandering through waste places, foreshadows doubt and failure, where promise of success was bright before you.
To dream of wasting your fortune, denotes you will be unpleasantly encumbered with domestic cares.
Watch.
To dream of a watch, denotes you will be prosperous in well-directed speculations. To look at the time of one, your efforts will be defeated by rivalry. To break one, there will be distress and loss menacing you.
To drop the crystal of one, foretells carelessness, or unpleasant companionship. For a woman to lose one, signifies domestic disturbances will produce unhappiness.
To make a present of one, denotes you will suffer your interest to decline in the pursuance of undignified recreations.
Water.
To dream of clear water, foretells that you will joyfully realize prosperity and pleasure.
If the water is muddy, you will be in danger and gloom will occupy Pleasure's seat.
If you see it rise up in your house, denotes that you will struggle to resist evil, but unless you see it subside, you will succumb to dangerous influences.
If you find yourself baling it out, but with feet growing wet, foreshadows trouble, sickness, and misery will work you a hard task, but you will forestall them by your watchfulness. The same may be applied to muddy water rising in vessels.
To fall into muddy water, is a sign that you will make many bitter mistakes, and will suffer poignant grief therefrom.
To drink muddy water, portends sickness, but drinking it clear and refreshing brings favorable consummation of fair hopes.
To sport with water, denotes a sudden awakening to love and passion.
To have it sprayed on your head, denotes that your passionate awakening to love will meet reciprocal consummation.
The following dream and its allegorical occurrence in actual life is related by a young woman student of dreams:
``Without knowing how, I was (in my dream) on a boat, I waded through clear blue water to a wharfboat, which I found to be snow white, but rough and splintry. The next evening I had a delightful male caller, but he remained beyond the time prescribed by mothers and I was severely censured for it.'' The blue water and fairy white boat were the disappointing prospects in the symbol.
Water-carrier.
To see water-carriers passing in your dreams, denotes that your prospects will be favorable in fortune, and love will prove no laggard in your chase for pleasure.
If you think you are a water-carrier, you will rise above your present position.
Waterfall.
To dream of a waterfall, foretells that you will secure your wildest desire, and fortune will be exceedingly favorable to your progress.
Water Lily.
To dream of a water lily, or to see them growing, foretells there will be a close commingling of prosperity and sorrow or bereavement.
Waves.[241]
To dream of waves, is a sign that you hold some vital step in contemplation, which will evolve much knowledge if the waves are clear; but you will make a fatal error if you see them muddy or lashed by a storm.
[241] See Ocean and Sea.
Wax Taper.
To dream of lighting wax tapers, denotes that some pleasing occurrence will bring you into association with friends long absent.
To blow them out, signals disappointing times, and sickness will forestall expected opportunities of meeting distinguished friends.
Way.[242]
See Road and Path.
Wealth.
To dream that you are possessed of much wealth, foretells that you will energetically nerve yourself to meet the problems of life with that force which compells success.
To see others wealthy, foretells that you will have friends who will come to your rescue in perilous times.
For a young woman to dream that she is associated with wealthy people, denotes that she will have high aspirations and will manage to enlist some one who is able to further them.
Weasel.
To see a weasel bent on a marauding expedition in your dreams, warns you to beware of the friendships of former enemies, as they will devour you at an unseemly time.
If you destroy them, you will succeed in foiling deep schemes laid for your defeat.
Weather.
To dream of the weather, foretells fluctuating tendencies in fortune. Now you are progressing immensely, to be suddenly confronted with doubts and rumblings of failure.
To think you are reading the reports of a weather bureau, you will change your place of abode, after much weary deliberation, but you will be benefited by the change.
To see a weather witch, denotes disagreeable conditions in your family affairs.
To see them conjuring the weather, foretells quarrels in the home and disappointment in business.
Weaving.
To dream that you are weaving, denotes that you will baffle any attempt to defeat you in the struggle for the up-building of an honorable fortune.
To see others weaving shows that you will be surrounded by healthy and energetic conditions.
Web.
To dream of webs, foretells deceitful friends will work you loss and displeasure. If the web is non-elastic, you will remain firm in withstanding the attacks of the envious persons who are seeking to obtain favors from you.
Wedding.[243]
To attend a wedding in your dream, you will speedily find that there is approaching you an occasion which will cause you bitterness and delayed success.
For a young woman to dream that her wedding is a secret is decidedly unfavorable to character. It imports her probable downfall.
If she contracts a worldly, or approved marriage, signifies she will rise in the estimation of those about her, and anticipated promises and joys will not be withheld.
If she thinks in her dream that there are parental objections, she will find that her engagement will create dissatisfaction among her relatives. For her to dream her lover weds another, foretells that she will be distressed with needless fears, as her lover will faithfully carry out his promises.
For a person to dream of being wedded, is a sad augury, as death will only be eluded by a miracle. If the wedding is a gay one and there are no ashen, pale-faced or black-robed ministers enjoining solemn vows, the reverses may be expected.
For a young woman to dream that she sees some one at her wedding dressed in mourning, denotes she will only have unhappiness in her married life. If at another's wedding, she will be grieved over the unfavorable fortune of some relative or friend. She may experience displeasure or illness where she expected happiness and health. The pleasure trips of others or her own, after this dream, may be greatly disturbed by unpleasant intrusions or surprises.
[243] See Marriage and Bride.
Wedding Clothes.
To see wedding clothes, signifies you will participate in pleasing works and will meet new friends. To see them soiled or in disorder, foretells you will lose close relations with some much-admired person.
Wedding Ring.
For a woman to dream her wedding ring is bright and shining, foretells that she will be shielded from cares and infidelity.
If it should be lost or broken, much sadness will come into her life through death and uncongeniality.
To see a wedding ring on the hand of a friend, or some other person, denotes that you will hold your vows lightly and will court illicit pleasure.
Wedge.
To dream of a wedge, denotes you will have trouble in some business arrangements which will be the cause of your separation from relatives.
Separation of lovers or friends may also be implied.
Wedlock.
To dream that you are in the bonds of an unwelcome wedlock, denotes you will be unfortunately implicated in a disagreeable affair.
For a young woman to dream that she is dissatisfied with wedlock, foretells her inclinations will persuade her into scandalous escapades.
For a married woman to dream of her wedding day, warns her to fortify her strength and feelings against disappointment and grief. She will also be involved in secret quarrels and jealousies. For a woman to imagine she is pleased and securely cared for in wedlock, is a propitious dream.
Weeding.
To dream that you are weeding, foretells that you will have difficulty in proceeding with some work which will bring you distinction.
To see others weeding, you will be fearful that enemies will upset your plans.
Weeping.
Weeping in your dreams, foretells ill tidings and disturbances in your family.
To see others weeping, signals pleasant reunion after periods of saddened estrangements. This dream for a young woman is ominous of lovers' quarrels, which can only reach reconciliation by self-abnegation.
For the tradesman, it foretells temporary discouragement and reverses.
Weevil.
To dream of weevils, portends loss in trade and falseness in love.
Weighing.
To dream of weighing, denotes that you are approaching a prosperous period, and if you set yourself determinedly toward success you will victoriously reap the full fruition of your labors.
To weigh others, you will be able to subordinate them to your interest.
For a young woman to weigh with her lover, foretells that he will be ready at all times to comply with her demands.
Well.
To dream that you are employed in a well, foretells that you will succumb to adversity through your misapplied energies. You will let strange elements direct your course.
To fall into a well, signifies that overwhelming despair will possess you.
For one to cave in, promises that enemies' schemes will overthrow your own.
To see an empty well, denotes you will be robbed of fortune if you allow strangers to share your confidence.
To see one with a pump in it, shows you will have opportunities to advance your prospects.
To dream of an artesian well, foretells that your splendid resources will gain you admittance into the realms of knowledge and pleasure.
To draw water from a well, denotes the fulfilment of ardent desires.
If the water is impure, there will be unpleasantness.
Welcome.
To dream that you receive a warm welcome into any society, foretells that you will become distinguished among your acquaintances and will have deference shown you by strangers. Your fortune will approximate anticipation.
To accord others welcome, denotes your congeniality and warm nature will be your passport into pleasures, or any other desired place.
Welsh Rarebits.
To dream of preparing or eating Welsh rarebits, denotes that your affairs will assume a complicated state, owing to your attention being absorbed by artful women and enjoyment of neutral fancies.
Wet.
To dream that you are wet, denotes that a possible pleasure may involve you in loss and disease. You are warned to avoid the blandishments of seemingly well-meaning people.
For a young woman to dream that she is soaking wet, portends that she will be disgracefully implicated in some affair with a married man.
Wet Nurse.

Whale.
To dream of seeing a whale approaching a ship, denotes that you will have a struggle between duties, and will be threatened with loss of property.
If the whale is demolished, you will happily decide between right and inclination, and will encounter pleasing successes.
If you see a whale overturn a ship, you will be thrown into a whirlpool of disasters.
Whalebone.
To see or work with whalebone in your dreams, you still form an alliance which will afford you solid benefit.
Wheat.
To see large fields of growing wheat in your dreams, denotes that your interest will take on encouraging prospects.
If the wheat is ripe, your fortune will be assured and love will be your joyous companion.
To see large clear grains of wheat running through the thresher, foretells that prosperity has opened her portals to the fullest for you.
To see it in sacks or barrels, your determination to reach the apex of success is soon to be crowned with victory and your love matters will be firmly grounded.
If your granary is not well covered and you see its contents getting wet, foretells that while you have amassed a fortune, you have not secured your rights and you will see your interests diminishing by the hand of enemies.
If you rub wheat from the head into your hand and eat it, you will labor hard for success and will obtain and make sure of your rights.
To dream that you climb a steep hill covered with wheat and think you are pulling yourself up by the stalks of wheat, denotes you will enjoy great prosperity and thus be able to distinguish yourself in any chosen pursuit.
Wheels.
To see swiftly rotating wheels in your dreams, foretells that you will be thrifty and energetic in your business and be successful in pursuits of domestic bliss.
To see idle or broken wheels, proclaims death or absence of some one in your household.
Whetstone.
To dream of a whetstone, is significant of sharp worries and close attention is needed in your own affairs, if you avoid difficulties.
You are likely to be forced into an uncomfortable journey.
Whip.
To dream of a whip, signifies unhappy dissensions and unfortunate and formidable friendships.
Whirlpool.
To dream of a whirlpool, denotes that great danger is imminent in your business, and, unless you are extremely careful, your reputation will be seriously blackened by some disgraceful intrigue.
Whirlwind.
To dream that you are in the path of a whirlwind, foretells that you are confronting a change which threatens to overwhelm you with loss and calamity.
For a young woman to dream that she is caught in a whirlwind and has trouble to keep her skirts from blowing up and entangling her waist, denotes that she will carry on a secret flirtation and will be horrified to find that scandal has gotten possession of her name and she will run a close risk of disgrace and ostracism.
Whisky.
To dream of whisky in bottles, denotes that you will be careful of your interests, protecting them with energy and watchfulness, thereby adding to their proportion.
To drink it alone, foretells that you will sacrifice your friends to your selfishness.
To destroy whisky, you will lose your friends by your ungenerous conduct.
Whisky is not fraught with much good. Disappointment in some form will likely appear.
To see or drink it, is to strive and reach a desired object after many disappointments. If you only see it, you will never obtain the result hoped and worked for.
Whispering.
To dream of whispering, denotes that you will be disturbed by the evil gossiping of people near you.
To hear a whisper coming to you as advice or warning, foretells that you stand in need of aid and counsel.
Whistle.
To hear a whistle in your dream, denotes that you will be shocked by some sad intelligence, which will change your plans laid for innocent pleasure.
To dream that you are whistling, foretells a merry occasion in which you expect to figure largely. This dream for a young woman indicates indiscreet conduct and failure to obtain wishes is foretold.
White Lead.
To dream of white lead, denotes relatives or children are in danger because of your carelessness. Prosperity will be chary of favor.
White Moth.
To dream of a white moth, foretells unavoidable sickness, though you will be tempted to accuse yourself or some other with wrong-doing, which you think causes the complaint. For a woman to see one flying around in the room at night, forebodes unrequited wishes and disposition which will effect the enjoyment of other people. To see a moth flying and finally settling upon something, or disappearing totally, foreshadows death of friends or relatives.
Whitewash.
To dream that you are whitewashing, foretells that you will seek to reinstate yourself with friends by ridding yourself of offensive habits and companions.
For a young woman, this dream is significant of well-laid plans to deceive others and gain back her lover who has been estranged by her insinuating bearing toward him.
Widow.

For a man to dream that he marries a widow, denotes he will see some cherished undertaking crumble down in disappointment.
Wife.
To dream of your wife, denotes unsettled affairs and discord in the home.
To dream that your wife is unusually affable, denotes that you will receive profit from some important venture in trade.
For a wife to dream her husband whips her, foretells unlucky influences will cause harsh criticism in the home and a general turmoil will ensue.
Wig.
To dream you wear a wig, indicates that you will soon make an unpropitious change.
To lose a wig, you will incur the derision and contempt of enemies.
To see others wearing wigs, is a sign of treachery entangling you.
Wild.
To dream that you are running about wild, foretells that you will sustain a serious fall or accident.
To see others doing so, denotes unfavorable prospects will cause you worry and excitement.
Wild Man.
To see a wild man in your dream, denotes that enemies will openly oppose you in your enterprises. To think you are one foretells you will be unlucky in following out your designs.
Will.
To dream you are making your will, is significant of momentous trials and speculations.
For a wife or any one to think a will is against them, portends that they will have disputes and disorderly proceedings to combat in some event soon to transpire.
If you fail to prove a will, you are in danger of libelous slander.
To lose one is unfortunate for your business.

Willow.
To dream of willows, foretells that you will soon make a sad journey, but you will be consoled in your grief by faithful friends.
Wind.
To dream of the wind blowing softly and sadly upon you, signifies that great fortune will come to you through bereavement.
If you hear the wind soughing, denotes that you will wander in estrangement from one whose life is empty without you.
To walk briskly against a brisk wind, foretells that you will courageously resist temptation and pursue fortune with a determination not easily put aside. For the wind to blow you along against your wishes, portends failure in business undertakings and disappointments in love. If the wind blows you in the direction you wish to go you will find unexpected and helpful allies, or that you have natural advantages over a rival or competitor.
Windmill.
To see a windmill in operation in your dreams, foretells abundant accumulation of fortune and marked contentment
To see one broken or idle, signifies adversity coming unawares.
Window.
To see windows in your dreams, is an augury of fateful culmination to bright hopes. You will see your fairest wish go down in despair. Fruitless endeavors will be your portion.
To see closed windows is a representation of desertion. If they are broken, you will be hounded by miserable suspicions of disloyalty from those you love.
To sit in a window, denotes that you will be the victim of folly. To enter a house through a window, denotes that you will be found out while using dishonorable means to consummate a seemingly honorable purpose.
To escape by one, indicates that you will fall into a trouble whose toils will hold you unmercifully close.
To look through a window when passing and strange objects appear, foretells that you will fail in your chosen avocation and lose the respect for which you risked health and contentment.
Wine.
To dream of drinking wine, forebodes joy and consequent friendships.
To dream of breaking bottles of wine, foretells that your love and passion will border on excess.
To see barrels of wine, prognosticates great luxury. To pour it from one vessel into another, signifies that your enjoyments will be varied and you will journey to many notable places.
To dream of dealing in wine denotes that your occupation will be remunerative.
For a young woman to dream of drinking wine, indicates she will marry a wealthy gentleman, but withal honorable.
Wine-cellar.
To dream of a wine-cellar, foretells superior amusements or pleasure will come in your way, to be disposed of at your bidding.
Wine-glass.
To dream of a wine-glass, foretells that a disappointment will affect you seriously, as you will fail to see anything pleasing until shocked into the realization of trouble.
Wings.
To dream that you have wings, foretells that you will experience grave fears for the safety of some one gone on a long journey away from you.
To see the wings of fowls or birds, denotes that you will finally overcome adversity and rise to wealthy degrees and honor.
Winter.
To dream of winter, is a prognostication of ill-health and dreary prospects for the favorable progress of fortune. After this dream your efforts will not yield satisfactory results.
Wire.
To dream of wire, denotes that you will make frequent but short journeys which will be to your disparagement.
Old or rusty wire, signifies that you will be possessed of a bad temper, which will give troubles to your kindred.
To see a wire fence in your dreams, foretells that you will be cheated in some trade you have in view.
Wisdom.
To dream you are possessed of wisdom, signifies your spirit will be brave under trying circumstances, and you will be able to overcome these trials and rise to prosperous living. If you think you lack wisdom, it implies you are wasting your native talents.
Witch.
To dream of witches, denotes that you, with others, will seek adventures which will afford hilarious enjoyment, but it will eventually rebound to your mortification. Business will suffer prostration if witches advance upon you, home affairs may be disappointing.
Witness.
To dream that you bear witness against others, signifies you will have great oppression through slight causes. If others bear witness against you, you will be compelled to refuse favors to friends in order to protect your own interest. If you are a witness for a guilty person, you will be implicated in a shameful affair.
Wizard.
To dream of a wizard, denotes you are going to have a big family, which will cause you much inconvenience as well as displeasure. For young people, this dream implies loss and broken engagements.
Wolf.
To dream of a wolf, shows that you have a thieving person in your employ, who will also betray secrets.
 To hear the howl of a wolf, discovers to you a secret alliance to defeat you in honest competition.
Women.
To dream of women, foreshadows intrigue.
To argue with one, foretells that you will be outwitted and foiled.
To see a dark-haired woman with blue eyes and a pug nose, definitely determines your withdrawal from a race in which you stood a showing for victory. If she has brown eyes and a Roman nose, you will be cajoled into a dangerous speculation. If she has auburn hair with this combination, it adds to your perplexity and anxiety. If she is a blonde, you will find that all your engagements will be pleasant and favorable to your inclinations.
Wooden Shoe.
To dream of a wooden shoe, is significant of lonely wanderings and penniless circumstances. Those in love will suffer from unfaithfulness.
Woods.
To dream of woods, brings a natural change in your affairs.
If the woods appear green, the change will be lucky.
If stripped of verdure, it will prove calamitous.
To see woods on fire, denotes that your plans will reach satisfactory maturity. Prosperity will beam with favor upon you.
To dream that you deal in firewood, denotes that you will win fortune by determined struggle.
Wood-pile.
To dream of a wood-pile, denotes unsatisfactory business and misunderstandings in love.
Wool.
To dream of wool, is a pleasing sign of prosperous opportunities to expand your interests.
To see soiled, or dirty wool, foretells that you will seek employment with those who detest your principles.
Work.
To dream that you are hard at work, denotes that you will win merited success by concentration of energy.
To see others at work, denotes that hopeful conditions will surround you.
To look for work, means that you will be benefited by some unaccountable occurrence.
Work house.[244]
To dream that you are in a workhouse denotes that some event will work you harm and loss.
[244] See Prison.
Workshop.
To see workshops in your dreams, foretells that you will use extraordinary schemes to undermine your enemies.
Worms.
To dream of worms, denotes that you will be oppressed by the low intriguing of disreputable persons.
For a young woman to dream they crawl on her, foretells that her aspirations will always tend to the material. If she kills or throws them off, she will shake loose from the material lethargy and seek to live in morality and spirituality.
To use them in your dreams as fish bait, foretells that by your ingenuity you will use your enemies to good advantage.
Wound.
To dream that you are wounded, signals distress and an unfavorable turn in business.
To see others wounded, denotes that injustice will be accorded you by your friends.
To relieve or dress a wound, signifies that you will have occasion to congratulate yourself on your good fortune.
Wreath.
To dream that you see a wreath of fresh flowers, denotes that great opportunities for enriching yourself will soon present themselves before you.
A withered wreath bears sickness and wounded love.
To see a bridal wreath, foretells a happy ending to uncertain engagements.
Wrecks.[245]
To see a wreck in your dream, foretells that you will be harassed with fears of destitution or sudden failure in business.
[245] See other like words.
Writing.[246]
To dream that you are writing, foretells that you will make a mistake which will almost prove your undoing.
To see writing, denotes that you will be upbraided for your careless conduct and a lawsuit may cause you embarrassment.
To try to read strange writing, signifies that you will escape enemies only by making no new speculation after this dream.
[246] See Letters.
``The Prophet that hath a dream let him tell a dream.''—Jer. XXIII., 28.
Yacht.
To see a yacht in a dream, denotes happy recreation away from business and troublesome encumbrances. A stranded one, represents miscarriage of entertaining engagements.
Yankee.
To dream of a Yankee, foretells that you will remain loyal and true to your promise and duty, but if you are not careful you will be outwitted in some transaction.
Yard Stick.
To dream of a yard stick, foretells much anxiety will possess you, though your affairs assume unusual activity.
Yarn.
To dream of yarn, denotes success in your business and an industrious companion in your home.
For a young woman to dream that she works with yarn, foretells that she will be proudly recognized by a worthy man as his wife.
Yawning.
If you yawn in your dreams, you will search in vain for health and contentment.
To see others yawning, foretells that you will see some of your friends in a miserable state. Sickness will prevent them from their usual labors.
Yearn.
To feel in a dream that you are yearning for the presence of anyone, denotes that you will soon hear comforting tidings from your absent friends.
For a young woman to think her lover is yearning for her, she will have the pleasure of soon hearing some one making a long-wished-for proposal. If she lets him know that she is yearning for him, she will be left alone and her longings will grow apace.
Yellow Bird.
To see a yellow bird flitting about in your dreams, foretells that some great event will cast a sickening fear of the future around you.
Yew Tree.
To dream of a yew tree, is a forerunner of illness and disappointment. If a young woman sits under one, she will have many fears to rend her over her fortune and the faithfulness of her lover. If she sees her lover standing by one, she may expect to hear of his illness, or misfortune. To admire one, she will estrange herself from her relatives by a mesalliance.
 Property will not console for this loss.
Yield.
To dream you yield to another's wishes, denotes that you will throw away by weak indecision a great opportunity to elevate yourself.

To receive poor yield for your labors, you may expect cares and worries.
Yoke.
To dream of seeing a yoke, denotes that you will unwillingly conform to the customs and wishes of others.
To yoke oxen in your dreams, signifies that your judgment and counsels will be accepted submissively by those dependent upon you. To fail to yoke them, you will be anxious over some prodigal friend.
Young.
To dream of seeing young people, is a prognostication of reconciliation of family disagreements and favorable times for planning new enterprises.
To dream that you are young again, foretells that you will make mighty efforts to recall lost opportunities, but will nevertheless fail.
 If the child seems to be dying, she will fall into ill fortune and misery will attend her.
To see the young in school, foretells that prosperity and usefulness will envelope you with favors. Yule Log.
To dream of a yule log, foretells that your joyous anticipations will be realized by your attendance at great festivities.
``Then thou scarest me with dreams, and terrifying me through visions; so that my soul chooseth strangling, and death rather than my life.''— Job xvii.,14-15.
Zebra.
To dream of a zebra, denotes that you will be interested in varying and fleeting enterprises.
To see one wild in his native country, foretells that you will pursue a chimerical fancy which will return you unsatisfactory pleasure upon possession.
Zenith.
To dream of the zenith, foretells elaborate prosperity, and your choice of suitors will be successful.
Zephyr.
To dream of soft zephyrs, denotes that you will sacrifice fortune to obtain the object of your affection and will find reciprocal affection in your wooing.
If a young woman dreams that she is saddened by the whisperings of the zephyrs, she will have a season of disquietude by the compelled absence of her lover.
Zinc.
To work with or to see zinc in your dreams, indicates substantial and energetic progress. Business will assume a brisk tone in its varying departments.
To dream of zinc ore promises the approach of eventful success.
Zodiac.
To dream of the zodiac is a prognostication of unparalleled rise in material worth, but also indicates alloyed peace and happiness.
To see it appearing weird, denotes that some untoward grief is hovering over you and it will take strenuous efforts to dispell it.
To study the zodiac in your dreams, denotes that you will gain distinction and favor by your intercourse with strangers.
If you approach it or it approaches you, foretells that you will succeed in your speculations to the wonderment of others and beyond your wildest imagination.
To draw a map of it, signifies future gain.
Zoological Garden.
To dream of visiting zoological gardens, denotes that you will have a varied fortune. Sometimes it seems that enemies will overpower you and again you stand in the front rank of success. You will also gain knowledge by travel and sojourn in foreign countries.


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Cantora ('Singer' in Spanish) is a friendly semi formal, semi condensed, semi sans serif. It has reminiscences of hand lettering, mixing straight and bowed stems, and natural curves.
It was born as an experiment in drawing from the outside to the inside (drawing the space surrounding the letters first, instead of drawing the letters themselves) in trying to apply the ideas and methods of Michael Harvey and Evert Bloemsma to my own glyphs construction.
Although Cantora is a sans, the lowercase letters have serif proportions. It's perfect for headlines (H1, H2, H3) in sizes larger than 20px.


The dag for computing P-SQUARE-MATRIX-MULTIPLY on matrices
Work is defined as total time needed to execute an entire multithreaded computation on one processor.
Span is defined as the longest time to needed to execute the strands along any path in the direct acyclic graph (DAG).
Suppose the work is the running time on a single processor. Consider it as.
Now suppose we have an unlimited number of processors then we can donate the span by.
The ratio of and that is gives the parallelism of the multithreaded computation.DAG Representation:
The two numbers in each of the rectangle gives the subscript of the matix element that is currently being accessed in the present invocation. The black circle in each of the rectangle shows whether the element is the part of the base case or the parallel call.The white circles show the strands where the result of the calculation is stored after the control returns from the parallel calls.
Analyzing the above diagram, it can be observed that each of the base case is being passed through eight different stages of calculation. It can be seen by counting the number of arrows that a base case is being driven through. This makes the total number of strands 8.
There are three different levels in which this entire calculation for a strand is taking place. The fourth level is the final answer itself. The calculations are being done upto the third level. Now move to the next stage.
Since there are total 8 strands.
Therefore,
Total work is .
Since the length of the largest strand is 3
Therefore, its span is .
Parallelism=
Pseudo code for a multithreaded algorithm of matrix multiplication
Spawn is a subroutine that executes or run at the same time as that of parent. So by spawning, both parent and child work simultaneously. The main motive behind for evolving the concept of spawning is to achieve parallelism, which results in increase the overall performance of computer.
Work is defined as total time required for completing the entire multithreaded computation on a single processor. Suppose in the below example each circle represents the strands which takes unit time. Therefore, total work done is 25 units.
Span is defined as the maximum time required for completing the strands along any path in the directed acyclic graph (DAG). It is an expensive path which contains maximum number of strands. The path highlighted in the above figure is known as span.
Work is the running time of a computation on a single processor. Consider it as.
Now suppose there areunlimited numbers of processors. Then the span is denoted by
The ratio of and, that is gives the parallelism of the multithreaded computation.Pseudo code:
The procedure P-MATRIX-MULTIPLY will get the multiplication of two matrices. X and Y are the matrices to be multiplied. Create a new matrix to hold the resultant of multiplication. Run two parallel loops to go through the matrix elements and call the procedure MATRIX_SUB to get the multiplication.
P-MATRIX-MULTIPLY
Let be a new matrix
parallel for to
parallel for to
MATRIX_SUB
return
Use the below procedure to get the multiplication. X and Y are the matrices to be multiplied. The row and column subscript i and j would represent the element that is currently being accessed. m and m’ would be used to partition the matrix based on the upper and the lower bound of matrix dimension for parallel multiplication.
MATRIX_SUB
if
return
else
spawn MATRIX_SUB
MATRIX_SUB
sync
re turn +
The multiplication is done typically as below:
Let A and B be two matrices as below:
Now perform the partition, so that the sub matrices can be given to separate threads for parallel computing.
Now, get the separate multiplication of the sub matrices:
Now, perform left shift on the lower part of the left sub part and an up shift in the right most part of the right sub part. This would be done to perform the recursive multiplication.
Now, perform the multiplication as below. Each sub matrix multiplication would be performed parallel to other multiplications.
Perform the left shift on the entire left part and the up shift on the entire right sub part. This would be done for the second recursive call.
Now, perform the multiplication again. All the below multiplications would be done in parallel.
The final answer would be the integration of all the sub matrices.
Analyzing the above modified algorithm:
Here three methods which are work, span and parallelism are used for analyzing the algorithm which is as follow:
Work:
Work of the P-MARIX-MULTIPLY can be calculated by computing the execution time of its serialization. In order to calculate the execution time of its serialization, replace parallel for loop by ordinary for loop.
Considerbe the work of the MATRIX_SUB (nested for loop).
Therefore … … (1)
MATRIX_SUB can be given by the recurrence (consider if-else and mid-point division)
… … (2)
By applying master theorem (In the analysis of the algorithm, master theorem gives the solution in asymptotic term for the recurrence relation),
Generic form of master theorem is:
Where, is the sum of cost of dividing the problem into sub-problems and the cost of combining these sub-problems outside the recurrence call.
Above recurrence relation is in form of
Here, according to the master theorem,
Then the solution of the recurrence relation become
Therefore from (1) and (2)
…… (3)
Hence total work of P-MATRIX-MULTIPLY algorithm is.
Span:
Span can be calculated by below recurrence-
In P-MATRIX-MULTIPLY() function, each iteration of second parallel for loop call MATRIX_SUB() function to multiply square matrix. Further each time the MATRIX_SUB() function half the space between 1 and nby calling itself again and again and does the constant time work. Therefore the span becomes.
That is,
Hence, Span of P-MATRIX-MULTIPLY algorithm is.
Parallelism:
Parallelism is the ratio of work by span that is ratio of by.
Therefore,
Parallelism=
=
Hence, Parallelism of P-MATRIX-MULTIPLY algorithm is.
Pseudo code for an efficient multithreaded algorithm of two matrix multiplication
Spawn is a subroutine that executes or run at the same time as that of parent. So by spawning, both parent and child work simultaneously. The main motive behind for evolving the concept of spawning is to achieve parallelism, which results in increase the overall performance of computer.
Work is defined as total time required for completing the entire multithreaded computation on a single processor. Suppose in the below example each circle represents the strands which takes unit time. Therefore, total work done is 25 units.
Span is defined as the maximum time required for completing the strands along any path in the directed acyclic graph (DAG). It is an expensive path which contains maximum number of strands. The path highlighted in the above figure is known as span.
Work is the running time of a computation on a single processor. Consider it as.
Now suppose there areunlimited numbers of processors. Then the span is denoted by
The ratio of and, that is gives the parallelism of the multithreaded computation.A pseudo code for an efficient multithreaded algorithm that multiplies matrix by a matrix
The procedure P-MATRIX-MULTIPLY will get the multiplication of two matrices. X and Y are the matrices to be multiplied. Create a new matrix to hold the resultant of multiplication; run two parallel loops to go through the matrix elements and call the procedure MATRIX_SUB to get the multiplication.
P_MATRIX_MULTIPLY (,)
//Find number of rows in X matrix
//Find number of columns in X matrix
//Find number of columns in Y matrix
letis a new matrix having rows and columns.
//use parallel for loop to traverseprows of X matrix
parallel for to
//use parallel for loop to traverse r columns of Y matrix
parallel for to
//Call MATRIX_SUB() function to split matrix into small matrix and then
//multiply it.
MATRIX_SUB
return
Use the MATRIX_SUB () procedure defined below to get the multiplication. X and Y are the matrices to be multiplied. The row and column subscript i and j would represent the element that is currently being accessed. m and m’ would be used to partition the matrix based on the upper and the lower bound of matrix dimension for parallel multiplication.
MATRIX_SUB
//using if statement to check upper and lower bound are same or not.
if
//return multiplication to calling function
return
else
//divide thematrix
//Again call MATRIX_SUB() to calculate the first half.
spawn MATRIX_SUB
//Again call MATRIX_SUB() function calculate the last half
MATRIX_SUB
Sync
return +
The algorithm would work as below:
Let the two matrices to be multiplied be A and B.
The matrices would first be divided in the sub matrices for assigning them to the parallel processors. The sub matrices would as below:
Now, the sub matrices would be multiplied to get the desired result. The matrix that does not get a corresponding sub matrix for multiplication would be discarded.
Now, get the resultant by adding the result of above calculations.
Analyzing the above modified algorithm:
Here three methods which are work, span and parallelism are used for analyzing the algorithm which is as follow:
Work:
Work of the above algorithm can be calculated by replacing the parallel for loop with ordinary for loop.
Consider the work of MATRIX_SUB is.
(Nested for loops runs up-to prtimes)
Therefore … … (1)
Since input size of the procedure MATRIX_SUB is
Because it is common in both the matrices
Therefore … … (2)
From (1) and (2)
Hence total work of modified P-MATRIX-MULTIPLY algorithm is.
Span:
In order to calculate the spanof the above algorithm, check the number of iteration each loop will have in it.
In general span of a parallel for loop, in which th iteration has span say is given by,
Therefore span in this case will be-
Hence span of modified P-MATRIX-MULTIPLY algorithm is.
Parallelism:
Parallelism is the ratio of work by span that is ratio of by .
Therefore,
Parallelism=
=When p is equal to 1 then parallelism becomes
Parallelism
When q is equal to 1 then parallelism becomes
Parallelism
When r is equal to 1 then parallelism becomes
Parallelism
Thus, algorithm should be highly parallel even if any of p, q, and r is 1. As the value of p,q and r is increases then correspondingly parallelism also increases.
Now if p, q, and r are 1 then according to above algorithm,
Parallelism
Thus, algorithm should be highly parallel even if p, q, and r is 1.
Pseudo code for a multithreaded algorithm to get then transpose of matrix is as follows:
Algorithm:
The algorithm given below finds the transpose of a matrix A of order. The variables x and y indicates the row and column number of the matrix that is currently being transposed.
This algorithm divides the matrix in two halves and makes a recursive call to the procedure to transpose the concerned matrix. The recursive call uses the divide-and-conquer technique.
P-MATRIX-TRANSPOSE
// Transpose the sub-matrix starting at.
if
return
else
//recursive call to the procedure for transposing the first half of matrix
spawn P-MATRIX-TRANSPOSE
//parallel call to the procedure for transposing the second half of matrix
spawn P-MATRIX-TRANSPOSE
//call to procedure for swapping the element
P-MATRIX-TRANSPOSE-SWAP
sync
Use the procedure below to swap the elements of matrix A to perform the transpose operation. The element at row and column would be swapped with the element at row and the column.
P-MATRIX-TRANSPOSE-SWAP
// Transpose the sub matrix starting at with the sub matrix
// starting at
if
P-MATRIX-TRANSPOSE-SWAP
else if
//this will make
exchangewith
else
spawn P-MATRIX-TRANSPOSE-SWAP
spawn P-MATRIX-TRANSPOSE-SWAP
sync
Explanation:
This would be an in place algorithm. It takes the matrix as input and replace the original matrix with its transpose.
The algorithm divides the matrix into smaller sub matrices. They are processed separately to find the transpose. Once all the sub parts are processed, the results are combined to get the transpose of the entire matrix.
Work is defined as total time required for completing the entire multithreaded computation on a single processor.
Span is defined as the maximum time required for completing the strands along any path in the directed acyclic graph (DAG). It is an expensive path which contains maximum number of strands.
Analyzing the above modified algorithm:
Work is the running time of a computation on a single processor. Consider it as.
Now suppose there are unlimited numbers of processors. Then the span is denoted by
The ratio of and, that is gives the parallelism of the multithreaded computation.
Calculate the work, span and parallelism for analyzing the efficiency of the algorithm.
Work:
Calculate the total running time of the matrix. Takingbe number of elements in the matrix.
In this case
Work of P-MATRIX-TRANSPOSE-SWAP say can be calculated by calculating the running time of its serialization,
That is
Using mater theorem (In the analysis of the algorithm, master theorem gives the solution in asymptotic term for the recurrence relation),
Calculate work of P-MATRIX-TRANSPOSE say by calculating the running time of its serialization.
The matrix of order will have elements.
From (1) and (3)
Hence total work of P-MATRIX-TRANSPOSE algorithm is.
Span:
Span of P-MATRIX-TRANSPOSE say will be maximum of the span of one of these recursive calls plus of P-MATRIX-TRANSPOSE-SWAP (from equation (3)) plus.
That is
Hence span of P-MATRIX-TRANSPOSE algorithm is.
Parallelism:
Parallelism is the ratio of work by span that is, ratio of and .
Therefore,
Parallelism=
=
=
Hence, parallelism of P-MATRIX-TRANSPOSE algorithm is.
Pseudo code for an efficient multithreaded algorithm of the Floyd-Warshall algorithm
The Floyd-Warshall Algorithm is used to solve the all-pairs shortest-paths for a given directed graph.It considers the intermediate vertex of a simple path. This algorithm uses dynamic programming approach.
The shortest distance between any two vertices is calculated by:
Graph may have the negative weight edges but there should not be any negative-weight cycles.
Work is defined as total time required for completing the entire multithreaded computation on a single processor.
Span is defined as the maximum time required for completing the strands along any path in the directed acyclic graph (DAG). It is an expensive path which contains maximum number of strands.
Work is the execution time of a computation on a single processor. Consider it as.
Now suppose there areunlimited numbers of processors. Then the span is denoted by
The ratio of and, that is gives the parallelism of the multithreaded computation.Multithreaded Implementation of the Floyd-Warshall algorithm:
Below given procedure will calculate the shortest path from all vertices of a graph to all other vertices. All the respective distances are stored in a matrix W. Every row shows a vertex and the columns of that row show the distances from that vertex to all other vertices.
Mt-FLOYD-WARSHALL (W)
parallel for to
parallel for to
//get the distance of the current node from all other nodes
for to
parallel for to
parallel for to
//find the minimum of distances
return
Suppose the shortest paths for the given graph have to be calculated.
The task of finding the shortest path would be distributed in the processes. Each process would find the possible path from any node to other.
So the matrices and respective updatesin the execution would be as below:
Now compute D matrix using given algorithm.
Initially the D matrix will be W matrix as shown below.
In the above matrix if there is any edge from vertices i to j then path will also exist between them and assign value of weight in (i, j)th position in the matrix.
Now for k=1, so, vertex “1” can be an intermediate node. Then the corresponding D1matrix will be as shown:
In the above matrix weight of d4,2 and d4,5 have been changed which are calculated by using the given formula:
Now for k=2, so, vertex “2” can be an intermediate node. Then the corresponding D2 matrix will be as shown:
In the above matrix, weight of d1,4, d3,4and d3,5 have been changed which are calculated by using the given formula:
Now for k=3, so, vertex “3” can be an intermediate node. Then the corresponding D3 matrix will be as shown:
In the above matrix weight of d4,2 has been changed which are calculated by using the given formula:
Now for k=4, so, vertex “4” can be an intermediate node. Then the corresponding D4 matrix will be as shown:
In the above matrix, weight of d2,1, d2,3, d2,5, d3,1, d3,5, d5,1, d5,2 and d5,3have been changed which are calculated by using the given formula:
Now for k=5, so, vertex “5” can be an intermediate node. Then the corresponding D5 matrix will be as shown:
In the above matrix weight of d1,2, d1,3 and d1,4 have been changed which are calculated by using the given formula:
Now, the shortest distances would be picked up and the final distance matrix would look like below:
Analyzing the above algorithm:
Here three methods which are work, span and parallelism are used for analyzing the algorithm which is as follow:
Work:
Work of the above Mt-FLOYD-WARSHALL (W) will be same as that ofthe execution time of its serialization. So in order to compute work, parallel for loop must be replaced with ordinary for loop.
Since for loop in above algorithm runs times so do and, therefore total running time will be.
That is,
Hence total work of the above algorithm is.
Span:
Span of the doubly nested parallel for loop will be.Since it runs under for loop for times therefore total span will be.
That is
Hence span of the above algorithm is.Parallelism:
Parallelism is the ratio of work by span that is ratio of by.
Therefore,
Parallelism=
=
=
Hence Parallelism of the above algorithm is.


| Name | Description |
|---|---|
| PartialAirGap | Partial airgap model |
| AirGapS | Airgap in stator-fixed coordinate system |
| AirGapR | Airgap in rotor-fixed coordinate system |
| Inductor | Space phasor inductor |
| SquirrelCage | Squirrel Cage |
| DamperCage | Squirrel Cage |
| ElectricalExcitation | Electrical excitation |
| PermanentMagnet | Permanent magnet excitation |
| PermanentMagnetWithLosses | Permanent magnet excitation |
| InductorDC | Ideal linear electrical inductor for electrical DC machines |
| PartialAirGapDC | Partial airgap model of a DC machine |
| AirGapDC | Linear airgap model of a DC machine |
| CompoundDCExcitation | Compound excitation = shunt + series |
| PartialCore | Partial model of transformer core with 3 windings |
| IdealCore | Ideal transformer with 3 windings |
| BasicTransformer | Partial model of three-phase transformer |


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